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Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Balbharti Maharashtra State Board 12th Biology Important Questions Chapter 11 Enhancement of Food Production Important Questions and Answers.

Maharashtra State Board 12th Biology Important Questions Chapter 11 Enhancement of Food Production

Multiple choice questions

Question 1.
Means of in situ germplasm conservation are ………………….
(a) forests
(b) Natural Reserves
(c) botanical gardens, seed banks
(d) both (a) and (b)
Answer:
(d) both (a) and (b)

Question 2.
Means of ex situ germplasm conservation are ………………….
(a) forests and seed banks
(b) natural Reserves
(c) botanical gardens, seed banks
(d) botanical garden and forests
Answer:
(c) botanical gardens, seed banks

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 3.
Germplasm includes ………………….
(a) only improved varieties of crop
(b) all cultivated varieties and wild relatives of a particular crop
(c) all hybridized varieties only
(d) only mutant varieties of a crop
Answer:
(b) all cultivated varieties and wild relatives of a particular crop

Question 4.
Taichung Native-1 is a variety of rice from ………………….
(a) China
(b) Korea
(c) Malaysia
(d) Taiwan
Answer:
(d) Taiwan

Question 5.
Which of the following is not a fungal disease ?
(a) Late blight of potato
(b) Brown rust of wheat
(c) Red rot of sugar cane
(d) Black rot of crucifers
Answer:
(d) Black rot of crucifer

Question 6.
…………………. variety of wheat is resistant to Hill bunt disease.
(a) Himgiri
(b) Pusa swarnim
(c) Kalyan sona
(d) Pusa A-4
Answer:
(a) Himgiri

Question 7.
Regina-II variety of …………………. is resistant to bacterial rot.
(a) wheat
(b) cabbage
(c) cauliflower
(d) Brassica
Answer:
(b) cabbage

Question 8.
The nectar-less cotton having smooth leaves has resistance against ………………….
(a) bollworms
(b) jassids
(c) aphids
(d) stem borers
Answer:
(a) bollworms

Question 9.
………………… gave concept of in vitro cell culture.
(a) Haberlandt
(b) Frank
(c) Yabuta and Sumiki
(d) None of these
Answer:
(a) Haberlandt

Question 10.
Tissue culture requirements are ………………….
(a) pH of nutrient medium 5 to 5.8
(b) Sterilized glassware, nutrient medium, explants, inoculation chamber
(c) Temperature 18 °C to 20 °C
(d) All of these
Answer:
(d) All of these

Question 11.
Hybrid maize with double the quantity of amino acids …………………. have been developed.
(a) lysine and tryptophan
(b) alanine and aspartic acid
(c) glutamic and proline
(d) histidine and cystine
Answer:
(a) lysine and tryptophan

Question 12.
Inbreeding increases ………………….
(a) homozygosity
(b) heterozygosity
(c) heterosis
(d) hemizygosity
Answer:
(a) homozygosity

Question 13.
Which hormone is used for MOET method?
(a) GH
(b) LH
(c) FSH
(d) ICSH
Answer:
(c) FSH

Question 14.
Find the odd one out.
(a) Sahiwal
(b) Sindhi
(c) Gir
(d) Holstein
Answer:
(d) Holstein

Question 15.
Pullorum is a …………………. disease.
(a) viral
(b) bacterial
(c) fungal
(d) parasitic
Answer:
(b) bacterial

Question 16.
Propolis is ………………….
(a) bee glu
(b) royal jelly
(c) bee venom
(d) none of these
Answer:
(a) bee glu

Question 17.
Select the incorrect pair.
(a) Apis dorsata – Rock bee
(b) Apis indica -Indian bee
(c) Apis florae – Little bee
(d) Apis mellifera – Wild bee
Answer:
(d) Apis mellifera – Wild bee

Question 18.
fishery takes place in Sundarban area of ………………….
(a) Estuarine, West Bengal
(b) Marine, Odisha
(c) Fresh water, West Bengal
(d) None of these
Answer:
(a) Estuarine, West Bengal

Question 19.
Which stage in the life cycle of silk moth secretes silk?
(a) Caterpillar
(b) Egg
(c) Pupa
(d) Adult
Answer:
(a) Caterpillar

Question 20.
Lac insect is a native of ………………….
(a) China
(b) India
(c) Africa
(d) Europe
Answer:
(b) India

Question 21.
Alcoholic fermentation is brought about by ………………….
(a) Lactobacillus
(b) Saccharomyces
(c) Trichoderma
(d) Streptomyces
Answer:
(b) Saccharomyces

Question 22.
…………………. and …………………. are alcoholic beverages produced without distillation.
(a) Wine, rum
(b) Wine, beer
(c) Whisky, brandy
(d) Brandy, beer
Answer:
(b) Wine, beer

Question 23.
Organic acid can be produced directly from glucose or formed as end products from ………………….
(a) pyruvate
(b) ethanol
(c) gluconic acid
(d) both (a) and (b)
Answer:
(d) both (a) and (b)

Question 24.
The microbial source of vinegar is ………………….
(a) Aspergillus niger
(b) Rhizopus arrhizus
(c) Acetobacter aceti
(d) Streptomyces venezuelae
Answer:
(c) Acetobacter aceti

Question 25.
Statins are produced by ………………….
(a) Monascus purpureus
(b) Streptococcus
(c) Aspergillus niger
(d) None of these
Answer:
(a) Monascus purpureus

Question 26.
…………………. is used as a ‘clot buster’.
(a) Pectinase
(b) Statin
(c) Invertase
(d) Streptokinase
Answer:
(d) Streptokinase

Question 27.
Aspergillus niger is used to manufacture ………………….
(a) pectinase, gluconic acid and vitamin C
(b) pectinase, gluconic acid and vitamin B12
(c) invertase, acetic acid and vitamin C
(d) pectinase, citric acid and invertase
Answer:
(a) pectinase, gluconic acid and vitamin C

Question 28.
The first Gibberellin was isolated by ………………….
(a) Frank
(b) Skoog
(c) Yabuta and Sumiki
(d) None of these
Answer:
(c) Yabuta and Sumiki

Question 29.
Once the BOD of waste water is reduced, it is passed into a ………………….
(a) settling tank
(b) primary sedimentation tank
(c) anaerobic sludge digesters
(d) aeration tank
Answer:
(a) settling tank

Question 30.
During biogas production species used to bring about hydrolysis or solubilization is ………………….
(a) Pseudomonas
(b) Rhizopus
(c) Methanococcus
(d) Methanobacillus
Answer:
(a) Pseudomonas

Question 31.
…………………. bacteria are used as herbicides.
(a) Pseudomonas spp., Xanthomonas spp., Agrobacterium spp.
(b) Bacillus thuringiensis, B. papilliae, B. lentimorbus
(c) Pseudomonas spp., Bacillus thuringiensis, B. papilliae
(d) Xanthomonas spp., Agrobacterium spp., Bacillus thuringiensis
Answer:
(a) Pseudomonas spp., Xanthomonas spp., Agrobacterium spp.

Question 32.
The weed Senecio jacobeac is controlled by ………………….
(a) Cactoblastis cactorum
(b) Xanthomonas spp
(c) Bacillus thuringiensis
(d) tyrea moth
Answer:
(d) tyrea moth

Question 33.
Nosema locustae is …………………. pathogen.
(a) bacteria
(b) fungal
(c) protozoan
(d) viral
Answer:
(c) protozoan

Question 34.
Which of the following bacterial pathogen is not used as herbicide ?
(a) Pseudomonas
(b) Xanthomonas
(c) Agrobacterium
(d) Azotobacter
Answer:
(d) Azotobacter

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 35.
Identity free living bacterial biofertlizer ………………….
(a) Rhizobium
(b) Azotobacter
(c) Nostoc
(d) Bacillus thuringiensis
Answer:
(b) Azotobacter

Question 36.
The ectomycorrhizae form …………………. on the root surface.
(a) root tuber
(b) mantle
(c) root hair
(d) arbuscles
Answer:
(b) mantle

Match the columns

Question 1.

Column I (Biofortified crop) Column II (Nutrient Enrichment)
(1) Maize (a) Five times more iron
(2) Rice (b) Twice the amount of lysine and tryptophan
(3) Wheat Atlas-66 (c) Enriched in vitamin A and minerals
(4) Carrots, spinach (d) High protein content

Answer:

Column I (Biofortified crop) Column II (Nutrient Enrichment)
(1) Maize (b) Twice the amount of lysine and tryptophan
(2) Rice (a) Five times more iron
(3) Wheat Atlas-66 (d) High protein content
(4) Carrots, spinach (c) Enriched in vitamin A and minerals

Question 2.

Column I (Organic Acids] Column II (Microbial source)
(1) Citric acid (a) Rhizopus arrhizus
(2) Fumaric acid (b) Acetobacter aceti
(3) Gluconic acid (c) Aspergillus niger
(4) Acetic acid (d) Aspergillus niger

Answer:

Column I (Organic Acids] Column II (Microbial source)
(1) Citric acid (c) Aspergillus niger
(2) Fumaric acid (a) Rhizopus arrhizus
(3) Gluconic acid (d) Aspergillus niger
(4) Acetic acid (b) Acetobacter aceti

Classify the following to form Column B as per the category given in Column A.

Question 1.
i. Alternaria crassa
ii. Agrobacterium spp.
iii. Cactoblastis cactorum
iv. Beavueria bassiana

Column A (Biocontrol agents) Column B (Host)
Microbial pesticide ————
Mycoherbicide ————
Insect as herbicide ————–
Bacterial herbicide —————

Answer:

Column A (Biocontrol agents) Column B (Host)
Microbial pesticide Beavueria bassiana
Mycoherbicide Alternaria crassa
Insect as herbicide Cactoblastis cactorum
Bacterial herbicide Agrobacterium spp.

Question 2.
i. Hairy leaves in wheat
ii. Nectar-less cotton having smooth leaves
iii. Hairy leaves in cotton
iv. Solid stem in wheat

Resistance to insects Morphological characters
Jassids ————
Cereal leaf beetle ————
Stem borers ————–
Bollworms —————

Answer:

Resistance to insects Morphological characters
Jassids Hairy leaves in cotton
Cereal leaf beetle Hairy leaves in wheat
Stem borers Solid stem in wheat
Bollworms Nectar-less cotton having smooth leaves

Very Short Answer Questions

Question 1.
What are the different methods of plant breeding?
Answer:
Different methods of plant breeding are introduction, selection, hybridization, mutation breeding, polyploidy breeding, tissue culture, r-DNA technology and SCP (Single cell protein).

Question 2.
Which variety of sugar cane having high sugar content and better yield is cultivated in South India?
Answer:
Saccharum ojficinarum variety of sugar cane has high sugar content and better yield. It is cultivated in South India.

Question 3.
What are the desirable characteristics in hybrid varieties millets developed in India?
Answer:
Hybrid varieties of millets developed in India are high yielding and resistant to water stress.

Question 4.
Give examples of natural physical mutagens.
Answer:
Natural physical mutagens are high temperature, high concentration of CO2, X-rays, UV rays.

Question 5.
Give examples of chemical mutagens.
Answer:
Chemical mutagens are nitrous acid, EMS (Ethyl – Methyl – Sulphonate), mustard gas, colchicine, etc.

Question 6.
How are seedlings or seeds mutated?
Answer:
Seedlings or seeds are mutated by irradiating them by CO-60 or exposing them to UV bulbs, X-ray machines, etc.

Question 7.
What are the effects of mutagens?
Answer:
Effects of mutagens are gene mutations and chromosomal aberrations.

Question 8.
Which biochemical characters are responsible for resistance against stem borers in maize?
Answer:
High aspartic acid, low nitrogen and sugar content are responsible for resistance against maize stem borers.

Question 9.
What does the plant tissue culture medium consists of?
Answer:
The plant tissue culture medium consists of water, all essential minerals, sources for carbohydrates, proteins and fats, growth hormones like auxins and cytokinins, vitamins. Agar is added to solidify nutrient medium for callus culture.

Question 10.
What are the types of tissue culture based on nature of explants?
Answer:
Cell culture, organ culture, pollen or anther culture, meristem culture and embryo culture are the types of tissue culture based on nature of explants.

Question 11.
What are the types of tissue culture based on the type of in vitro growth?
Answer:
Callus culture and suspension culture are the type of tissue culture based on the type of in vitro growth.

Question 12.
What is the necessity of subculturing?
Answer:
Both the callus and suspension cultures die in due course of time when nutrients get consumed. Therefore, a part of callus or suspension of cells is transferred to the flask containing new nutrient medium. This is subculturing, which is necessary to ensure continuous nutrient supply essential for continuous growth.

Question 13.
Enlist substances that are used as substrate for the production of SCP.
Answer:
Agricultural waste like corn cobs, sugar cane molasses, wood shavings, sawdust, paraffin, N-alkanes, human and animal wastes are the substrates used for the production of SCR.

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 14.
How biofortified crops are produced?
Answer:
Biofortified crops are produced by conventional selective breeding practices and r-DNA technology.

Question 15.
What per cent of world livestock population is present in India and China and what is the productivity?
Answer:
India and China have 70% of world livestock populations, but the productivity is only 25% of the world farm produce.

Question 16.
What is silage made up of?
Answer:
Silage is fermented fodder made up of legumes, grasses, maize and jowar.

Question 17.
What is the supplementary food to silage?
Answer:
Silage is supplemented with oilcakes, minerals, vitamins and salts.

Question 18.
What is layer?
Answer:
The hen which is reared to obtain eggs is called a layer.

Question 19.
What is broiler?
Answer:
The hen which is reared to obtain meat is called a broiler.

Question 20.
What are the allied professions to poultry?
Answer:
The allied professions to poultry are processing of eggs and meat, marketing of poultry products, compounding and sale of poultry feed, poultry equipment, pharmaceuticals, feed additives, etc.

Question 21.
Which areas are suitable for bee keeping?
Answer:
The areas having sufficient wild shrubs, cultivated crops of sunflower, mustard, safflower, chilly, cabbage, cucumber, legumes, etc. and fruit orchards of apple, mangoes, citrus, etc. are suitable for bee keeping.

Question 22.
What is indicated by yellow spots?
Answer:
Yellow spots indicate shrinking of female lac insect.

Question 23.
What is indicated by orange spots on the eggs of lac insect?
Answer:
Orange spots indicate that eggs are about to hatch.

Question 24.
What is the main function of a fermenter?
Answer:
The main function of a fermenter is to provide a controlled environment for growth of specific microorganisms or a defined mixture of microorganisms, to obtain the desired product.

Question 25.
What is known as Brewer’s yeast?
Answer:
Saccharomyces cerevisiae var. ellipsoids is commonly known as Brewer’s yeast.

Question 26.
Which fermenter is used for large scale preparation of alcohol?
Answer:
Tubular tower fermenter is used for large scale preparation of alcohol.

Question 27.
What is the use of gluconic acid?
Answer:
Gluconic acid is used in medicine for solubility of Ca++

Question 28.
What is the use of citric acid?
Answer:
Citric acid is used in confectionary.

Question 29.
What is the use of fumaric acid?
Answer:
Fumaric acid is used in resins as wetting agents.

Question 30.
Give examples of diseases which are treated using antibiotics.
Answer:
Diseases like plague, whooping cough, diphtheria and leprosy are treated using antibiotics.

Question 31.
What is the mechanism of actions of statins?
Answer:
Statins produced by yeast Monascus purpureus are blood cholesterol lowering agents. They are competitive inhibitors of the enzyme that catalyzes synthesis of cholesterol.

Question 32.
Enlist the various enzymes produced using microorganisms.
Answer:
Amylase, cellulase, protease, lipase, pectinase, streptokinase, invertase enzymes are produced using microorganisms.

Question 33.
Gibberellin was first isolated from which plant?
Answer:
Gibberellin was first isolated from rice plant infected by fungus Gibberella Jujikuroi.

Question 34.
How many different types of Gibberellins have been isolated?
Answer:
About 15 different types of Gibberellins have been isolated.

Question 35.
Give the chemical composition of biogas.
Answer:
The biogas consists of methane (50-60%), CO2 (30 to 40%), H2S (0-3%) and other gases like CO, N2, H2 in traces.

Question 36.
Which substrates are used for biogas production?
Answer:
Substrates like cattle dung (most commonly used substrate, a rich source of cellulose from plants), plant wastes, animal wastes, domestic wastes, agriculture waste, municipal wastes, forestry wastes, etc. are used for biogas production.

Question 37.
Which are the most commonly used models of biogas plants ?
Answer:
Models of biogas plants developed by KVTC (Khadi and Village Industries Commission) and IARI (Indian Agricultural Research Institute) are the most commonly used in India.

Question 38.
Which bacteria transform acetic acid into biogas?
Answer:
The acetic acid is transformed into biogas by methanogenic bacteria like Methanococcus, Methanobacterium and Methanobacillus.

Question 39.
What are the four groups of biocontrol agents?
Answer:
The four groups of biocontrol agents are bacteria, fungi, viruses and protozoans.

Question 40.
What is mycoherbicide ?
Answer:
The pathogenic fungus which kills or inhibits the growth of a weed is called mycoherbicide.

Question 41.
What are the three types of bacterial biofertilizers on the basis of function?
Answer:
On the basis of function, bacterial biofertilizers are of three types – nitrogen fixing, phosphate solubilizing and compost making biofertilizers.

Question 42.
What are the eight different types of mycorrhiza as per recent classification?
Answer:
Nowadays, mycorrhiza are classified into 8 different types – ectomycorrhizae, endomycorrhizae, ectendomycorrhizae, orchidaceous mycorrhizae, ericoid mycorrhizae, arbutoid mycorrhizae, monotrapoid mycorrhizae and ophioglossoid mycorrhizae.

Question 43.
What is heterocyst?
Answer:
Cynobacteria possess specialized colourless cells called heterocysts which are the sites of nitrogen fixation.

Question 44.
Give the role of heterocyst.
OR
Give the importance of heterocyst in cyanobacteria.
Answer:
The heterocysts are the sites of nitrogen fixation in cyanobacteria.

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 45.
Who discovered mycorrhizae?
Answer:
Mycorrhizae were discovered by Frank (1885).

Give definitions of the following

Question 1.
Food
Answer:
Food is defined as solid or liquid substance, which is swallowed, digested and assimilated in the body, keeping us well.

Question 2.
Plant breeding
Answer:
Plant breeding is the improvement or purposeful manipulation in the heredity of crops and the production of new superior varieties of existing crop plants.

Question 3.
Germplasm collection
Answer:
Germplasm collection is the entire collection having all the diverse alleles for all genes in a given crop.

Question 4.
Mutation
Answer:
Mutation is defined as the sudden heritable change in the genotype, which is caused naturally.

Question 5.
Tissue culture
Answer:
Tissue culture is growing isolated cells, tissues, organs ‘in vitro’ on a solid or liquid nutrient medium, under aseptic and controlled conditions of light, humidity and temperature, for achieving various objectives.

Question 6.
Explant
Answer:
The part of plant used in tissue culture is known as explant.

Question 7.
Totipotency
Answer:
An inherent ability of living plant cell to grow, divide, redivide and give rise to a whole plant is known as totipotency.

Question 8.
Callus
Answer:
Callus is defined as a mass of undifferentiated cells, formed by division and redivision of the cells of explant.

Question 9.
Single cell protein
Answer:
Single cell protein is defined as a crude or a refined edible protein, extracted from pure microbial cultures or from dead or dried cell biomass.

Question 10.
Biofortiflcation
Answer:
Biofortification is a method of developing crops having higher quantity and quality of vitamins, minerals and fats, to overcome problem of malnutrition.

Question 11.
Animal husbandry
Answer:
Animal husbandry is an agricultural practice of breeding and raising livestock.

Question 12.
Inbreeding
Answer:
Breeding of closely related individuals for 4 to 6 generations is known as inbreeding.

Question 13.
Outbreeding
Answer:
Breeding of unrelated animals either of the same breed but having no common ancestors for 4 to 6 generations (outcrossing) or of different breeds (crossbreeding) or even of different species (interspecific hybridization), is known as outbreeding.

Question 14.
Outcrossing
Answer:
Breeding of animals of the same breed but having no common ancestors for 4 to 6 generations is known as outcrossing.

Question 15.
Crossbreeding
Answer:
Breeding of superior male of one breed with superior female of another breed is known as crossbreeding.

Question 16.
Interspecific hybridization
Answer:
Breeding of animals of two different but related species is known as interspecific hybridization.

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 17.
Apiculture
Answer:
Apiculture is an artificial rearing of honey bees to obtain bee products like honey, wax, pollens, bee venom, propolis (bee glue) and royal jelly and to use honey bees as pollinating agents for crop plants.

Question 18.
Antibiotics
Answer:
Antibiotics are organic substances produced in small amounts by certain microbes to kill or inhibit the growth of other microbes.

Question 19.
Biotechnology
Answer:
Biotechnology is defined as the applications of scientific and engineering principles for the processing of materials by biological agents to provide goods and service to humans or for human welfare.

Question 20.
Biocontrol or biological control:
Answer:
Biocontrol is the natural method of eliminating and controlling insects, pests and other disease-causing agents by using their natural, biological enemies.

Question 21.
Biocontrol agents
Answer:
Biocontrol agents are the organisms like insects, bacteria, fungi, viruses and protozoans which are employed for biocontrol.

Question 22.
Fertilizers
Answer:
Fertilizers Eire the nutrients necessary for plant growth and which increase the productivity of cultivated plants.

Question 23.
Biofertilizers
Answer:
Biofertilizers are commercial preparation of ready-to-use live bacterial, cyanobacterial (mostly N2 fixing) or fungal formulations which enhance the nutrient quality of soil.

Name the Following

Question 1.
Hybrid wheat varieties in India.
Answer:
Sonalika and Kalyan Sona

Question 2.
Semi-dwarf rice varieties in India.
Answer:
Jaya, Padma and Ratna

Question 3.
Sugar cane varieties developed at Coimbatore, Tamil Nadu.
Answer:
CO-419, 421, 453

Question 4.
Hybrid varieties of millets developed in India.
Answer:
Ganga-3 (maize), CO-12 (Jowar), Niphad (Bajra)

Question 5.
Fungal disease of plants.
Answer:
Brown rust of wheat, Red rot of sugar cane, Late blight of potato

Question 6.
Bacterial disease of plants.
Answer:
Black rot of crucifers

Question 7.
Viral disease of plants.
Answer:
Tobacco mosaic disease

Question 8.
Mutant variety of rice.
Answer:
Jagannath

Question 9.
Mutant variety of wheat.
Answer:
NP 836 (rust resistant)

Question 10.
Mutant variety of cotton.
Answer:
Indore-2 (resistant to bollworm)

Question 11.
Mutant variety of cabbage.
Answer:
Regina-II

Question 12.
The most preferred tissue culture medium.
Answer:
MS (Murashige and Skoog) medium.

Question 13.
High yielding varieties of banana used in Maharashtra.
Answer:
Shrimati, Basarai, G-9

Question 14.
The fungi used for the production of SCP.
Answer:
Aspergillus niger, Trichoderma viride, Saccharomyces cerevisiae, Candida utilis.

Question 15.
Algae used for the production of SCR
Answer:
Spirulina spp, Chlorella pyrenoidosa

Question 16.
Bacteria used for the production of SCR
Answer:
Methylophilus methylotrophus, Bacillus megasterium

Question 17.
A new breed of sheep developed from crossing of Bikaneri ewe and Marino rams in Punjab.
Answer:
Hisardale

Question 18.
Indian breeds of cows.
Answer:
Sahiwal, Sindhi, Gir

Question 19.
Exotic breeds of cows.
Answer:
Jersey, Brown Swiss, Holstein

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 20.
Breeds of bufaaloes in India.
Answer:
Jaffarabadi, Mehsana, Murrah, Nagpuri, Nili, Surati.

Question 21.
Common breeds of cattle and poultry in the farms, found in your area.
Answer:
Khillari, Gir (breeds of cows), Aseel, Kadaknath (poultry)

Question 22.
American poultry breeds.
Answer:
Plymouth Rock, New Hampshire, Rhode Island Red

Question 23.
Asiatic poultry breeds.
Answer:
Brahma, Cochin and Langshan

Question 24.
Mediterranean poultry breeds.
Answer:
Leghorn, Minorca

Question 25.
English poultry breed.
Answer:
Australorp

Question 26.
Indian poultry breeds.
Answer:
Chittagong, Aseel, Brahma and Kadaknath.

Question 27.
Best layer.
Answer:
Leghorn

Question 28.
Best broilers.
Answer:
Plymouth rock, Rhode Island Red, Aseel, Brahma and Kadaknath

Question 29.
Viral diseases of poultry.
Answer:
Ranikhet, Bronchitis, Avian influenza (bird flu), Bird flu

Question 30.
Bacterial diseases of poultry.
Answer:
Pullorum, Cholera, Typhoid, TB, CRD (chronic respiratory disease), Enteritis.

Question 31.
Fungal diseases of poultry.
Answer:
Aspergillosis, Favus and Thrush.

Question 32.
Parasitic diseases of poultry.
Answer:
Lice infection, roundworm, caecal worm infections, etc.

Question 33.
Protozoan diseases of poultry.
Answer:
Coccidiosis

Question 34.
Domesticated species of bees.
Answer:
Apis mellifera, Apis indica

Question 35.
Lac insect.
Answer:
Trachardia lacca

Question 36.
Silk moth.
Answer:
Bombyx mori

Question 37.
The common fresh water fish.
Answer:
Labeo rohita (rohu), Catla (catla), Cirrihanus mrigala (mrigala) and other carps.

Question 38.
The common marine fish.
Answer:
Harpadon (Bombay duck), Sardinella (sardine), Rastrelliger (mackerel) and Stromateus (pomphret).

Question 39.
Estuaries found in Maharashtra and where these estuaries are located.
Answer:
Thane creek, Manori creek, Rajapuri creek, Kalbadevi Estuary in Ratnagiri, Damanganga estuary and Narmada estuary

Question 40.
Different fish found at an estuary.
Answer:
Clupeids, mullets, catfishes, perches, Mugil cephalus gar fishes, halfbeaks, eels, flatfishes, sharks, rays, oysters and migratory fishes include Hilsa ilisha, Polynemus spp., Pampana, Tachysurus spp, Pangasius spp., etc.

Question 41.
Best Silk.
Answer:
Mulberry silk

Question 42.
Silk of inferior quality.
Answer:
Tussar silk, Eri silk

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 43.
Distilled alcoholic beverages.
Answer:
Whisky, brandy, rum

Question 44.
Traditional drink made by fermenting the sugar sap extracted from palm plants and coconut palm.
Answer:
Toddy

Question 45.
The wine of Goa, made by fermenting fleshy pedicels of cashew fruits.
Answer:
Fenny

Question 46.
The microbes used in fermentation of dhokla.
Answer:
Lactobacilli

Question 47.
Microbes used in the production of vitamin B2.
Answer:
Neurospora gossypii, Eremothecium ashbyi

Question 48.
Microbes used in the production of vitamin B12.
Answer:
Pseudomonas denitrtficans

Question 49.
Microbes used in the production of vitamin C.
Answer:
Aspergillus niger

Question 50.
Symbiotic N2 fixing microorganisms.
Answer:
Rhizobium, Anabaena, Frankia.

Question 51.
Free-living or Non-Symbiotic N2 fixing microorganisms.
Answer:
Azotobacter, Nostoc, Clostridium, Beijerinkia, Klebsiella, etc.

Question 52.
Phosphate solubilizing biofertilizers.
Answer:
Pseudomonas striata, Bacillus polymyxa, Agrobacterium, Microccocus, Aspergillus spp., etc.

Question 53.
Nitrogen fixing cyanobacteria.
Answer:
Anabaena, Nostoc, Plectonema, Oscillatoria.

Question 54.
Cyanobacteria associated with lichens.
Answer:
Anabaena, Nostoc and Tolypothrix

Question 55.
Cyanobacteria associated with plants like Azolla and Cycas.
Answer:
Anabaena

Question 56.
The aquatic fern commonly used in paddy field as a biofertilizer.
Answer:
Azolla.
Give functions or significance

Question 1.
Hybridization
Answer:

  1. Hybrdization is an effective means of combining together the desirable characters of two or more varieties.
  2. New genetic combinations of already existing characters and new genetic variations can be created by hybridization.
  3. Hybridization exploits and utilizes hybrid- vigour.

Question 2.
Food
Answer:

  1. Food is organic, energy rich, non-poisonous, edible and nourishing substance.
  2. It provides nutrients for growth and development of body.
  3. It provides energy for metabolic reactions.
  4. It keeps us alive, strong and healthy.

Question 3.
Antibiotics
Answer:

  1. Antibiotics are secondary metabolites of therapeutic importance, produced in small amounts by certain microbes like bacteria, fungi and a few algae.
  2. They inhibit growth of other microbial pathogens like fungi and bacteria.
  3. Thus, they are antifungal and antibacterial in nature.
  4. Antibiotics are used in treatment of deadly diseases like plague, whooping cough, diphtheria, leprosy, etc.

Distinguish between the following

Question 1.
Callus culture and Suspension culture.
Answer:

Callus Culture Suspension culture
1. Solid nutrient medium is used in callus culture. 1. Liquid nutrient medium is used in suspension culture.
2. No shaker or agitator is needed. 2. Shaker or agitator is needed.
3. Cells of explants divide and redivide to form callus. 3. Callus is not formed.
4. Callus a mass of undifferentiated cells. 4. Suspension culture consists of single isolated cells or small groups of cells.
5. It shows slow growth. 5. It shows faster growth.

Question 2.
Outcrossing and Crossbreeding.
Answer:

Outcrossing Crossbreeding
1. Breeding of animals of the same breed but having no common ancestors for 4 to 6 generations is known as outcrossing. 1. Breeding of superior male of one breed with superior female of another breed is known as crossbreeding.
2. Progeny is known as outeross. 2. Progeny is known as hybrid.
3. New breeds are not developed by outcrossing. 3. New breeds or hybrids are formed by crossbreeding.
4. An outcross helps to overcome inbreeding depression. 4. Hybrids are subjected to inbreeding and new stable breeds are developed by crossbreeding.

Question 3.
Inorganic fertilizers and Organic fertilizers / biofertilizers.
Answer:

Inorganic fertilizers Organic fertilizers / biofertilizers
1. They are non-renewable nutritional resources. 1. They are renewable nutritional resources.
2. Inorganic fertilizers are synthetic and are in the form of chemicals. 2. They are biological in origin.
3. They are mixtures of mineral salts of NPK in definite proportions. 3. Organic fertilizers are farmyard manure, green manure and compost.
Whereas, bio fertilizers are live bacterial, cyanobacterial (mostly N<sub>2</sub> fixing) or fungal formulations which enhance the nutrient quality of soil.
4. Excessive use of inorganic fertilizers results in pollution of soil, groundwater and air. 4. They do not cause pollution.
5. They are not part of sustainable agriculture. 5. They are part of organic farming and sustainable agriculture.

Question 4.
Ectomycorrhizae and Endomycorrhizae.
Answer:

Ectomycorrhizae Endomycorrhizae
1. Mycelium of ectomycorrhizal fungi form a sheath called mantle on the surface of roots. 1. Most of the endomycorrhizal hyphae penetrate in the root cortex.
2. Few hyphae form hartig-net in the intercellular spaces of root cortex. 2. Fungal hyphae do not produce hartig-net.
3. Arbuscles and vesicles are not formed. 3. Arbuscles and vesicles are formed.

Give reasons

Question 1.
Why are honey bees called as best pollinators?
Answer:

  1. About 80% of insect pollination is carried by honey bees.
  2. They pollinate various crops like sunflower, mustard, safflower, chilly, cabbage, cucumber, legumes, fruits like apple, mango, citrus, etc.
  3. They increase the productivity of crops.
  4. Hence, honey bees are important pollinators.

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 2.
Regular visit of veterinary doctor to dairy farm is mandatory.
Answer:
Daily visit of veterinary doctor to dairy farm is mandatory to diagnose health problems, diseases and for their rectification.

Question 3.
Apis mellifera and Apis indica are known as domesticated species.
Answer:

  1. Apis mellifera and Apis indica are suitable for apiculture.
  2. Hence, they are known as domesticated species.

Question 4.
Cages of silkworm larvae must be well managed and protected.
Answer:

  1. Silkworm larvae may get infected by protozoans, viruses and fungi.
  2. Ants, crows, other birds and predators may attack these larvae.
  3. Hence, cages of silkworm larvae must be well managed and protected.

Question 5.
Buttermilk is used in the dough of dhokla.
Answer:

  1. Buttermilk contains the lactobacilli.
  2. These lactobacilli bring about the fermentation of gram flour.
  3. CO2 produced during fermentation increases the volume of the dough.
  4. It escapes during the steaming of dough, making dhokla porous and spongy.
  5. Hence, buttermilk is used in the dough of dhokla.

Question 6.
We include mushrooms in our diet.
Answer:

  1. Mushrooms are directly used as food.
  2. They produce large, fleshy fruiting bodies which are edible.
  3. They are low calorie, sugar free, fat free, but rich in proteins, vitamins, minerals and amino acids.
  4. Hence, we include mushrooms in our diet.

Question 7.
Vitamins are to be consumed through food or tablets or capsules.
Answer:

  1. Vitamins B and K are produced in the body.
  2. But some vitamins like C, D and E are not produced in the body.
  3. If our body does not get these vitamins in the required quantity, then the deficiency of these vitamins may result in various diseases.
  4. Therefore, vitamins are to be consumed through food or tablets or capsules.

Question 8.
Enzymes are essential for survival of living organisms.
Answer:

  1. Enzymes are proteins which act as biocatalysts.
  2. They speed up the chemical reactions without undergoing any change themselves.
  3. They catalyze reactions more quickly and efficiently at body temperature.
  4. Thus they play key role in metabolic reactions.
  5. Hence, enzymes are essential for survival of living organisms.

Question 9.
Biogas plants are more often built in rural areas.
Answer:

  1. Biogas is a non-conventional and renewable source of energy obtained by microbial fermentation.
  2. Cattle dung (the main substrate), domestic wastes, agricultural waste, agro industrial wastes, forestry wastes, etc. are utilized as substrates for production of biogas.
  3. Biogas is eco-friendly and does not cause pollution, can be used as domestic fuel.
  4. As the raw material for its production is readily available, the biogas plants are more often built in rural areas.

Question 10.
Why are healthy root nodules pink in colour?
Answer:

  1. Rhizobium has symbiotic relationship with roots of leguminous plants.
  2. It infects root cortex and form root nodules.
  3. Root nodules are the site of nitrogen fixation.
  4. Enzyme nitrogenase which catalyzes nitrogen fixation, gets inhibited by oxygen.
  5. But root nodule contain a pigment called leghaemoglobin which acts as oxygen scavanger and protects nitrogenase from getting inhibited.
  6. Leghaemoglobin is pink in colour.
  7. Hence, healthy root nodules are pink in colour.

Give Short Notes

Question 1.
Callus culture.
Answer:

  1. In callus culture, nutrient medium is solidified using agar-agar is used.
  2. Shaker or agitator is not required.
  3. Sterilized explant is placed on solid nutritive medium.
  4. The cells of explants absorb nutrients and start multiplying.
  5. This results in the formation of callus.
  6. Callus is a mass of undifferentiated cells, formed by division of the cells of explants.
  7. Growth hormones, auxins and cytokinins are provided to callus in specific proportion to induce formation of organs.
  8. If auxins are in more quantity, roots are formed (rhizogenesis) and if the cytokinins are in more quantity, shoot formation takes place (caulogenesis).
  9. Thus new plantlets are formed.
  10. Callus culture required subculturing to ensure its continuous growth.

Question 2.
Suspension culture.
Answer:

  1. In suspension culture, small groups of cells or a single cell are transferred to liquid nutritive medium as explants.
  2. The liquid medium is constantly agitated by using shakers (agitators).
  3. The agitation serves the purpose of aeration, mixing of medium and prevents the aggregation of cells.
  4. Generally the suspension culture shows a high proportion of single isolated cells and small clumps of cells.
  5. Suspension culture grows much faster than callus culture.
  6. Suspension culture is used for cell biomass production which can be utilized for biochemical isolation, regeneration of new plants, etc.

Question 3.
Applications of micropropagation.
Answer:

  1. Micropropagation involves in rapid multiplication of genetically similar plants (clones).
  2. A large number of plantlets are obtained within a short period and in a small space.
  3. Plants are obtained throughout the year, under controlled conditions, independent of seasons.
  4. As micropropagation results in the formation of clones, desirable characters (genotype and sex) of superior variety can be maintained for many generations.
  5. The rare plant and endangered species are multiplied and conserved using this technique.
  6. With the help of somatic hybrids (cybrids), new variety can be obtained in short time span.
  7. Micropropagation is involved in commercial production of ornamental plants like v orchids, Chrysanthemum, Eucalyptus, etc. and fruit plants like banana, grapes, Citrus, etc.

Question 4.
Applications of tissue culture.
Answer:
Applications of tissue culture are as follows:

  1. Production of healthy plants from diseased plants using apical meristems as explants.
  2. Production of stress resistant plants.
  3. Production of haploid plantlets by pollen culture.
  4. Production of secondary metabolites such as alkaloids, enzymes, hormones, etc.
  5. Multiplication of rare and endangered plants.
  6. Production of somaclonal variants.
  7. Use of micropropagation techniques to produce large number of genetically identical plants.
  8. Protoplast culture
  9. Tissue culture has applications in forestry, agriculture, horticulture, genetic engineering and physiology.

Question 5.
Single cell protein (SCP).
Answer:

  1. Single-cell protein is a crude or a refined edible protein, extracted from pure microbial cultures or from dead or dried cell biomass.
  2. Microorganisms like algae, fungi, yeast and bacteria with high protein content in their biomass, are grown using waste and inexpensive substrates.
  3. Substrates used for growing microbial biomass are wood shavings, sawdust, corn cobs, paraffin, N-alkanes, sugar cane molasses, even human and animal wastes.
  4. SCP is rich in proteins, vitamins, vitamin B complex, minerals and fats.
  5. It can be used as fodder for achieving fattening of calves, pigs, in breeding fish and even in poultry and cattle farmimg.
  6. Fungi like Aspergillus niger, Trichoderma viride, Saccharomyces cerevisiae, Candida utilis, algae like Spirulina spp, Chlorella pyrenoidosa, bacteria like Methylophilus, methylotrophus and Bacillus megasterium are used for the production of SCR

Question 6.
Advantages of Single Cell Protein.
Answer:

  1. Microbes that are used as SCP have very high protein contents in their biomass – 43% to 85% (W/W basis).
  2. SCP is a good source of vitamins, vitamin B complex, fats, amino acids, minerals, crude fibres, etc.
  3. As microorganisms multiply fast, large quantity of biomass can be produced in a short duration.
  4. The microbes can be grown using waste materials and inexpensive substrates. This decreases pollution.
  5. The microbes can be genetically modified to vary the amino acid composition.
  6. SCPs can be used as fodder for achieving fattening of calves, pigs, in breeding fish, poultry and cattle farming.

Question 7.
Inbreeding.
Answer:

  1. Inbreeding is the mating of two closely related individuals of the same breed for 4 to 6 generations.
  2. During inbreeding superior males and superior females of the same breed are identified. The superior males and superior females from this progeny are identified and used for further mating.
  3. Due to inbreeding, homozygosity is increased and harmful recessive genes are exposed. Inbreeding is done when a pure line of an animal is expected.
  4. Inbreeding helps in accumulation of superior genes and elimination of harmful or less desirable genes.
  5. Continued inbreeding usually reduces fertility and productivity. This is called inbreeding depression.

Question 8.
Fish farming.
Answer:
Fish farming is the practice of culturing the edible and commercially important fish species in the ponds, lakes or reservoirs. Fish farming helps in boosting the productivity and the economy of the nation.

For maintaining a fish farm, following aspects are taken into consideration:

  • selection of the site
  • excavation of the pond
  • managing hatchery
  • nursery
  • looking after rearing ponds and
  • stocking ponds besides managing the water source, supplying fertilizer and supplementary feed, etc.

Question 9.
Microbes in industrial vitamin production.
Answer:
(1) Vitamins are nitrogenous organic compounds, required in minute quantities for normal growth and development of the body.

(2) The microbes are involved in the industrial production of vitamins like thiamine (vitamin B1, riboflavin (vitamin B2), pyridoxine, folic acid, pantothenic acid, biotin, vitamin B12, ascorbic acid (Vitamin C), beta-carotene (provitamin A) and ergosterol (provitamin D).

(3) Examples of some vitamins produced by fermetaion using different microbial sources are-

  • Vitamin B2 – Neurospora gossypii, Eremothecium ashbyi
  • Vitamin B12 – Pseudomonas denitrijicans
  • Vitamin C – Aspergillus niger

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 10.
Industrial uses of enzymes.
Answer:

  1. Enzymes are used to improve the quality of the fabrics in the textile industry.
  2. In the pulp and paper industry, they are involved in biomechanical pulping and bleaching.
  3. In food industry, enzymes are used in the fermentation processes to produce bread and alcoholic beverages such as wine and beer.
  4. They are used in the extraction of carotenoids and olive oil.
  5. Enzymes are also used in cosmetics, animal feed and agricultural industries.
  6. Lipases are used to remove oil stains and to increase the brightness in detergent industry. They have superior cleaning properties.
  7. Streptokinase is used as a ‘clot buster’ for clearing blood clots in the blood vessels in heart patients.

Question 11.
Microorganisms in sewage.
Answer:

  1. Sewage contains pathogenic bacteria, viruses, fungi, protozoa which cause dysentery, cholera, typhoid, polio and infectious hepatitis, etc. It also contains nematodes and algae.
  2. Their number and type of microorganisms in sewage depends on the composition and source of sewage.
  3. Millions of bacteria per ml may be present in raw untreated sewage.
  4. Bacteria in sewage include coliforms, fecal Streptococci, anaerobic spore forming bacilli and other bacteria found in the intestinal tract of humans.
  5. The sewage also contains soil bacteria.
  6. During sewage decomposition, initially aerobic and facultative anaerobic organisms predominate which are followed by strict anaerobic especially methogenic bacteria that produce methane (CH4) and CO2.

Question 12.
Rhizobia as a biofertilizer
Answer:

  1. Rhizobia [Singular – Rhizobium) are rod¬shaped, motile, aerobic, gram negative, non- spore forming, nitrogen-fixing bacteria.
  2. They contain Nod genes and Nif genes.
  3. They live in symbiotic association with leguminous roots.
  4. They form nodule on the roots of leguminous plants and multiply inside the nodule.
  5. Nodules are the site of nitrogen fixation. They are pink in colour and contain enzyme nitrogenase and oxygen scavenger leghaemoglobin.
  6. Rhizobia fix atmospheric nitrogen into organic forms, which can be used by plants as nutrients. The host plant in return provides food and water to the bacterium (Rhizobia).
  7. Rhizobia are host specific e.g. leguminosarum is specific to pea R. phaseoli is specific to beans.
  8. In a laboratory, pure cultures of specific Rhizobium species are raised which are used for the preparation of biofertilizer.

Question 13.
Azotobacter as a biofertilizer
Answer:

  1. Azotobacter is a free living, nitrogen fixing, aerobic, non-photosynthetic, non-nodule forming bacterium.
  2. It is associated with roots of grasses and certain plants.
  3. It is used as a biofertilizer for non-leguminous plants like rice, cotton, vegetables, etc.

Question 14.
Azospirillumas as a biofertilizer
Answer:

  1. Azospirillum acts as a biofertilizer for non- leguminous plants like cereals, millets, cotton, oilseed, etc.
  2. It is a free living, aerobic nitrogen fixing bacterium associated with roots of corn, wheat and jo war.
  3. It fixes the nitrogen (20-40 kg N/ha).

Question 15.
Anabaena as a biofertilizer
Answer:

  1. Anabaena is a cyanobacterial biofertilizer.
  2. It is multicellular, filamentous nitrogen fixing organism that exits as plankton.
  3. It can fix nitrogen both in free living conditions as well as by forming symbiotic associations.
  4. Anabaena forms symbiotic relationship with Azolla, Anthoceros and Cycas.
  5. It is found in dorsal leaf lobe in Azolla, thallus of Anthoceros and in coralloid roots of Cycas.
  6. It has specialized colourless cells known as heterocysts.
  7. Heterocysts are the sites for nitrogen fixation.

Question 16.
Benefits of Biofertilizers.
Answer:

  1. Biofertilizers increase soil fertility.
  2. They are low cost and can be used by marginal farmers.
  3. They do not cause pollution.
  4. BGA secret growth promoting substances, organic acids, proteins and vitamins.
  5. Azotobacter supplies nitrogen and antibiotics in the soil.
  6. Use of biofertilizers improves physico-chemical properties of soil-like texture, structure, pH, water holding capacity of soil by providing nutrients and organic matter.
  7. The use of chemical fertilizers gets reduced and the pollution also becomes less.

Short Answer Questions

Question 1.
What are the objectives of plant breeding?
Answer:
Objectives of plant breeding are as follows:

  1. To increase crop yield,
  2. To improve quality of produce.
  3. To increase tolerance to environmental stresses.
  4. To develop varieties of plants resistant to pathogens and insect pest.
  5. To alter the life span.

Question 2.
What are the different types of hybridization in plants?
Answer:
The different types of hybridization in plants are as follows:

  1. Intravarietal : It is the hybridization between plants of same variety.
  2. Intervarietal : It is the hybridization between two varieties of the same species.
  3. Interspecific : It is the hybridization between two species of the same genus.
  4. Intergeneric : It is the hybridization between two genera of the same family.
  5. Wide/distant crosses : These are the crosses between distantly related parental plants.

Question 3.
How aseptic conditions are maintained in tissue culture?
Answer:

  1. Glassware is sterilized by using detergents and hot air oven.
  2. Nutrient medium is autoclaved under constant pressure of 15 lb/sq inch, continuously for 20 minutes to sterilize it.
  3. Explant is treated with 20% ethyl alcohol and 0.1% HgCl2.
  4. Sterilization of inoculation chamber (Laminar air flow) is done using UV ray tube for 1 hour before actual inoculation of explant on the sterilized nutrient medium.

Question 4.
What are the objectives of biofortification ?
Answer:
Objectives of biofortification are as follows:

  1. Improvement in protein content and quality.
  2. Improvement in oil content and quality.
  3. Improvement in vitamin content.
  4. Improvement in micronutrient content and quality.
  5. To overcome the problem of malnutrition.

Question 5.
What are the objectives of animal breeding?
Answer:
Objectives of animal breeding are as follows:

  1. To increase the yield of animals.
  2. To improve the production of milk, quality of milk product, quality of meat or maximum yield of eggs per year, etc.
  3. To develop breeds with desirable characters.

Question 6.
What is artificial insemination? What are its advantages?
Answer:

  1. Artificial insemination is the technique used for controlled breeding experiments.
  2. Superior males of a particular commercial breed are selected.
  3. Semen from such superior males is collected and injected into the genital tract of female.
  4. This insemination is either done immediately or semen is frozen and used later on.
  5. In frozen semen, sperms can remain alive for long duration. They are also convenient for transport.
  6. Artificial insemination is preferred as it is easy and helpful to overcome several problems of normal mating.

Question 7.
What is Multiple Ovulation Embryo Transfer (MOET) technology? Where is it used?
OR
Explain the technique of multiple ovulation embryo transfer (MOET) in animal breeding.
Answer:

  1. Multiple Ovulation Embryo Transfer (MOET) technology is used to increase chances of successful production of hybrids.
  2. In this technique, cow is administered with Follicle Stimulating Hormone (FSH) which induces follicular maturation and then the super ovulation is brought about.
  3. By such technique in each cycle, 6 to 8 eggs mature simultaneously.
  4. The cow is then either mated with a superior bull or she is artificially inseminated.
  5. The blastocysts at 8 to 32 cell stage are recovered non-surgically and transferred to surrogate mothers.
  6. The genetic mother who gave the egg is then again subjected to another round of super ovulation.
  7. This technology is used for cattle, sheep, rabbits, buffaloes, etc.
  8. The MOET is used to produce high milk yielding breeds of female and high quality meat yielding bulls with lean meat containing less lipids. It helps in increasing favourable herd size in a short period.

Question 8.
As a dairy owner what measures will you adopt to improve the quality of milk?
Answer:

  1. In order to improve the quality of milk, following measures should be taken at every stage of dairy farming:
  2. Good breeds having high yielding potential should be selected.
  3. The breeds selected should be suitable for the local climatic conditions.
  4. The breeds selected should have proper resistance to diseases.
  5. Cattles should be well looked after with proper care.
  6. The feed should be of suitable quality and quantity. Feed includes silage made from legumes, grasses, maize and jowar. Silage should be supplemented with oilcakes, minerals, vitamins and salts.
  7. Utmost care should be taken about cleanliness and hygiene of the cattle as well as the handlers who handle the cattle.
  8. This is especially important during milking, storage and transport of milk and its products. Mechanized processes should be adopted as far as possible as they reduce chance of direct contact of produce with the handlers.
  9. The shed must be clean and well maintained. Similarly the dairy should be spacious with adequate facilities for feeding, watering and light.
  10. Help of veterinary doctor should be sought from time to time for the identification of health problems, diseases and rectification.
  11. Transportation of milk, processing, marketing and distribution play a vital role in dairy industry. If all the above care is taken then the quality of milk will surely improve.

Question 9.
Explain in short the poultry management.
Answer:
For the management of poultry, following aspects are to be taken care of:

  1. Selection of proper and disease free breed, suitable and safe farm conditions.
  2. Proper feeding practice and the quality of feed and water.
  3. Hygiene and health care of the birds.
  4. Management of layers is done by selecting high yielding chicken. Their farms are kept clean, dry and well ventilated. They are given proper feed at proper times. Other aspects such as debeaking, etc. are also taken care of.
  5. In the farm, importance is given to infrastructure such as proper and adequate lighting, placing waterer at places, looking after sanitation, culling and vaccination.
  6. Management of broiler similarly includes selection of breed, housing, temperature, ventilation, lighting, observing the floor space and broiler feed.

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 10.
What is apiculture? What is its importance?
Answer:

  1. Apiculture is artificial rearing of honey bees to obtain various bee products.
  2. Various products such as honey, wax, pollen, bee venom, propolis (bee glue) royal jelly, etc. are obtained from this cottage industry. Honey is an important item as ayurvedic medicine and in food due to its nutritional value.
  3. Bees also help in the cross pollination of various crops. Hence in pastures, wild shrubs, fruit orchards and cultivated crops, honeybees play an important role as pollinators.
  4. Bee keeping in crop fields increases the productivity of both honey and the crop.
  5. Apiculture itself is a means for employment for rural youth. It is an age old cottage industry which can be done along with agriculture.

Question 11.
What are the requirements of bee keeping?
Answer:

  1. Bee keeping requires bee hive boxes which consist of comb foundation sheets.
  2. In addition, the bee veil, smoker, bee brush, gloves, gumshoes, uncapping knives, swarm net, queen excluder, overall hive tool, etc. are required.
  3. Bee keeping requires familiarity with the habits of bees, selection of suitable location, catching and hiving of swarms, management of hives during different seasons, handling and collection of honey, bee wax and other products.
  4. Successful bee keeping also requires periodic inspection for cleanliness of hive boxes, activity of bees and queen, condition of brood, provision of water.

Question 12.
What are the main divisions of fishery?
Answer:

  1. Fishery can be capture fishery and culture fishery.
  2. Three main divisions of capture fishery are : Inland fishery, estuarine fishery and marine fishery.
  3. Inland fishery : It is culturing and capturing of from fresh water bodies. It is carried out on about 40 to 50 lakh acres of fresh water bodies such as rivers, ponds, lakes and dams.
  4. Marine fishery : It includes capturing fish from sea water. India has a coastline of about 7500 km.
    Estuarine fishery : It includes capture of fish from estuaries.
  5. Culture fishery is either of polyculture or of monoculture type. In polyculture, different species are cultured simultaneously at the same time in the same pond. In monoculture, only a single species is cultured.

Question 13.
Can “fishery” be a sustainable job option?
Answer:

  1. Fishery can never be a job. It is a livelihood or can be an occupation.
  2. Fish is a renewable resource. If managed properly, it can be a sustainable resource.
  3. The sustainability is dependent upon the availability of fishes and other edible organisms. But due to climate change, pollution and overexploitation of fish resources, these are depleting rapidly, it is estimated by the scientists that by 2050, no fish will be left in the seas.
  4. However, if aquaculture is done to raise fishes, partly it can be sustaining. But there . are many environmental regulations that can hamper the business of aquaculture.

Question 14.
Describe sericulture in brief.
Answer:

  1. Sericulture is the practice of rearing silkworms for the production of silk.
  2. The silkworm (Bombyx mort) is reared for obtaining best quality of silk called mulberry silk. Tussar silk and Eri silk are other varieties of silk which are inferior to the mulberry silk.
  3. Larvae of silkworm are fed on the mulberry leaves. Quality and quantity of silk depends on the quality of mulberry leaves.
  4. These larvae are reared, developed and well looked after by the skilful labour keeping a constant watch.
  5. Silkworm larvae may be infected by protozoans, viruses and fungi. Ants, crows, birds, and other predators are ready to attack these insects, hence the cages of these larvae must be managed to prevent predators attack.
  6. Silk is obtained from the cocoon of the silkworm.
  7. Sericulture is an age old practice and can be started with low investment and small space. It requires scientific knowledge and skill. Disabled, older and handicapped people also can practise it.

Question 15.
What are the different stages found in the life cycle of silkworm?
Answer:

  1. Stages of development in the life cycle of silkworm are egg, larva, pupa and adult.
  2. The larva is the silkworm caterpillar.
  3. The adult (imago) stage is the silkworm moth.

Question 16.
Describe the process of cocoon formation.
Answer:

  1. The eggs of silkworm hatch into larvae.
  2. The larvae develop into a caterpillar.
  3. Caterpillar feeds on fresh mulberry leaves.
  4. After its growth and moulting, the silkworm secretes a silk fibre to form cocoon.
  5. The silk is a continuous filament comprising fibroin protein, secreted from salivary glands of silkworm and a gum called sericin, which cements the filaments.
  6. The silk solidifies when it contacts the air.
  7. The silkworm spins approximately one mile of filament and completely encloses itself in a cocoon in about two or three days.

Question 17.
Which process is involved in silk production from cocoon?
Answer:

  1. The silk is a continuous filament comprising fibroin protein, secreted from salivary glands of silkworm and a gum ailed sericin.
  2. To remove the sericin, which cements,the filaments, cocoons are placed in hot water.
  3. It frees the silk filaments and readies them for reeling. This is known as the degumming process.
  4. The sillworm pupa gets killed in hot water.
  5. Single filaments are combined to form thread.
  6. The threads are plied to form yarn.
  7. After drying, the raw silk is packed according to quality.

Question 18.
Give the economic importance of lac.
OR
State the economic importance of ‘lac culture’.
Answer:
Lac is used for the following purposes:

  1. For making bangles.
  2. For making different types of toys.
  3. It is used in wood works.
  4. Polish is made from lac.
  5. Inks can be prepared from lac.
  6. Lac is largely used for silvering mirrors.

Question 19.
Tribal people from India have a great contribution in production of lac. But it needs certain trees. Name at least two such trees which give food yield of lac. How is lac purified?
Answer:

  1. Like her, peepal, palas, kusum, babul, etc. are used for feeding lac insects during the practice of lac culture.
  2. Natural lac is contaminated and hence it is washed and purified. This helps to obtain shellac in pure form.

Question 20.
Give an account of alcoholic beverages.
Answer:

  1. Alcoholic beverages are the products of alcoholic fermentation of particular substrates.
  2. Tubular tower fermenters are used to produce alcoholic beverages on a large scale.
  3. Beer is produced from barley by fermentation. For the production of beer, strains of Saccharomyces cerevisiae are used.
  4. Wine is prepared from grapes.
  5. Whisky is prepared by fermenting mixed grains of wheat, barley and corn followed by the distillation of the products of fermentation.
  6. Liquors like beer, wine are produced without distillation.
  7. Whisky, rum and brandy are distilled alcoholic beverages.
  8. Toddy is prepared by fermenting the sugar sap extracted from palms and coconut palms.
  9. Fenny is fermented by fleshy pedicels of cashew fruits.

Question 21.
Industrial production of which substances involves fermentation by microbes? What is the nature of these substances and which factors determine the synthesis of specific products?
Answer:

  1. During fermentation of substrates, various useful products like alcoholic beverages, organic acids, vitamins, growth hormones, enzymes, antibiotics and other molecules of medical significance are produced.
  2. They are secondary metabolites produced during idio phase and are not required for their growth.
  3. A specific secondary metabolite is produced depending on the type of microorganism and the type of substrate.

Question 22.
Can antibiotics kill viruses?
Answer:

  1. Antibiotics work by targeting cell wall or other metabolic pathways in bacteria.
  2. But viruses do not have cell walls and they do not carry out any metabolic reaction when outside the host.
  3. Hence, antibiotics cannot kill viruses.

Question 23.
What are gibberellins? Give the applications of gibberellins.
Answer:
Gibberellins are growth hormones produced by higher plants and fungi.

Applications of gibberellins are as follows:

  1. Gibberellins induce parthenocarpy in fruits like pear and apple.
  2. Gibberellins promote growth by stem elongation.
  3. They break the dormancy of seeds.
  4. They induce flowering in long day plants in short day conditions.
  5. They are used to enlarge the size of grapes.

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 24.
What is sewage? Describe its composition.
Answer:

  1. Sewage is the waste matter carried off on drainage.
  2. Composition of sewage varies depending upon its industrial source, e.g. textile, chemicals, pharmaceuticals, dairy, canning, brewing, meat packing, tannery, oil refineries and meat industries, etc.
  3. Sewage consists of human excreta, animal dung, household waste, slaughter house waste, dissolved organic matter, algae, nematodes, pathogenic bacteria, viruses and protozoa, discharged waste water from hospitals, industries (contains toxic dissolved organic and inorganic chemicals), tannery and pharmaceutical waste, etc.
  4. Bacteria in sewage include coliforms, fecal Streptococci, anaerobic spore forming bacilli and other bacteria found in human intestinal tract.
  5. Sewage consists of about water (99.5% to 99.9%) and inorganic and organic matter (0.1 to 0.5%) in suspended and soluble form.

Question 25.
State whether BOD will be high or low
(a) in water after primary treatment
(b) in water after secondary treatment.
Answer:
(a) After primary treatment, the primary effluent present in the primary sedimentation tank, still contains large amount of dissolved organic matter. Hence, the BOD is high.

(b) Secondary treatment is a biological treatment. Primary effluent is passed into aeration tank, where aerobic bacteria and fungi form flocks and consume the major part of organic matter in the effluents. Hence, the BOD is reduced.

Question 26.
Enlist the advantages of biogas.
Answer:
Advantages of biogas are as follows:

  1. Biogas is a cheap, safe, non-conventional and renewable source of energy.
  2. It can be easily generated, stored and transported.
  3. Biogas burns with a blue flame without producing smoke.
  4. Biogas is of great help in improving ‘ the sanitation of the surrounding.
  5. Biogas is an eco-friendly gas. It does not cause pollution and imbalance of the environment.
  6. Leftover sludge can be used as fertilizer.
  7. It is used as domestic and industrial fuel. Biogas can be used for domestic lighting, street lighting, cooking, small scale industries, etc.

Question 27.
Explain how Bacillus thuringiensis acts as a bio-control agent.
Answer:

  1. Bacillus thuringiensis (Bt) is an effective biocontrol agent against butterfly, caterpillars.
  2. Dried spores of Bacillus thuringiensis are mixed with water and sprayed onto vulnerable plants such as Brassicas and fruit trees.
  3. When insect larvae eat the leaves, they get killed by the toxin (cry protein) released in their gut by bacteria.

Question 28.
Explain how Trichoderma acts as a bio-control agent.
Answer:

  1. Trichoderma is an effective biocontrol agent against soil borne fungal plant pathogens.
  2. It is a free-living fungus found in the root ecosystem (rhizosphere).
  3. It produces substances like viridin, gliotoxin, gliovirin, etc. that inhibit the soil borne pathogens which infect root and rhizomes to cause rot disease.

Question 29.
What are bioherbicides? Give any two examples.
Answer:

  1. Bacteria, fungi and insects which kill the dicot herbs which acts as weeds in the fields of monocot cereal crops, are known as bioherbicides.
  2. Pseudomonas spp. and Xanthomonas spp. kill several weeds.
  3. Fungus Alternaria crassa controls water hyacinth.

Question 30.
What is composting? Which microorganisms are found in active compost?
Answer:

  1. Composting is a natural process in which organic matter is converted into a dark rich compost or humus.
  2. During composting, microorganisms break down organic matter into compost.
  3. Microorganisms found in active compost are bacteria, fungi, actinobacteria, protozoa and rotifers.

Question 31.
What are cyanobacteria? Give any two examples cyanobacteria as biofertilizers.
Answer:

  1. Cyanobacteria are aerobic, photosynthetic, N2 fixing microorganisms.
  2. They are aquatic or terrestrial.
  3. They may be free-living or symbiotic.
  4. They may be heterocystous or non- heterocystous. Heterocyst is the site of nitrogen fixation.
  5. e.g. Free living cyanobacteria are Anabaena, Nostoc, Tolypothrix, Plectonema, Oscillatoria.
  6. Anabaena and Nostoc have symbiotic relationship with lichens.
  7. Anabaena is also symbiotically associated with Azolla and Cycas.

Chart based or table based questions

Question 1.
Complete the table given below.

Crop Variety Resistant to disease
Wheat ————– Leaf and stripe rust, Hill bunt
————- Pusa swarnim White rust
Cauliflower ————– Black rot and Curl blight black rot
Chilli Pusa sadabahar —————

Answer:

Crop Variety Resistant to disease
Wheat Himgiri Leaf and stripe rust, Hill bunt
Brassica Pusa swarnim White rust
Cauliflower Pusashubhra Black rot and Curl blight black rot
Chilli Pusa sadabahar Chilli mosaic virus, Tobacco mosaic virus, leaf curl

Question 2.
Complete the table given below.

Crop Variety Insect pest
Brassica Pusa Gaurav ————-
————- Pusa sem 2 m Pusa sem 3 Jassids, aphids, fruit borer
Okra ————– Shoot and fruit borer

Answer:

Crop Variety Insect pest
Brassica Pusa Gaurav Aphids
Flat bean Pusa sem 2 m Pusa sem 3 Jassids, aphids, fruit borer
Okra Pusa Sawani, Pusa A-4 Shoot and fruit borer

Diagram based questions

Question 1.
a. Identify A and B in the following diagram.
b. What is organogenesis?
c. What is meant by hardening?
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 1
a. A : Explant, B : Callus

b. When auxins are provided to callus in more quantity compared to cytokinins, it gives rise to roots (rhizogenesis) and when cytokinins are provided in more quantity, there is development of shoot (caulogenesis). This induction of organ formation in callus by providing growth hormones in proper proportion is known as organogenesis.

c. Plantlets produced in tissue culture laboratory are transferred to polythene bags containing sterilized soil and are kept on low light and high humidity conditions for suitable period of time. This is known as hardening.

Question 2.
a. Identify honey bees A, B and C in the given diagram.
b. They belong to which species?
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 2
a. A : Worker honey bee, B : Queen honey bee, C : Drone of honey bee
b. They belong to species Apis mellifera.

Question 3.
Identify A, B, C and D in the given diagram.
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 3
Answer:
A : Honey super
B : Queen excluder
C : Hive bodies
D : Entrance reducer

Question 4.
Identify fish A, B, C and D in the given diagram.
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 4
Answer:
A : Rohu fish,
B : Mrigal fish,
C : Grass carp and
D : Silver carp

Question 5.
a. Identify A, B and C in the given diagram.
b. The given diagram represent life cycle of _____
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 5
a. A : Mature caterpillar, B : Cocoon and C : Adult female
b. Silk moth (Bombyx mori)

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 6.
a. Identify stages A and B in the given diagram.
b. Larvae are also called …………..
c. The diagram represent life cycle of ……………
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 6
Answer:
a. A : Hatching, B : Pupa
b. Crawlers
c. Lac insect

Question 7.
Draw a labelled diagram of Tubular tower fermenter.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 7

Question 8.
Draw a labelled diagram of biogas plant.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 8

Question 9.
a. Identify A in the given diagram.
b. Name the bacteria which form ‘A’ in roots of leguminous plants.
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 9
Answer:
a. A : Root nodules
b. Rhizobia form root nodules in leguminous plants.

Question 10.
Draw a labelled diagram of T.S. of root nodule.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 10

Question 11.
Identify and describe the plant in the given diagram.
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 11
Answer:
The plant in the given diagram is Azolla.
Azolla is an aquatic fern that has symbiotic association with nitrogen fixing cyanobacterium Anabaena.
It propagates vegetatively and spreads in rice fields very rapidly.
It has a floating rhizome with small overlapping bilobed leaves and roots.
Azolla provides habitat to Anabaena.
The leaf shows dorsal and ventral lobe.
7. Anabaena filaments are present in the aerenchyma of dorsal lobe.

Question 12.
a. Identify A, B and C in the given diagram.
b. Name the plant which has symbiotic relationship with ‘A’.
Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production 12
Answer:
a. A : Anabaena, B : Photosynthetic zone. C : Dorsal lobe.
b. Azolla m

Long Answer Questions

Question 1.
Explain concept of outbreeding and its types.
Answer:
(1) Outbreeding involves breeding of two unrelated animals.
(2) It is of three types, viz. outcrossing, cross-breeding and interspecific hybridization.

(3) Outcrossing:

  • Outcrossing involves mating of animals of same breed, which do not have a common ancestors on either side of mating partners up to 4 to 6 generations.
  • The progeny obtained from such mating is called an outcross.
  • Outcrossing is done to overcome inbreeding depression.

(4) Crossbreeding:

  • In crossbreeding superior males of one breed are mated with superior females of another breed.
  • New animal breeds of desirable characters are developed by this method.
  • Example : Hisardale breed of sheep is developed in Punjab by crossing Bikaneri ewes and Marino rams.

(5) Interspecific hybridization:

  • It involves breeding of animals of two different but related species.
  • It is used to produce animals with desirable characters from both the parents.
  • e.g. Mule is a breed obtained from horse and donkey.
  • It may not be always successful.

Question 2.
Which dairy products are prepared using microorganisms? How?
Answer:

  1. Dairy products prepared using microorganisms are curds, yogurt, butter milk and cheese.
  2. The starter or inoculum used in preparation of dairy products contains millions of lactic acid bacteria (LAB).
  3. Curd is prepared by inoculating milk with Lactobacillus acidophilus. It ferments lactose sugar of milk into lactic acid. Lactic acid causes coagulation and partial digestion of milk protein casein. Thus, milk is changed into curd. It also checks growth of disease causing microbes.
  4. Yogurt is produced by curdling milk with the help of Streptococcus thermophilus and Lactobacillus bulgaricus.
  5. Buttermilk is the acidulated liquid left after churning of butter from curd, is called buttermilk.
  6. During the preparation of cheese, the milk is coagulated with LAB. The curd formed is filtered and whey is separated. The solid mass is then ripened with growth of mould that develops flavour in it. Characteristic texture, flavour and taste of cheese are developed by different specific microbes.

The ‘Roquefort cheese is ripened by blue green mold Penicillium roquejortii. Camembert cheese is ripened by blue-green mold P. camembertii. The large holes in Swiss cheese are developed due to production of a large amount of CO2 by a bacterium known as Propionibacterium shermanii.

Maharashtra Board Class 12 Biology Important Questions Chapter 11 Enhancement of Food Production

Question 3.
What are biofertilizers? Explain what are the different types of biofertilizers with suitable examples.
Answer:

  1. Biofertilizers are commercial ready to use live bacterial, cyanobacterial or fungal formulations.
  2. When they are applied to plants, in soil or in composting pits, soil fertility increases. Biofertilizers are cost effective and eco-friendly.

Types of biofertilizers as follows:
1. Bacterial biofertilizers:

  • Nitrogen fixing bacterial biofertilizers : They convert atmospheric nitrogen into compounds of nitrogen like ammonia, nitrites and nitrates. The nitrogen fixing bacteria Rhizobium forms symbiotic association with roots of leguminous plants. Free living nitrogen fixing bacteria are Azotobacter and Azospirillum.
  • Phosphate solubilizing biofertilizers : They are the bacteria which solubilize the insoluble inorganic phosphate compound, e. g. Pseudomonas striata, Bacillus polymyxa, Agrobacterium, Microccocus, Aspergillus spp., etc.
  • Bacteria are also involved in composting.

2. Cyanobacterial biofertilizers:

  • They are nitrogen fixing biofertilizers.
  • Heterocysts are the site of nitrogen fixation.
  • Free living cyanobacteria are Anabaena, Nostoc, Tolypothrix, Plectonema, Oscillatoria.
  • Anabaena and Nostoc have symbiotic relationship with lichens
  • Anabaena is also symbiotically associated with Azolla and Cycas.

3. Fungal biofertilizers:

  • Fungal biofertilizers are mycorrhizae which form symbiotic association with roots of higher plants. There may be ectomycorrhiza and endomycorrhiza (VAM).
  • Ectomycorrhizae increase the absorptive surface area of rots and increase uptake of water and nutrients.
  • Plants with endomycorrhizae grow well even in less irrigated lands.

4. Microbes involved in composting:
During composting, microorganisms break down organic matter into compost. E.g. bacteria, fungi, actinobacteria, protozoa and rotifers.

Question 4.
Describe in details different types of mycorrhizae.
Answer:
Mycorrhizae are fungi that form symbiotic association with the roots of higher plants in humid forests.
There are two types as follows:
(1) Ectomycorrhizae:

  • Mycelium of these fungi form mantle on the surface of the roots.
  • Due to this absorptive surface area of roots increases and uptake of water and nutrients (N, P Ca and K) improves.
  • The plant vigour, growth and yield increase.
  • Some hyphae may penetrate into the root and form hartig-net in ‘the intercellular spaces of root cortex.

(2) Endomycorrhizae:

  • Fugal hypahe of endomycorrhizae penetrate the root cortex and form branched arbuscules intracellularly. They also form vesicles mostly in the intercellular spaces.
  • Hence, they are called Vesiculo Arbuscular Mycorrhizae (VAM). Nowadays they are described as AM fungi.
  • The plants associated with VAM grow luxuriantly in less irrigated lands.
  • VAM increase the productivity of field.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Balbharti Maharashtra State Board 11th Physics Important Questions Chapter 7 Thermal Properties of Matter Important Questions and Answers.

Maharashtra State Board 11th Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 1.
State various units of heat and relate them to SI unit of heat.
Answer:

  1. CGS unit of heat: erg and it is related to SI unit as, 1 J = 107 erg
  2. Thermodynamic unit of heat: calorie (cal) and it is related as 1 cal = 4.184 J

Question 2.
What is thermal equilibrium?
Answer:

  1. When two bodies at different temperatures come into the contact with each other, they exchange heat.
  2. After some time, temperature of two bodies become equal and heat transfer between them stops.
  3. The two bodies are then said to be in thermal equilibrium with each other.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 3.
State true of false. Correct the statement and rewrite if false.
i. Heat transfer takes place between the body and the surrounding medium until the body and the surrounding medium are at the same temperature.
ii. Whenever two bodies are in contact, there is a transfer of heat.
Answer:

  1. True.
  2. False.

Whenever two bodies at different temperature are in contact, there is a transfer of heat.

Question 4.
Give reason: Temperature is said to be a measure of average kinetic energy of the atoms/molecules of the body.
Answer:

  1. Matter consists of particles which are in continuous vibrational motion and thereby possess kinetic energy.
  2. When external energy is provided to these particles, internal energy of particles increases.
  3. This increase in internal energy is in the form of increased kinetic energy of atoms/molecules and raises temperature of body (except at melting or boiling point of the body).
  4. Greater the kinetic energy, faster the atoms/ molecules move and temperature of body becomes higher.
  5. Thus, temperature of body is directly proportional to its kinetic energy.
    Hence, temperature is said to be a measure of average kinetic energy of the atoms and molecules of the body.

Question 5.
Why do solid particles possess potential energy?
Answer:
The solid particles possess potential energy due to the interatomic forces that hold the particles together at some mean fixed positions.

Question 6.
What happens when heat is supplied to a solid at its melting point?
Answer:

  1. When heat is supplied to a solid at its melting point, average kinetic energy of constituent particles does not change.
  2. As a result, temperature of body remains constant.
  3. Supplied energy is used to weaken the bonds between constituent particles.
  4. While order of magnitude of average distance between the molecules remains almost same as solid, substance melts, i.e., changes into liquid state, at melting point.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 7.
Why do solids have definite shape and volume?
Answer:
The solid particles possess potential energy due to the interatomic forces that hold the particles together at some mean fixed positions.
Hence, solids have definite shape and volume.

Question 8.
Why is density of liquid at melting point nearly same as density of solids at melting point?
Answer:

  1. During change of state from solid to liquid, mass of substance does not change.
  2. Also, mean distance between particles during change of state does not alter at melting point.
  3. Density depends upon mass and volume, in turn, on mean distance between particles.
    Hence, density of liquid at melting point is nearly same as density of solids at melting point.

Question 9.
State true or false. If false correct the statement and rewrite.
Due to weakened interatomic bonds liquid do not possess definite volume but have definite shape.
Answer:
False.
Due to weakened bonds liquids do not possess definite shape but have definite volume.

Question 10.
What happens when heat is supplied to liquid its freezing point (melting point)?
Answer:

  1. On heating, the atoms/molecules in liquid gain kinetic energy and temperature of the liquid increases.
  2. If liquid is continued to heat further, at the boiling point, the constituents overcome the interatomic/molecular forces.
  3. The mean distance between the constituents increases so that the particles are farther apart.
  4. At boiling point, the liquid gets converted into gaseous state.

Question 11.
Why, according to kinetic theory of gases, gases have neither definite volume nor shape?
Answer:
As per kinetic theory of gases, for an ideal gas, there are no forces between the molecules of a gas. Hence, gases neither have a definite volume nor shape.

Question 12.
Match the pairs.
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 1
Answer:
i – b,
ii – c,
iii – a

Question 13.
Distinguish between an adiabatic wall and diathermic wall.
Answer:

Adiabatic wall

Diathermic wall

i. An ideal wall or partition separating two systems such that no heat exchange can take place between the systems is called adiabatic wall. A wall that allows exchange of heat energy between two systems is said to be diathermic wall.
ii. It is a perfect thermal insulator. It is not a perfect thermal insulator.
iii. It does not exist in reality. Partition like thin sheet of copper acts as diathermic wall.
iv. It is generally represented as thick cross-shaded (slanting lines region). It is represented as a thin dark region.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 14.
State and explain zeroth law of thermodynamics.
Answer:
Statement: If two bodies A and B are in thermal equilibrium and also A and C are in thermal equilibrium then B and C are also in thermal equilibrium.
Explanation:

  1. Consider two sections of a container separated by an adiabatic wall containing two different gases as system A and system B.
  2. Systems A and B are independently brought in thermal equilibrium with a system C.
  3. When the adiabatic wall separating systems A and B is removed, there will be no transfer of heat from system A to system B or vice versa.
  4. This indicates that systems A and B are also in thermal equilibrium.
  5. This means, if systems A and B are separately in thermal equilibrium with a system C, then A and B are also mutually in thermal equilibrium.

Question 15.
What is thermometry? What is thermometer?
Answer:
Thermometry is the science of temperature and its measurement. The device used to measure temperature is a thermometer.

Question 16.
State the principle used to measure the temperature of a system using a thermometer.
Answer:
When two or more systems/bodies are in thermal equilibrium, their temperatures are same. This principle is used to measure the temperature of a system by using a thermometer.

Question 17.
Explain how thermal equilibrium is attained between thermometer and the patient holding thermometer, in mouth.
Answer:

  1. Thermometer indicating lower temperature is held in mouth by patient.
  2. As body of patient is at higher temperature, heat energy is transferred from patient to thermometer.
  3. When temperature of thermometer becomes same as temperature of patient, heat exchange stops and thermal equilibrium is attained between thermometer and body of patient.

Question 18.
Define the following terms.
i) Ice point
ii) Steam point
Answer:

  1. Ice point: The temperature at which pure water freezes at one standard atmospheric pressure is called as ice point or freezing point.
  2. Steam point: The temperature at which pure water boils into steam or steam changes to liquid water at one standard atmospheric pressure is called as steam point or boiling point.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 19.
Explain Celsius and fahrenheit scale of temperature. Give relation between the two scales with the help of the graph.
Answer:

  1. Celsius scale:
    • The ice point (melting point of pure ice) is marked as 0 °C (lower point) and steam point (boiling point of water) is marked as 100 °C (higher point).
    • Both are taken at one atmospheric pressure.
    • The interval between these points is divided into loo equal pans. Each of these parts is called as one degree celsius and it is written as 1 oc.
  2. Fahrenheit scale:
    • The ice point (melting point of pure ice) is marked as 32 °F and steam point (boiling point of water) is marked as 212 °F.
    • The interval between these two reference points is divided into 180 equal parts. Each part is called as degree fahrenheit and is written as 1 °F.
  3. Relation between fahrenheit temperature and celsius temperature:
    \frac{\mathrm{T}_{\mathrm{F}}-32}{180} = \frac{T_{C}-0}{100}
    Where, TF = temperature in fahrenheit scales.
    TC = temperature in celsius scale.
    The graph of TF versus TC is as shown
    Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 2

Question 20.
What is thermometer? Explain with examples, the thermometric property used in a thermometer.
Answer:

  1. An instrument designed to measure temperature is called as thermometer.
  2. Any property of a substance which changes sufficiently with temperature can be used as a basis of constructing a thermometer and is known as the thermometric property.
  3. There are different types of thermometers.
    • In a constant volume gas thermometer, the pressure of a fixed volume of gas (measured by the difference in height) is used as the thermometric property.
    • The liquid-in-glass thermometer depends on the change in volume of the liquid with temperature. Small change in temperature changes the volume of liquid considerably. Two such liquids are mercury and alcohol. Mercury thermometers are used for measurement of temperature range -39 °C to 357 °C while alcohol thermometers are used only to measure temperatures near ice point (melting point of pure ice).
    • The resistance thermometer uses the change of electrical resistance of a metal wire with temperature.
    • Normally in research laboratories, a thermocouple is used to measure the temperature. A thermocouple is a junction of two different metals or alloys eg.: copper and iron joined together.
    • When two such junctions at the two ends of two dissimilar metal rods are kept at two different temperatures, an electromotive force is generated that can be calibrated to measure the temperature.
  4. Thermometers are calibrated so that a numerical value may be assigned to a given temperature. The standard fixed points are melting point of ice and boiling point of water.

Question 21.
State characteristics of thermometer.
Answer:

  1. Thermometer must be sensitive, i.e., a noticeable change in the thermometric property should be observed for a very small change in temperature.
  2. It has to be accurate.
  3. It should be easily reproducible.
  4. It is important that the system attains thermal equilibrium with the thermometer quickly.

Question 22.
Explain relation between unknown temperature T and thermodynamic property PT at temperature T.
Answer:
If the values of a thermometric property are P1 and P2 at the ice point (0 °C) and steam point (100 °C) respectively and the value of this property is PT at unknown temperature T, then T is given by the following equation.
T = \frac{100\left(P_{T}-P_{1}\right)}{P_{2}-P_{1}}

Question 23.
State true or false. If false correct the statement and rewrite.
Ideally, there should be no difference in temperatures recorded on two different thermometers.
Answer:
True.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 24.
List an advantage and a disadvantage of constant volume gas thermometer.
Answer:
Advantage: There is no difference in temperatures recorded on two different constant volume gas thermometers. Hence, it is very accurate.
Disadvantage: Constant volume gas thermometer is bulky instrument. Hence, it is not easily portable.

Question 25.
Give short note on liquid-in-glass thermometer.
Answer:

  1. Liquid-in-glass thermometer depends on the change in volume of the liquid with temperature.
  2. When the bulb is heated, the liquid in a glass bulb expands upward in a capillary tube.
  3. The liquid is such that it is easily seen and expands (or contracts) rapidly and by a large amount over a wide range of temperature.
  4. Most commonly used liquids are mercury and alcohol as they remain in liquid state over a wide range. Mercury freezes at -39 °C and boils at 357 °C; alcohol freezes at -115 °C and boils at 78 °C.

Question 26.
What are thermochromic liquids? Give two examples.
Answer:

  1. Thermochromic liquids are ones which change colour with temperature.
  2. These liquids are very sensitive to temperature, especially in range of room temperature.
  3. Hence, only specific liquids display distinct colour variations at normal temperature.
    Examples: Titanium dioxide and zinc oxide are white at room temperature but when heated change to yellow.

Question 27.
Write a note on resistance thermometer.
Answer:

  1. Resistance thermometer uses the change of electrical resistance of a metal wire with temperature.
  2. It measures temperature accurately in the range -2000 °C to 1200 °C is best for steady temperatures.
  3. It is bulky and hence not easily portable.

Solved Examples

Question 28.
If the temperature in the room is 29 °C, what is its temperature in degree fahrenheit?
Solution:
Given: TC = 29 °C
To find: Temperature in degree fahrenheit (TF)
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 3
Answer:
Temperature in the room in degree fahrenheit is 84.2 °F.

Question 29.
Average room temperature on a normal day is 27 °C. What is the room temperature in °F?
Solution:
TC = 27 °C
Room temperature in °F
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 4
Answer:
Room temperature in °F is 80.6 °F.

Question 30.
Normal human body temperature in fahrenheit is 98.4 °F. What is the body temperature in °C?
Solution:
TF = 98.4 °F
Formula: Body temperature in °C (TC)
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 5
Body temperature in °C is 36.89 °C.

Question 31.
The length of a mercury column in a mercury-in-glass thermometer is 25 mm at the ice point and 180 mm at the steam point. What is the temperature when the length is 60 mm?
Solution:
Here the thermometric property P is the length of the mercury column.
Using equation,
T = \frac{100\left(\mathrm{P}_{\mathrm{T}}-\mathrm{P}_{1}\right)}{\left(\mathrm{P}_{2}-\mathrm{P}_{1}\right)}
For P1 = 25 mm,
P2 = 180 mm,
PT = 60 mm
T = \frac{100(60-25)}{(180-25)}
= 22.58 °C
The temperature corresponding to the length of 60 mm is 22.58 °C.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 32.
A resistance thermometer has resistance 95.2 Ω at the ice point and 138.6 Ω at the steam point. What resistance would be obtained if the actual temperature is 27 °C?
Solution:
Here the thermometric property P is the resistance. If R is the resistance at 27 °C,
Using equation,
T = \frac{100\left(\mathrm{P}_{\mathrm{T}}-\mathrm{P}_{1}\right)}{\left(\mathrm{P}_{\mathrm{T}}-\mathrm{P}_{1}\right)}
For T = 27 °C, P1 = 95.2 Ω, P2 = 138.6 Ω .
∴ 27 = \frac{100(\mathrm{R}-95.2)}{(138.6-95.2)}
∴ R = \frac{27 \times(138.6-95.2)}{100} + 95.2
= 11.72 + 95.2
= 106.92Ω
The resistance obtained would be 106.92 Ω.

Question 33.
Explain the need for thermodynamic (absolute) scale.
Answer:

  1. The two fixed point scale, Celsius scale and Fahrenheit scale had a practical shortcoming for calibrating the scale.
  2. It was difficult to precisely control the pressure and identify the fixed points, especially for the boiling point as the boiling temperature is very sensitive to changes in pressure.
  3. Hence, a one fixed point scale was adopted to define a temperature scale.
  4. This scale is called the absolute scale or thermodynamic scale.

Question 34.
What is triple point of water? State its physical significance.
Answer:

  1. The triple point of water is that point where water in a solid, liquid and gas state co-exists in equilibrium and this occurs only at a unique temperature and a pressure.
  2. To know the triple point, one has to see that three phases coexist in equilibrium and no one phase in dominating. This occurs for each substance at a single unique combination of temperature and pressure.
  3. Thus, if three phases of water solid ice, liquid water and water vapour coexist, the pressure and temperature are automatically fixed.
  4. Internationally, triple point of water has been assigned as 273.16 K at pressure equal to 6.11 × 102 Pa or 6.11 × 10-3 atmosphere, as the standard fixed point for calibration of thermometers.
  5. The physical significance of triple point of water is that, it represents unique condition and it is used to define the absolute temperature.

Question 35.
Write a short note on absolute scale of temperature.
Answer:

  1. The absolute scale of temperature, is so termed since ills based on the properties of an ideal gas and does not depend on the property of any particular substance.
  2. The zero of this scale is ideally the lowest temperature possible although it has not been achieved in practice.
  3. It is termed as Kelvin scale after Lord Kelvin with its zero at -273.15 °C and temperature intervals same as that on the Celsius scale. It is written as K (without °).

Question 36.
Draw a neat and well labelled diagram to show comparison of kelvin, Celsius and fahrenheit temperature scales.
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 6

Question 37.
Answer the following:
i) The triple-point of water is a standard fixed point in modern thermometry. Why? What is wrong in taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale)?
ii) The absolute temperature (Kelvin scale) T is related to temperature tc on the Celsius scale by tc = T – 273.15. Why do we have 273.15 in this relation and not 273.16?
Answer:
i) The triple point of water has been assigned a fixed value of 273.15 K. This number represents a unique value associated with a unique condition of temperature and pressure in which all the three phases of water co-exist. On the other hand, melting point of ice and boiling point of water do not have a unique set of values as they are subject to changes in pressure and volume. For this reason, triple point of water is a standard fixed point in modem thermometry.

ii) On Celsius scale, the melting point of ice at normal pressure has a value 0 °C. The value corresponding to this value on the absolute scale is 273.15 K. The value 273.16 K denotes the triple point of water which has a value,
273.16 – 273.15 = 0.01 °C on Celsius scale as per the given relation.

Question 38.
State Charles’ law and give its formula.
Answer:
Charles’ law:
At constant pressure, volume of a fixed mass of gas is directly proportional to its absolute temperature.
Mathematically,
V ∝ T … ( at constant pressure)
∴ V = kT
where k is constant of proportionality
\frac{\mathrm{V}}{\mathrm{T}} = k = constant
For two gases, \frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}} = constant.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 39.
State Pressure law and give its formula.
Answer:
Pressure (Gay Lussac’s) law:
At constant volume, pressure of a fixed mass of gas is directly proportional to its absolute temperature.
Mathematically,
P ∝ T .. .(at constant volume)
∴ P = kT
Where, k is constant of proportionality P
\frac{\mathrm{P}}{\mathrm{T}} = k = constant
For two gases, \frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}} = constant

Question 40.
State Boyle’s law and give its formula.
Answer:
Boyle’s law:
At constant temperature, the volume of a fixed mass of a gas is inversely proportional to its pressure.
Mathematically,
V ∝ \frac{1}{\mathrm{P}}.. ..(at constant temperature)
V = k × \frac{1}{\mathrm{P}}
where, k is constant of proportionality.
PV = k = constant For two gases,
P1V1 = P2V2 = constant

Question 41.
Derive ideal gas equation PV = nRT.
Answer:

  1. The relation between three variables of a gas i.e., pressure, volume and absolute temperature is called as ideal gas equation.
    From Boyle’s law,
    V ∝ \frac{\mathrm{T}}{\mathrm{P}}, at constant temperature ….(1)
    From Charles’ law,
    V ∝ T, at constant pressure … .(2)
  2. Combining equations (1) and (2) we get,
    ∴ V ∝ \frac{\mathrm{T}}{\mathrm{P}}
    \frac{\mathrm{PV}}{\mathrm{T}}= constant
  3. For one mole of a gas,
    \frac{\mathrm{PV}}{\mathrm{T}} = R or PV = RT … (3)
    where R is the constant of proportionality.
  4. Equation (3) is called ideal gas equation. The value of constant R is same for all gases. Therefore, R is called as universal gas constant. R = 8.31 JK-1mol-1.
  5. For ‘n’ moles of gas, i.e. if the gas contains ‘n’ moles, equation (3) can be written as,
    PV = nRT

Solved Examples

Question 42.
Express T = 24.57 K in Celsius and fahrenheit.
Solution:
Given: TK = 24.57 K
To find: Temperature in Celsius (TC),
Temperature in fahrenheit (TF)
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 7
Calculation:
From formula,
∴ TC = TK – 273.15
= 24.57 – 273.15
= -248.58 °C
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 8
Temperature in celsius (TC) is – 248.58 °C
Temperature in fahrenheit (TF) is -415.44 °F

Question 43.
Calculate the temperature which has the same value on fahrenheit scale and kelvin scale.
Solution:
Given: TK = TF = x
To find: Temperature at which Kelvin and Fahrenheit scales coincide (x)
Formula: \frac{\mathrm{T}_{\mathrm{F}}-32}{180} = \frac{\mathrm{T}_{\mathrm{K}}-273.15}{100}
Calculation: From formula.
\frac{x-32}{180} = \frac{x-273.15}{100}
∴ 5(x – 32) = 9(x – 273.15)
∴ 5x – 160 = 9x – 2458.35
∴ 4x = 2298.35
∴ x = \frac{2298.35}{4} = 574.6
∴ x = 574.6 °F
The temperature at which kelvin and fahrenheit scales coincide is 574.6 °F.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 44.
The triple points of neon and carbon dioxide are 24.57 K and 216.55 K, respectively. Express these temperatures on
the celsius and fahrenheit scales. (NCERT)
Solution:
Given: For neon, TK = 24.57 K
For carbon dioxide, TK = 216.55 K
To find:
i) Triple point of neon on celsius (TCN) and fahrenheit scale (TFN)
ii) Triple point of carbon dioxide on Celsius (TCC) and fahrenheit scale (TFC)

Formulae:
i) TK – 273.15 = TC
ii) \frac{\mathrm{T}_{\mathrm{K}}-273.15}{100} = \frac{\mathrm{T}_{\mathrm{c}}-32}{180}
Calculation: From formula (i),
TC = TK – 273.15
For neon, TCN = 24.57 – 273.15
∴ TCN = -248.58 °c
For carbon dioxide.
TCC = 216.55 – 273.15
∴ TCC = -56.60 °c
From formula (ii),
TF = \frac{9}{5}(Tk – 273.15) + 32
For neon, Tk = 24.57 K
∴ TFN = \frac{9}{5}[24.57 – 273.15] + 32
∴ TFN = -415.44 °F
For CO2, TK = 216.55 K
∴ TFC = \frac{9}{5}(216.55 – 273.15) + 32
∴ TFC = -69.88 °F
i) Triple point of neon on celsius scale is -248.58 °c and on a fahrenheit scale is -415.44 °F.
ii) Triple point of carbon-dioxide on celsius scale is -56.60 °C and on fahrenheit scale is -69.88 °F.

Question 45.
Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between TA and TB?
Solution:
Triple point of water is, T = 273.16 K
Since the absolute scales measure the triple point as 200 A and 350 B.
∴ 200A = 350B = 273.16 K
∴ 1A = \frac{273.16}{200}K and 1B = \frac{273.16}{350}K
If TA and TB are the temperatures on the two scales, then
\frac{273.16}{200}TA = \frac{273.16}{350}TB
∴ TA = \frac{200}{350} TB = \frac{4}{7}TB
\frac{\mathbf{T}_{\mathbf{A}}}{\mathbf{T}_{\mathbf{B}}} = \frac{4}{7}
The relation between TA and TB is TA : TB = 4 : 7

Question 46.
The pressure reading in a thermometer at steam point is 1.367 × 103 Pa. What is pressure reading at triple point knowing the linear relationship between temperature and pressure?
Solution:
Given: P = 1.367 × 103 Pa at steam point (T) i.e., at 273.15 + 100 = 373.15 K.
Linear relationship between temperature and pressure means that.
P ∝ T ⇒ P1T1 = P2T2
To find: Pressure reading (Ptriple)
Formula: Ptriple = 273.16 × \left(\frac{\mathrm{P}}{\mathrm{T}}\right)
where Ptriple and P are the pressures at temperature of triple point (273.16 K) and T (375.15 K) respectively.
Calculation: From formula,
∴ Ptriple = 273.16 × \left(\frac{1.367 \times 10^{3}}{373.15}\right)
= 1000 × 103 Pa
Pressure reading is 1.000 × 103 Pa.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 47.
When the pressure of 0.75 litre of a gas at 27 °C is doubled, its temperature rises to 111°C. Calculate the final volume of a gas.
Solution:
Given: V1 = 0.75 litre = 750 cm3,
T1 = 27 + 273.15 = 300.15 K,
T2 = 111 + 273.15 = 384.15 K,
P2 = 2P1
To find: Final volume (V2)
Formula: \frac{\mathrm{P}_{1} \mathrm{~V}_{1}}{\mathrm{~T}_{1}} = \frac{\mathrm{P}_{2} \mathrm{~V}_{2}}{\mathrm{~T}_{2}}
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 9
∴ V2 = 480 cm3
The final volume of the gas is 480 cm3.

Question 48.
A certain mass of a gas at 20 °C is heated until both its pressure and volume are doubled. Calculate the final temperature.
Solution:
T1 = 20 + 273.15 = 293.15 K,
P2 = 2P1, and V2 = 2V1
To find: Final temperature (T2)
Formula: \frac{\mathrm{P}_{1} \mathrm{~V}_{1}}{\mathrm{~T}_{1}} = \frac{\mathrm{P}_{2} \mathrm{~V}_{2}}{\mathrm{~T}_{2}}
Calculation: From formula,
\frac{\mathrm{P}_{1} \mathrm{~V}_{1}}{\mathrm{~T}_{1}} = \frac{\left(2 \mathrm{P}_{1}\right)\left(2 \mathrm{~V}_{1}\right)}{\mathrm{T}_{2}}
\frac{1}{\mathrm{~T}_{1}} = \frac{4}{\mathrm{~T}_{2}}
∴ T2 = 4 × 293.15 = 1172.6 K
= 1172.6 – 273.15 = 899.45 °C
∴ T2 = 1172.6 K or 899.45 °C
The final temperature of the gas is 1172.6 K or 899.45 °C.

Question 49.
Explain how substances expand on the basis of vibrational motion of atoms.
Answer:

  1. The atoms in a solid vibrate about their mean positions.
  2. When heated, they vibrate faster and force each other to move a little farther apart. This results into expansion.
  3. The molecules in a liquid or gas move with certain speed.
  4. When heated, they move faster and force each other to move a little farther apart. This results
    in expansion of liquids and gases on heating.
  5. The expansion is more in liquids than in solids; gases expand even more.

Question 50.
What is thermal expansion? List types of thermal expansion.
Answer:

  1. A change in the temperature of a body causes change in its dimensions.
  2. The increase in the dimensions of a body due to an increase in its temperature is called thermal expansion.
  3. There are three types of thermal expansion:
    • Linear expansion
    • Areal expansion
    • Volume expansion

Question 51.
Define linear expansion of solids.
Answer:
The expansion in length of a solid due to thermal energy is called linear expansion.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 52.
Define coefficient of linear expansion of solid. State its unit and dimensions.
Answer:

  1. The coefficient of linear expansion of a solid is defined as increase in the length per unit original length at 0 °C per degree rise in temperature.
    It is denoted by α and given by,
    α = \frac{l_{2}-l_{1}}{l_{1}\left(\mathrm{~T}_{2}-\mathrm{T}_{1}\right)}
    where l1 = initial length at temperature T1 °C
    l2 = final length at temperature T2 °C
  2. Unit: °C-1 or K-1
  3. Dimensions: [L0M0T0K-1]

Question 53.
Derive an expression for the coefficient of linear expansion in solid.
Answer:
i) If the substance is in the form of a long rod of length l, then for small change ∆T, in temperature, the fractional change ∆l/l, in length is directly proportional to ∆T.
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 10
[Note: Linear expansion ∆l is exaggerated for explanation.]
\frac{\Delta l}{l} ∝ ∆T
\frac{\Delta l}{l} = α∆T … (1)
where, α is called the coefficient of linear expansion of solid.

ii) Rearranging terms in equation (1),
α = \frac{\Delta l}{l \Delta \mathrm{T}}
= \frac{l_{\mathrm{T}}-l_{0}}{l_{0}\left(\mathrm{~T}-\mathrm{T}_{0}\right)}
where,
l0 = length of rod at 0 °C,
lT = length of rod when heated to T °C,
T0 = 0 °C (initial temperature)
T = final temperature,
∆l = lT – T0 = change in length,
∆T = T – T0 = rise in temperature.

iii) If l0 = 1 m and T – T0 = 1 °C, then α = lT – l0 (numerically).

iv) As magnitude of α varies negligibly with temperature, it is assumed to be constant for a particular material.
Hence, it is not essential to take initial temperature as 0 °C.
This modifies equation (2) into,
α = \frac{l_{2}-l_{1}}{l_{1}\left(\mathrm{~T}_{2}-\mathrm{T}_{1}\right)}
where l1 = initial length at temperature T1 °C
l2 = final length at temperature T2 °C

Question 54.
State true or false. If false correct the statement and rewrite.
i) Coefficient of linear expansion is same for all substances.
ii) Metals have high values for the coefficient of linear expansion, than non-metals.
Answer:

  1. False.
    Coefficient of linear expansion is different for different substances.
  2. True.

Question 55.
Define areal expansion of solids.
Answer:
The increase in the surface area of a solid, on heating is called areal expansion or superficial expansion of solids.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 56.
Define coefficient of superficial (areal) expansion of a solid, state its unit and dimensions.
Answer:

  1. Coefficient of superficial (areal) expansion of a solid is defined as the increase in area per unit original area at 0 °C per degree rise in temperature.
    It is denoted by β and given by,
    β = \frac{A_{2}-A_{1}}{A_{1}\left(T_{2}-T_{1}\right)}
    where, A1 = Area of solid sheet at T1 °C,
    A2 = Area of solid sheet at T2 °C
  2. Unit: 0°C-1 or K-1
  3. Dimensions: [L0M0T0K-1

Question 57.
Derive expression for coefficient of areal expansion.
Answer:
i) If a substance is in the form of a plate of area A, then for small change ∆T in temperature, the fractional change in area, ∆A/A in figure given below, is directly proportional to ∆T.
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 11
[Note: Areal expansion ∆A is exaggerated for explanation]
\frac{\Delta \mathrm{A}}{\mathrm{A}} ∝ ∆T
\frac{\Delta \mathrm{A}}{\mathrm{A}} = β∆T … (1)
where β is called the coefficient of areal expansion of solid.

ii) Rearranging terms in equation (1),
β = \frac{\Delta \mathrm{A}}{\mathrm{A} \Delta \mathrm{T}}
= \frac{A_{T}-A_{0}}{A_{0}\left(T-T_{0}\right)}
where,
A0 = volume at 0 °C,
AT = volume when heated to T °C,
T0 = 0 °C (initial temperature),
T = final temperature,
∆A = AT – A0 = change in area,
∆T = T – T0 = rise in temperature.
iii) If A0 = 1 m2, T – To = 1 °C, then β = AT – A0 (numerically).
iv. As, β does not vary significantly with temperature. Hence, if A1 is the area of a metal plate at T1 °C and A2 is the area at higher temperature at T2 °C, then
β = \frac{A_{2}-A_{1}}{A_{1}\left(T_{2}-T_{1}\right)}

Question 58.
Define volume expansion of solids.
Answer:
The increase in volume due to heating is called volume expansion or cubical expansion.

Question 59.
Define coefficient of cubical (volume) expansion of a solid. State its unit and dimensions.
Answer:
i) Coefficient of cubical (volume) expansion:
Coefficient of cubical (volume) expansion of a solid is defined as increase in volume per unit original volume at O °C per degree rise in temperature.
It is denoted by γ and is given by,
γ = \frac{V_{2}-V_{1}}{V_{1}\left(T_{2}-T_{1}\right)}
where,
V1 = Volume of solid at T1 °C,
V2 = Volume of solid at T2 °C
ii) Dimensions: [L0M0T0K-1]

[Note: Units and dimension of areal expansion in solid (β) and cubical expansion in solid (γ) are same as that of linear expansion in solid (α).

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 60.
Derive an expression for coefficient of cubical expansion.
Answer:
i) If the substance is in the form of a cube of volume V, then for small change ∆T in temperature, the fractional change, ∆/V in volume is directly proportional to ∆T.
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 12
[Note: Volume expansion ∆V is exaggerated for explanation.)
ii) γ = \frac{\Delta \mathrm{V}}{\mathrm{V} \Delta \mathrm{T}} = \frac{\mathrm{V}_{\mathrm{T}}-\mathrm{V}_{0}}{\mathrm{~V}_{0}\left(\mathrm{~T}-\mathrm{T}_{0}\right)}
where, V0 = volume at 0 °C,
VT = volume when heated to T °C,
T0 = 0 °C (initial temperature),
T = final temperature.
∆V = VT – V0 = change in volume,
γ = VT – T0 = rise in temperature.

iii) If V0 = 1 m3, T – T0 = 1 °C, then γ = VT – V0 (numerically).

iv) If V1 is the volume of a body at T1 °C and V2 is the volume at higher temperature T2 °C, then
γ1 = \frac{\mathrm{V}_{2}-\mathrm{V}_{1}}{\mathrm{~V}_{1}\left(\mathrm{~T}_{2}-\mathrm{T}_{1}\right)}
γ1, is the coefficient of volume expansion at temperature T1 °C.

Question 61.
How does coefficient of volume expansion depend upon temperature?
Answer:

  1. As compared to coefficient of linear expansion (α) and coefficient of areal expansion (β), γ changes more with temperature.
  2. It is constant only at high temperatures.

Question 62.
Do coefficient of areal expansion and coefficient of volume expansion depend upon nature of material?
Answer:
Yes, coefficient of areal expansion and coefficient of volume expansion depend upon nature of material.

Question 63.
Explain expansion in fluids.
Answer:

  1. Since fluids possess definite volume and take the shape of the container, they exhibit only change in volume significantly.
  2. Equations valid for cubical or volume expansion of fluids are:
    γ = \frac{\Delta V}{V \Delta T}=\frac{V_{T}-V_{0}}{V_{0}\left(T-T_{0}\right)}
    where, V0 = volume at 0 °C,
    VT = volume when heated to T °C,
    T0 = 0 °C (initial temperature),
    T = final temperature,
    ∆V = VT – V0 = change in volume,
    ∆T = T – T0 = rise in temperature.
    and γ1 = \frac{V_{2}-V_{1}}{V_{1}\left(T_{2}-T_{1}\right)}
    where, V1 is volume of body at T1 °C, V2 is volume of body at higher temperature T2 °C and γ1 is coefficient volume expansion at T1 °C.
  3. As fluids are kept in containers, while dealing with the volume expansion of fluids, expansion of the container also needs to be considered.
  4. If expansion of fluid results in a volume greater than the volume of the container, the fluid overflows if the container is open.
  5. If the container is closed, volume expansion of fluid causes additional pressure on the walls of the container.

Question 64.
Use the data given in the table below:

Materials γ(K-1)
Invar 2 × 10 -6
Steel (3.3 – 3.9) × 10-5
Aluminium 6.9 × 10“-5
Mercury 18.2 × 10-5
Water 20.7 × 10-5
Paraffin 58.8 × 10-5
Gasoline 95.0 × 10-5
Alcohol (ethyl) 110 × 10-5

What conclusions can be drawn using the data?
Answer:

  1. Coefficient of volume expansion (γ) is a characteristic of the substance.
  2. It (γ) has higher order of magnitude for liquids than that of solids.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 65.
Explain how behaviour of water is different than solids and liquids when heat is supplied.
Answer:

  1. Normally solids and liquids expand on heating. Hence their volume increases on heating.
  2. Since the mass is constant, it results in a decrease in the density on heating.
  3. Water expand on cooling from 4 °C to 0 °C.
  4. Hence its density decreases on cooling in this temperature range.

Question 66.
Derive relation between coefficient of linear expansion (α) and coefficient of areal expansion (β).
Answer:
Consider a square plate of side l0 at 0 °C and h at T °C.

  1. lT = lo (1 + αT) .
    If area of plate at 0 °C is Ao, Ao = l_{0}^{2}
    If area of plate at T °C is AT,
    AT = l_{\mathrm{T}}^{2} = l_{0}^{2}(1 + αT)2
    or AT = A0(1 + αT)2 …. (1)
    Also,
    AT = A0(1 + βT) … (2)
    Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 13.1
  2. Using Equations (1) and (2), A0(1 + αT)2 = A0(1 + βT)
    ∴ 1 + 2αT + α2T2 = 1 + βT
  3. Since the values of a are very small, the term α2T2 is very small and may be neglected, ∴ β = 2α
  4. The result is general because any solid can be regarded as a collection of small squares.

Question 67.
Derive relation between coefficient of linear expansion (α) and coefficient of cubical expansion (γ).
Answer:

  1. Consider a cube of side lo at 0 °C and lT at T°C.
    ∴ lT = lo(l + αT)
    If volume of the cube at 0 °C is V0, V0 = l_{0}^{3}
    If volume of the cube at T °C is
    VT, VT = l_{\mathrm{T}}^{3} = l_{0}^{3}(1 + αT)3
    VT = V0 (1 + αT)3 ….(1)
    Also,
    VT = V0(1 + γT) ….(2)
    Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 14
  2. Using Equations (1) and (2),
    Vo(1 + αT)3 = V0(1 + γT)
    ∴ 1 + 3αT + 3α2T2 + α3T3 = 1 + γT
  3. Since the values of a are very small, the terms with higher powers of a may be neglected.
    ∴ γ = 3α
  4. The result is general because any solid can be regarded as a collection of small cubes.

Question 68.
State the relation between α, β and γ and write their meaning.
Answer:
Relation between α, β and γ is given by,
α = \frac{\beta}{2} = \frac{\gamma}{3}
where, α = coefficient of linear expansion.
β = coefficient of superficial expansion.
γ = coefficient of cubical expansion.

Solved Examples

Question 69.
The length of a rail on a railway line is 25 m at 10 °C. During summer, maximum temperature attained in the region is 50 °C. Find the minimum gap between the rails, (a = 1.2 × 10-5/°C)
Solution:
Given: L1 = 25 m, T1 = 10 °C, T2 = 50 °C,
α = 1.2 × 10-5/°C
To find: Minimum gap between rails (L2 – L1)
Formula: L2 – L1 = L1α(T2 – T1)
Calculation: From formula,
L2 – L1 = 25 × 1.2 × 10-5 × (50 – 10)
= 25 × 1.2 × 10-5 × 40
= 1.2 × 10-2 m
∴ L2 – L1 = 1.2 cm
The minimum gap between the rails is 1.2 cm.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 70.
The length of a metal rod at 27 °C is 4 cm. The length increases to 4.02 cm when the metal rod is heated upto 387 °C. Determine the coefficient of linear expansion of the metal rod.
Solution:
Given: T1 = 27 °C, T2 = 387 °C
L1 = 4 cm = 4 × 10-2 m
L1 = 4.02 cm = 4.02 × 10-2 m
To find: Coefficient of linear expansion
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 15
Coefficient of linear expansion is 1.389 × 10-5/°C

Question 71.
The length of a metal rod is 150 cm at 25 °C. Find its length when it is heated to 150 °C. (αsteel = 2.2 × 105 /°C)
Solution:
Given. L1 = 150 cm, T1 = 25 °C, T2 = 150 °C,
αsteel = 2.2 × 105 /°C
To find: Length of rod (L2)
Formula: α = \frac{L_{2}-L_{1}}{L_{1}\left(T_{2}-T_{1}\right)}
Calculation: From formula,
L2 – L1 = L1 α(T2 – T1)
∴ L2 = L1[1 + α(T2 – T1)]
= 150[1 + 2.2 × 105 × (150 – 25)]
= 150(1 + 2.2 × 105 × 125)
= 150(1 + 0.00275)
= 150× 1.00275 = 150.4125
∴ L2 = 150.4cm
Length of the rod at 150 °C) is 150.4 cm.

Question 72.
Length of a metal rod at temperature 27 °C is 4.256 m. Find the temperature at which the length of the same rod increases to 4.268 m. (α for iron = 1.2 × 105 K-1)
Solution:
Given: T1 = 27°C, L1 = 4.256 m, L2 = 4.268 m,
α = 1.2 × 105 K-1
To find: Temperature (T2)
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 47
= antilog [log 1114.912 – log 4.256]
= antilog [3.0468 – 0.6290]
= antilog [2.4 1781
= 2.617 × 102
= 261.7°C
Required temperature is 261.7 °C.

Question 73.
A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper = 1.70 × 10-5 °C-1.
Solution:
Given: d1 = 4.24 cm, ∆T = 227 – 27 = 200 °C,
α = 1.70 × 10-5 °C-1
To find: Change in diameter (∆d)
Formula: α = \frac{d_{2}-d_{1}}{d_{1} \Delta T}=\frac{\Delta d}{d_{1} \Delta T}
Calculation: From formula.
∆d = α x d1 x αT
= 1.70 × 10 × 4.24 × 200
∴ ∆d = 1.44 × 10-2 cm
The change in diameter of the hole is 1.44 × 10-2 cm.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 74.
A thin aluminium plate has an area 286 cm2 at 20 °C. Find its area when it is heated to 180 °C.
(β for aluminium = 4.9 × 10-5 °C)
Solution:
Given: T1 = 20°C, T2 = 180°C, A1 = 286 cm2
β = 4.9 × 10-5 °C
To find: Final area (A2)
Formula: β = \frac{A_{2}-A_{1}}{A_{1}\left(T_{2}-T_{1}\right)}
Calculation: From formula,
A2 = A1 [1 + β(T2 – T1)]
= 286[1 + 4.9 × 10-5 (180 – 20)]
= 286[1 + 4.9 × 10-5 × 160]
= 286 [1 + 784.0 × 10]
= 286 [1 + 0.00784]
= 286 [1.00784]
∴ A2 = 288.24 cm2
Its area when its heated is 288.24 cm2.

Question 75.
The surface area of the metal plate is 2.4 × 10-2 m2 at 20°C. When the plate is heated to 185 °C, its area increases by 0.8 cm2. Find the coefficient of areal expansion of metal.
Solution:
Given: T1 = 20 °C, A1 = 2.4 × 10-2 m2,
T2 = 185°C,
∆A = 0.8cm2 = 0.8 × 10-4 m2
To find: Coefficient of areal expansion (β)
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 48
The coefficient of areal expansion of the metal is 2.02 × 10-5/ °C.

Question 76.
A liquid occupies a volume of 2 × 10-4 m3 at 0 °C. Calculate the increase in its volume If It is heated to 80 °C. [The coefficient of cubical expansion of the liquid is 4 × 10-4 K-1]
Solution:
Given: V0 = 2 × 10-4 m3, T0 = 0°C,T = 80°C,
γr = 4 × 10-4 K-1,
T – T0 = 80 – 0 = 80°C
To find: Increase in volume (∆V)
Formula. ∆V = V0γr(T – T0)
Calculation: From formula.
∆V = (2 × 10-4) (4 × 10-4) × 80
∴ ∆V = 6.4 × 10-6 m3
Increase m volume of the liquid is 6.4 × 10-6 m3.

Question 77.
A liquid at O °C is poured in a glass beaker of volume 600 cm3 to fill it completely. The beaker is then heated to 90 °C. How much liquid will overflow?
liquid = 1.75 × 10-4/ °C, γglass = 2.75 × 10-5/ °C)
Solution:
Given: V1 = 600 cm3, T1 = 0 °C, T2 = 90 °C
γliquid = 1.75 × 10-4/°C,
γglass = 2.75 × 10-4/°C
To find: Volume of liquid that overflows
Formula: γ = \frac{\mathrm{V}_{2}-\mathrm{V}_{1}}{\mathrm{~V}_{1}\left(\mathrm{~T}_{2}-\mathrm{T}_{1}\right)}
Calculation: From formula,
Increase is volume = V2 – V1
= γ V1(T2 – T1)
Increase in volume of beaker
= γglass × V1 (T2 – T1)
= 2.75 × 10-5 × 600 × (90 – 0)
= 2.75 × 10-5 × 600 × 90
= 148500 × 10-5 cm3
∴ Increase in volume of beaker = 1.485 cm3
Increase in volume of liquid
= γliquid × V1 (T2 – T1)
= 1.75 × 10-4 × 600 × (90 – 0)
= 1.75 × 10-4 × 600 × 90
= 94500 × 10-4 cm3
∴ Increase in volume of liquid = 9.45 cm3
∴ Volume of liquid which overflows
= (9.45 – 1.485) cm3
= 7.965 cm3
Volume of liquid that overflows is 7.965 cm3.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 78.
The surface area of an iron plate is 80 cm2 at 20 °C. Find its surface area at 120 °C. (αiron = 1.25 × 10-5 / °C)
Solution:
Given: A1 = 80 cm2, T1 = 20 °C, T2 = 120 °C,
αiron = 1.25 × 10-5 / °C
To find: Surface area (A2)
Formula: A2 = A1 [1 + β (T2 – T1)]
Calculation: βiron = 2 × αiron = 2.5 × 10-5 / °C
From formula,
A2 = 80[1 + 2.5 × 10-5 (120 – 20)]
∴ A2 = 80.2 cm2
Surface area of the iron plate at 120 °C is 80.2 cm2.

Question 79.
A sheet of brass is 50 cm long and 8 cm broad at 0 °C. If the surface area at 100 °C is 401.57 cm2 find the coefficient of linear expansion of brass.
Solution:
Given: l = 50 cm, b = 8cm.
∴ A1 = l × b = 50 x 8 = 400 cm2,
T1 = 0°C, T2 = 100°C,
A2 = 401.57 cm2
To find: coefficient of linear expansion (α)
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 49
Coefficient of linear expansion of brass is 1.962 × 10-5/°C.

Question 80.
On heating a glass block of 10.000 cm3 from 25 °C to 40 °C, its volume increases by 4 cm3. Calculate coefficient of linear elipansion of glass.
Solution:
Given: V = 10,000 cm3, ∆V = 4 cm3,
∆T = 40 – 25 = 15°C,
To find: Coefficient of linear expansion (α)
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 50
Coefficient of linear expansion of the glass block is 8.89 × 10-6 /°C.

Question 81.
Explain in detail what is specific heat or specific heat capacity of a substance.
Answer:

  1. Specific heat capacity is defined as the amount of heat per unit mass absorbed or given out by the substance to change its temperature by one uni! (one degree) Le., 1 °C or 1 K.
  2. The amount of heat (∆Q) required to change the temperature of a substance is directly proportional to:
    • the mass of the substance (m).
    • change in temperature of the substance (∆T).
      ∴ ∆Q ∝ m and ∆Q ∝∆T
      ∴ ∆Q ∝ m∆T
      ∴ ∆Q = sm∆T …………….. (1)
      where ‘s’ is specific heat or specific heat capacity of a substance.
      From equation (1).
      s = \frac{\Delta Q}{m \Delta T}
      If m = 1 kg and ∆T = 1 °C,then s = ∆Q.
  3. Unit: S.I. unit of specific heat is J kg-1 °C-1 or J kg-1 K-1 and C.G.S. unit is erg g-1 K-1 or erg g-1 °C-1.
  4. Example: The specific heat of water is 4.2 J kg-1 °C-1
    It means that 4.2 J of energy must be added to 1 kg of water to rise its temperature by 1 °C.
  5. The specific heat capacity is a property of the substance.
  6. Specific heat capacity weakly depends on temperature of object. Except for very low temperatures. the specific heat capacity is almost constant for all practical purposes.

Question 82.
State the heat equation.
Answer:
Heat received or given out (Q)
= mass (m) temperature change (∆T) × specific heat capacity (s).
or Q = m × ∆T × s

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 83.
Write a note on: Molar specific heat.
Answer:

  1. If the amount of substance is specified in terms of moles (μ) instead of mass (m) in kg. then the specific heat is called molar specific heat (C).
  2. It is given by, C = \frac{1}{\mu} \frac{\Delta Q}{\Delta \mathrm{T}}
  3. The SI unit of molar specific heat capacity is J/mol °C or J/mol K.
  4. Like specific heat, molar specific heat also depends on the nature of the substance and its temperature.

Question 84.
Give reason: Water is used as a coolant in automobile radiators.
Answer:

  1. Water has the highest specific heat capacity compared to other substances.
  2. As a result, water requires higher amount of energy to get heated.
  3. This allows water to absorb heat readily while increasing its temperature minimally.
    Hence, water is used as a coolant in automobile radiators.

Question 85.
Give reason: Water is preferred as heater in hot water hag than other liquids.
Answer:

  1. Water has the highest specific heat capacity compared to other substances.
  2. This means certain mass of water heated to certain temperature contains more heat than the same mass of any other liquid heated to same temperature.
  3. As a result, water takes longer time to cool than any other liquid heated to same temperature.
    Hence, water is preferred as heater in hot water bag than other liquids.

Question 86.
Explain why specific heat capacity of a gas at constant pressure is greater than that at constant volume.
Answer:

  1. When the gas is heated at constant volume. there is no work done against external pressure.
  2. Hence, all the supplied heat is used in raising the temperature of the gas.
  3. But when the gas is heated at constant pressure, volume of the gas changes.
  4. Due to this, part of the supplied heat is used by the gas to expand against external pressure and remaining part of heat supplied is used to raise the temperature.
  5. Because of this, for the same rise in temperature, the heat to be supplied at constant pressure is greater than that for heating at constant volume.
    Hence, specific heat capacity of a gas at constant pressure is greater than specific heat capacity at constant volume.

Question 87.
Define principal and molar specific heat of a gas at constant volunie and constant pressure.
Answer:

  1. Principal specific heat:
    • Principal specific heat of a gas at constant volume (sv):
      Principal specific heat of a gas at constant volume is defined as the quantity of heat absorbed or released for rise or fall temperature of unit mass of a gas through 1 K (or 1 °C), when its volume is kept constant.
    • Principal specific heat of a gas at constant pressure (sp): Principal specfic heat of a gas at constant pressure is defined as the quantity of heat absorbed or released for rise or fall the temperature of unit mass of a gas through 1 K (or 1 °C), when its pressure is kept constant.
  2. Molar specific heat:
    • Molar specific heat of a gas at constant volume (CV): Molar specific heat of a gas at Constant volume is defined as the quantity of absorbed or released for rise or fall the temperature of one mole of the gas through 1 K (or 1 °C), when its volume is kept constant.
    • Molar specific heat of a gas at constant pressure (CP): Molar specific heat of a gas at constant pressure is defined as the quantity of heat absorbed or released for rise or fall the temperature of one mole of the gas through 1 K (or 1 °C), when its pressure is kept constant.

Question 88.
State the relation between principal specific heat capacity and molar specific heat capacity for a gas.
Answer:
Molar specific heat capacity = Molecular weight × principal specific heat capacity.
i.e. CV = μ × SP and CV = μ × SV
where, μ is the molecular weight of the gas.
[Note: Symbols (SV) and (SP) are used as per standard convention.]

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 89.
What is heat capacity?
Answer:

  1. Heat capacity or thermal capacity of a body is the quantity of heat needed to raise or lower the temperature of the whole body by 1 o°C (or 1 K).
  2. Heat capacity can be written as Heat received or given out
    = mass × 1 × specific heat capacity
    Heat capacity = Q = m × s
    Heat capacity (thermal capacity) is measured in J/°C.

Solved Examples

Question 90.
If the temperature of 4 kg mass of a material of specific heat capacity 300 J/ kg °C rises from 20 °C to 30 °C. Find the heat received.
Solution:
m = 4 kg, s = 300 J/kg °C
∆T = 30 – 20 = 10 °C
To find: Heat received (Q)
Formula: Q = ms∆T
Calculation: From formula,
Q = 4 × 300 × 10
∴ Q = 12000 J
Heat received is 12000 J.

Question 91.
How much heat is required to raise temperature of 750 g of copper pot from 20 to 50 °C?
(The specific heat of copper is 0.094 kcal/kg °C)
Solution:
Given: s = 0.094 kcal/kg°C,
m = 750 g = 0.750kg,
T1 = 20°C and T2 = 50°C
Rise in temperature,
∆T = T2 – T1 = 50 – 20 = 30°C
To find: Heat required (Q)
Formula: Q = m × s × ∆T
Calculation: From formula,
Q = 0.750 × 0.094 × 30
∴ Q = 2.115 kcal
Heat required to raise the temperature of copper pot is 2.115 kcal.

Question 92.
Calculate the difference in the temperatures between the water at the top and bottom of a water fall 200 m high. Specific heat of water is 4200 J kg-1 °C-1.
Solution:
Given: s = 4200 J kg-1 °C-1, h = 200 m
To find: Difference in temperatures (∆T)
Formulae:
i) Q = ms∆T
ii) P.E. = mgh
Calculation: From formulae (j) and (ii)
When water falls from top to bottom. assuming no loss in energy, potential energy is converted into heat energy.
∴ Q = P.E.
∴ ms∆T = mgh
∴ s∆T = gh
∴ ∆T = \frac{\mathrm{gh}}{\mathrm{s}}=\frac{9.8 \times 200}{4200}
∴ ∆T = 0.467 °C
The difference in temperatures between the water at top and bottom is 0.467 °C.

Question 93.
Find thermal capacity for a copper block of mass 0.2 kg, if specific heat capacity of copper is 290 J/kg °C.
Solution:
Given: m = 0.2 kg, s = 290 J/kg °C
To find: Thermal capacity
Formula: Thermal capacity = m × s
Calculation: From formula,
Thermal capacity = 0.2 × 290
= 58 J/ °C
Thermal capacity is 58 J/ °C.

Question 94.
What is calorimetry?
Answer:
Calorimetry is an experimental technique for quantitative measurement of heat exchange.

Question 95.
Explain construction of calorimeter with the help of a labelled diagram.
Answer:

  1. A device in which heat measurement can be made is called calorimeter.
  2. It consists of a cylindrical vessel and stirrer as well as lid of the same material like copper or aluminium.
  3. The vessel is kept inside a wooden jacket which contains heat insulating materials like glass. wool etc. to prohibit any transfer of heat into or out of the calorimeter.
    Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 26

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 96.
State the principle behind working of calorimeter.
Answer:
Calorimeter being isolated system works on the principle of conservation of energy, where heat gained equals heat lost.

Question 97.
Explain the technique “method of mixtures’.
Answer:

  1. Method of mixtures is a technique used to determine specific heat capacity of a material using calorimeter.
  2. In this technique a sample ‘A’ of the substance is heated to a high temperature which is accurately measured.
  3. The sample ‘A’ is then placed quickly in the calorimeter containing water.
  4. The contents are stirred constantly until the mixture attains a final common temperature.
  5. The heat lost by the sample ‘A’ will be gained by the water and the calorimeter.
  6. The specific heat of the sample ‘A’ of the substance can be calculated as follows:
    • Let,
      m1 = mass of the sample ‘A’
      m22 = mass of the calorimeter and the stirrer
      m3 = mass of the water in calorimeter
      s1 = specific heat capacity of the substance of sample ‘A’
      s2 = specific heat capacity of the material of calorimeter (and stirrer)
      s3 = specific heat capacity of water
      T1 = initial temperature of the sample ’A’
      T2 = initial temperature of the calorimeter stirrer and water
      T = final temperature of the combined system
    • Using heat equation,
      Heat lost by the sample ‘A’ = m1s1 (T1 – T)
      Heat gained by the calorimeter and the stirrer = m2s2 (T – T2)
      Heat gained by the water = m3s3 (T – T2)
    • c. Assuming no loss of heat to the surroundings, the heat lost by the sample goes into the calorimeter, stirrer and water,
      ∴ m1s1(T1 – T) = m2s2(T – T2) + m3s3(T – T2) ………….. (1)
    • Knowing the specific heat capacity of water and copper material of the calorimeter and the stirrer, specific heat capacity (si) of material of sample ‘A’ can be calculated.
      e. Rearranging terms of equation (1),
      s1 = \frac{\left(\mathrm{m}_{2} \mathrm{~s}_{2}+\mathrm{m}_{3} \mathrm{~s}_{3}\right)\left(\mathrm{T}-\mathrm{T}_{2}\right)}{\mathrm{m}_{1}\left(\mathrm{~T}_{1}-\mathrm{T}\right)}
  7. One can find specific heat capacity of water or any liquid using the following expression, if the specific heat capacity of the material of calorimeter and sample is known
    s3 = \frac{\mathrm{m}_{1} \mathrm{~s}_{1}\left(\mathrm{~T}_{1}-\mathrm{T}\right)}{\mathrm{m}_{3}\left(\mathrm{~T}-\mathrm{T}_{2}\right)}-\frac{\mathrm{m}_{2} \mathrm{~s}_{2}}{\mathrm{~m}_{3}}

Question 98.
In method of mixtures, why is it essential that density of solid sample be greater than the liquid in calorimeter?
Answer:

  1. In method of mixtures, solid sample gives away heat to liquid, and heat exchange between, solid, liquid and calorimeter is considered as isolated.
  2. If density of solid sample is lesser than liquid in calorimeter, sample will float on liquid.
  3. This will cause partial heat loss to air inside the calorimeter and standard heat equations of calorimeter will no longer be applicable.
    Hence, in method of mixtures it is essential that density of solid sample be greater than liquid in calorimeter.

Solved Examples

Question 99.
A sphere of aluminium of 0.06 kg is placed for sufficient time in a vessel containing boiling water so that the sphere is at 100 °C. It is then immediately transferred to 0.12 kg copper calorimeter containing 0.30 kg of water at 25 °C. The temperature of water rises and attains a steady state at 28 °C. Calculate the specific heat capacity of aluminium.
(Specific heat capacity of water, sw = 4.18 × 103 J kg-1 K-1, specific heat capacity of copper, sCu = 0.387 × 103 J kg-1 K-1)
Solution:
Given: Mass of aluminium sphere = m1 = 0.06 kg
Mass of copper calorimeter = m2 = 0.12 kg
Mass of water in calorimeter = m3 = 0.30 kg
Specific heat capacity of copper
= SCu = s2 = 0.387 × 103 J/kg K = 387 J/kg K
Specific heat capacity of water
= Sw = s3 = 4.18 × 103 J/kg K = 4180 J/kg K
Initial temperature of aluminium sphere
= T1 = 100 °C
Initial temperature of calorimeter and water
= T2 = 25 °C
Final temperature of the mixture = T = 28 °C
To find: Specific heat capacity of aluminium (sal)
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 27
= 903.08 J/kg K
Specific heat capacity of aluminium is 903.08 J/kg K.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 100.
A copper sphere of 100 g mass is heated to raise its temperature to 100 °C and is released in water of mass 195 g and temperature 20 °C in a copper calorimeter. If the mass of calorimeter is 50 g, what will be the maximum temperature of water? (Given: specific heat of copper = 0.1 cal/g °C and specific heat of calorimeter = 0.1 cal/g °C)
Solution:
Let copper sphere, water and calorimeter attain final temperature T °C.
We have,
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 28
Heat lost by copper sphere
Q = msphere × Ssphere × ∆T
= 100 × 0.1 × (100 – T)
Heat gained by water in calorimeter
Q1 = mwater × Swater × ∆T
= 195 × 1 × (T – 20)
Heat gained by calorimeter
Q2 = mcalorimeter × mcalorimeter × ∆T
= 50 × 0.1 × (T – 20)
According to principle of heat exchange,
Q = Q1 + Q2
∴ 10 × (100 – T) = 195 × (T – 20) + 5 × (T – 20)
∴ 1000 – 10T = 200(T – 20)
∴ 210 T = 5000
∴ T ≈ 23.8 °C
Maximum temperature of water will be 23.8 °C.

Question 101.
What is a change of state? When does it occur?
Answer:

  1. Matter normally exists in three states: solid. liquid and gas. A transition from one of these states to another is called a change of state.
  2. This change can occur when exchange of heat takes place between the substance and its surroundings.

Question 102.
Explain the following temperature vs time graph obtained during process of boiling water.
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 29
Variation of temperature with time
Answer:

  1. The given temperature v/s time graph demonstrates the behaviour of water when heated continuously and uniformly.
  2. Line segment AB indicates temperature of ice remaining constant at 0 °C for certain period of time.
    • This means, amount of heat (latent heat of fusion) supplied to ice is entirely used for changing its state from solid to liquid.
    • Thus, line segment AB denotes conversion of ice at 0 °C into water at 0 °C.
  3. Line segment BC indicates continuous rise in temperature of water from 0 °C to 100 °C.
    • At point C, boiling point of water is
      reached and heat energy (latent heat of vaporisation) supplied further is used to convert water into steam.
    • During this transformation, temperature remains unchanged as represented by line segment CD.
    • Thus, line segment CD denotes conversion of water at 100 °C into steam at 100 °C.
  4. Beyond point D, thermometer again shows rise in temperature.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 103.
Write a note on latent heat of substance.
Answer:

  1. Latent heat of a substance is the quantity of heat required to change the state of unit mass of the substance without changing its temperature.
  2. Mathematically, if mass m of a substance undergoes a change from one state to the other then the quantity of heat absorbed or released is given by, Q = mL
    where. L is known as latent heat.
  3. It is characteristic of the substance.
  4. Its SI unit is J/kg.
  5. The value of L depends on the pressure and is usually quoted at one standard atmospheric pressure.

Question 104.
Explain the following terms.
i) Latent heat of fusion
ii) Latent heat of vaporisation
Answer:

  1. Latent heat of fusion:
    • The quantity of heat required to convert unit mass of a substance from its solid state to the liquid state, at its melting point, without any change in its temperature is called its latent heat of fusion.
    • The S.I. unit of latent heat of fusion is J/kg and its C.G.S. unit is cal/’g.
  2. Latent heat of vaporisation:
    • The quantity of heat required to convert unit mass of a substance from its liquid state to vapour state, at its boiling point, without any change in its temperature is called its latent heat of vaporisation.
    • The S.I. unit of latent heat of vaporization is J/kg and its C.G.S unit is cal/g.

Question 105.
Explain why latent heat of vaporisation is much larger than latent heat of fusion.
Answer:

  1. The energy required to completely separate the molecules or atoms in liquids is greater than the energy needed to break the rigidity (rigid bonds between the molecules or atoms) in solids.
  2. Also, when the liquid is converted into vapour, it expands. Work has to be done against the surrounding atmosphere to allow this expansion.
    Hence, latent heat of vaporisation is larger than latent heat of fusion.

Question 106.
A plot of temperature versus heat energy for a given quantity of water is shown below. What can be inferred studying it?
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 30
Temperature versus heat for water at one standard atmospheric pressure (not to scale)
Answer:
Inferences:

  1. When heat is added (or removed) during a change of state, the temperature remains constant.
  2. Also the slopes of the phase lines are not all the same, which indicates that specific heats of the various states are not equal.
  3. For water, the latent heat of fusion and vaporisation are Lf = 3.33 × 105 J kg-1 and Lv = 22.6 × 105 J kg-1 respectively, i.e., 3.33 × 105 J of heat is needed to melt 1 kg of ice at 0 °C and 22.6 × 105 J of heat is needed to convert 1 kg of water to steam at 100 °C.
  4. This means, steam at 100 °C carries 22.6 × 105 J kg-1 more heat than water at 100 °C.

Question 107.
Compare change of state from solid to liquid and from liquid to vapour.
Answer:

Solid to liquid Liquid to vapour
i. The change of state from solid to liquid is called melting and from liquid to solid is called solidification. The change of state from liquid to vapour is called vaporisation while that from vapour to liquid is called condensation.
ii. Both the solid and liquid states of the substance co-exist in thermal equilibrium during the change of states from solid to liquid or vice versa. Both the liquid and vapour states of the substance coexists in thermal equilibrium during the change of state from liquid to vapour.
iii. The temperature at which the solid and the liquid states of the substance are in thermal equilibrium with each other is called the melting point of solid or freezing point of liquid. The freezing point describes the liquid to solid transition while melting point describes solid to liquid transition. The temperature at which the liquid and the vapour states of the substance coexist is called the boiling point of liquid. This is also the temperature at which water vapour condenses to form liquid.
iv. It is the characteristic of the substance and also depends on pressure. It is characteristic of substance and depends on pressure.

Question 108.
What is normal melting point?
Answer:
The melting point of a substance at one standard atmospheric pressure is called its normal melting point.
Example: Normal melting point of water is 0°C.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 109.
State true or false. If false correct the statement and rewrite.
Normal freezing point ice is 32 °C.
Answer:
False.
Normal freezing point ice is 0 °C or 32 °F.

Question 110.
What is normal boiling point?
Answer:
The boiling point of a substance at one standard atmospheric pressure is called its normal boiling point.
Example: Normal boiling point of water is 99.97 °C,

Question 111.
Distinguish between boiling and evaporation of liquid.
Answer:

Boiling of liquid Evaporation of liquid
i. Boiling of liquid takes place at boiling point which is fixed for a given pressure and unique for a given liquid. Evaporation of liquid can take place at any temperature.
ii. It occurs throughout the liquid. It occurs only at surface of liquid.
iii. The process does not depend on area of liquid surface exposed. The process depends upon area of liquid surface exposed. Higher the exposed surface area, higher the rate of evaporation.
iv. Source of energy is needed. Energy is taken from surrounding.
V. Boiling does not reduce temperature of liquid. When evaporation takes place, temperature of liquid decreases.
vi. During boiling process, bubbles are formed in liquid. During evaporation, no bubbles are formed in liquid.

Question 112.
Explain evaporation in terms of kinetic energy of liquid molecules.
Answer:

  1. Molecules in a liquid are moving about randomly.
  2. The average kinetic energy of the molecules decides the temperature of the liquid.
  3. However, all molecules do not move with the same speed.
  4. Some with higher kinetic energy may escape from the surface region by overcoming the interatomic forces.
  5. This process can take place at any temperature and is termed as evaporation.

Question 113.
Explain the dependence of evaporation on temperature of liquid.
Answer:

  1. If the temperature of the liquid is higher, more is the average kinetic energy.
  2. This implies that the number of fast moving molecules is more.
  3. Hence the rate of losing such molecules to atmosphere will be higher.
  4. Thus, higher is the temperature of the liquid, greater is the rate of evaporation.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 114.
Why does evaporation gives a cooling effect to the remaining liquid?
Answer:

  1. In the process of evaporation, faster moving molecules escape from surface of liquid overcoming the interatomic forces.
  2. Since faster molecules are lost, the average kinetic energy of the liquid is reduced.
  3. As a result, the temperature of the liquid is lowered.
    Hence, evaporation gives a cooling effect to the remaining liquid.

Question 115.
Explain two applications of evaporation in details.
Answer:

  1. Drying of clothes:
    • Clothes dry faster when hanged exposing more surface area than when kept folded.
    • Due to more surface area, water in clothes gets evaporated faster, drying clothes quickly.
  2. Using a spirit swab on skin before injecting gives cooling effect:
    • Before giving an injection to a patient, normally a spirit swab is used to disinfect the region.
    • A cooling effect is experienced by skin of patient due to evaporation of the spirit as explained before.

Question 116.
Write a note on sublimation.
Answer:

  1. All substances do not pass through the three states: solid-liquid-gas.
  2. There are certain substances which normally pass from the solid to the vapour state directly and vice versa.
  3. The change from solid state to vapour state without passing through the liquid state is called sublimation and the substance is said to sublime.
    Examples: Dry ice (solid CO2) and iodine.
  4. During the sublimation process, both the solid and vapour states of a substance coexist in thermal equilibrium.
  5. Most substances sublime at very low pressures.

Question 117.
What is a phase? Give an example.
Answer:
A phase is a homogeneous composition of a material.
Example: Graphite and diamond are two phases of carbon.

Question 118.
What is a phase diagram?
Answer:
A pressure-temperature (P-T) diagram particularly convenient for comparing different phases of a substance is called as a phase diagram.

Question 119.
Study phase diagrams given below and answer the following questions.
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 31
i)Explain vaporisation curve (l – v).
ii) Explain fusion curve (l – s).
iii) Explain sublimation curve (s – v).
iv) Explain triple point.
Answer:

    • The curve labelled l – v represents those points where the liquid and vapour phases are in equilibrium.
    • It is a graph of boiling point versus pressure.
    • The l – v curve of water correctly shows that at a pressure of 1 atmosphere, the boiling point of water is 100 °C and the boiling point gets lowered for a decreased pressure.
    • The l – v curve for CO2 yields that CO2 cannot exist as a liquid under normal atmospheric pressure conditions.
    • The curve l – s represents the points where the solid and liquid phases coexist in equilibrium.
    • It is a graph of the freezing point versus pressure.
    • At one standard atmosphere pressure, the freezing point of water is 0 °C which can be depicted using l – s curve of water.
    • At a pressure of one standard atmosphere water is in the liquid phase if the temperature is between 0 °C and 100 °C but is in the solid or vapour phase if the temperature is below 0 °C or above 100 °C.
    • Also, l – s curve for water slopes upward to the left i.e., fusion curve of water has a slightly negative slope.
    • This is true only of substances that expand upon freezing.
    • However, for most materials like CO2, the l – s curve slopes upwards to the right i.e., fusion curve has a positive slope. The melting point of C02 is -56 °C at higher pressure of 5.11 atm.
    • The curve labelled s – v is the sublimation point versus pressure curve.
    • Water sublimates at pressure less than 0.0060 atmosphere, while carbon dioxide, which in the solid state is called dry ice, sublimates even at atmospheric pressure at temperature as low as -78 °C.
    • The temperature and pressure at which the fusion curve, the vaporisation curve and the sublimation curve meet and all the three phases of a substance coexist is called the triple point of the substance.
    • The triple point of water is that point where water in solid, liquid and gaseous states coexist in equilibrium and this occurs only at a unique temperature and pressure.
    • The triple point of water is 273.16 K and 6.11 × 10-3 Pa and that of CO2 is -56.6 °C and 5.1 × 10 -5 Pa.

Question 120.
What is critical temperature of a gas?
Answer:
In order to liquefy a gas, it must be cooled to a certain temperature. This temperature is called critical temperature.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 121.
Compare gas and vapour.
Answer:

Gas

Vapour

i. A substance that is in gaseous phase above its critical temperature is called a gas. A substance that is in gaseous phase below its critical temperature is call vapour.
ii. Gas cannot be liquified only by pressure alone. Vapour can be liquified simply by increasing pressure.
iii. Gas exerts pressure. Vapour exerts pressure

Solved Examples

Question 122.
Calculate the amount of heat energy to be supplied to convert 2 kg of ice at 0 °C completely into water at 0 °C if latent heat of fusion for ice is 80 cal/g.
Solution:
Given:
Mass (m) = 2 kg = 2 × 103 g. latent heat of fusion for ice (L) = 80 cal/g.
To find: Heat energy (Q)
Formula: Q = mL
From formula,
Q = 2 x× 103 × 80 = 160000 cal
= 160 kcal
Heat energy to be supplied is 160 kcal.

Question 123.
When 0.1 kg of ice at 0 °C is mixed with 0.32 kg of water at 35 °C in a container. The resulting temperature of the mixture is 7.8 °C. calculate the heat of fusion of ice (swater = 4186 J kg-1 K-1).
Solution:
Given:
mice = 0.1 kg, mwater = 0.32 kg,
Tice = 0 °C, Twater = 35 °C, TF = 7.8 °C
swater = 4186 J kg-1 K-1
To find: Heat of fusion (Lf)

Formula: i) Heat lost by water
Q1 = mwater × swater × (Twater – TF)
ii) Heat required to melt ice
Q2 = mice LF
iii) Heat required to raise temperature of molten ice (water now) to find temperature
Q3 = miceswater (T – Tice)
Calculation: From formula (j),
Q1 = 0.32 × 4186 × (35 – 7.8)
= 36434.944 J
From formula (ii),
Q2 = 0.1 × Lf
From formula (iii),
Q3 = 0.1 × 4186 × (7.8 – 0) = 3265.08J
According to principle of heat conservation,
heat lost = heat gained
Q1 = Q2 + Q3
∴ 36434.944 = 0.1 Lf + 3265.08
∴ Lf = \frac{36434.944-3265.08}{0.1}
= 331698.64 J kg-1
Rounding off to correct significant figure,
Lf = 3.31699 × 105 J kg-1
Heat of fusion of ice 3.3 1699 × 10 5 J kg-1.

Question 124.
If 80 g steam of temperature 97 °C is released on an ¡ce slab of temperature 0 °C, how much ice will melt? How much energy will be transferred to the ice when the steam will be transformed to water?
(Given: Latent heat of melting the ice = Lmelt =80 cal/g ; Latent heat of vaporisation of water Lvap = 540 cal/g)
Solution:
Mass of steam (ms) = 80 g,
Change in temperature (∆T)
= 97 – 0 = 97 °C
We know that: Latent heat of melting of ice = Lmelt = 80 cal/g
Latent heat of vaporisation of water = Lvap = 540 cal/g
Specific heat of water cw = 1 cal /g °C
To find: i) Energy transferred (Q)
ii) Mass of ice that melts (mi)

Formula: i) Heat released during conversion of steam into water at 97 °C (Q1)= ms × Lvap
ii) Heat released during decrease of temperature of water from 97°C to 0°C (Q2) = ms × cw × ∆T
iii) Heat gained by ice (Q)= mi × Lmelt

From formula (i),
Q1 = 80 × 540 cal
From formula (ii),
Q2 = 80 × 1 × (97 – 0) = 80 × 97 cal
According to principle of heat conservation,
Total heat gained by ice
Q = Q1 + Q2
= 80 × 540 + 80 × 97
= 80 × (540 + 97)
= 80 × 637
= 50960 cal
This energy would cause m; mass of ice to melt,
From formula (iii),
∴ mi × Lmelt = 50960
∴ mi = \frac{50960}{80}=\frac{80 \times 637}{80} = 637 g
Energy transferred to ice is 50960 cal and it will melt 637 g of ice.

Question 125.
Name three modes of heat transfer.
Answer:
Three modes of heat transfer are conduction, convection and radiation.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 126.
Define conduction. State conditions for conduction of heat.
Answer:
Conduction is the process by which heat flows from the hot end to the cold end of a solid body without any net bodily movement of the particles of the body.
Conditions for conduction:

  1. The two points should be at different temperatures.
  2. There should be a medium between the two points.

Question 127.
Explain process of conduction in solid.
Answer:

  1. Heat passes through solids by conduction only.
  2. When one end of a rod is heated, the molecules near the hot end receive the thermal energy and start oscillating with larger amplitudes.
  3. In doing so, they collide with the neighbouring molecules and transfer a part of their energy to these molecules.
  4. The molecules which receive the energy vibrate with increased amplitudes and collide with the neighbouring molecules. Thus, energy of thermal motion is transferred by molecular collisions down the rod.
  5. As the distance of a molecule from the hot end increases, its amplitude of oscillation decreases and hence there is continuous decrease in temperature.
  6. This transfer of heat continues till two ends of the object are at the same temperature.
  7. In metals, mainly free electrons conduct the heat energy.

Question 128.
Define good conductors and bad conductors.
Answer:
Good conductors:
The substances which conduct heat easily are called good conductors of heat.
All metals are good conductor.
eg: Steel, silver, Aluminium etc.

Insulators:
The substances which do nor conduct heal easily are called insulators or bad condiciors of heal.
eg.: Glass. wood, air, paper. etc.
[Note: In general, good conductors of heat are also good conductors of electricity, while bad conductors of hear are had conductors of electricity.]

Question 129.
Explain why metals are good conductors of heat and electricity.
Answer:

  1. Metals like iron, copper. aluminium etc, contain free electrons in their atoms.
  2. These free electrons assist the atoms in transfer of thermal energy as well as electrical energy.
  3. Therefore, metal are good conductors of heat and electricity.

Question 130.
What is thermal conductivity?
Answer:

  • Thermal conductivity of a solid is a measure of the ability of the solid ¡o conduct heat through it.
  • Thus good conductors of heat have higher thermal conductivity than bad conductors.

Question 131.
Give reason: Hot water when poured in glass beaker, it cracks.
Answer:

  1. When hot water is poured in a glass beaker the inner surface of the glass expends on heating.
  2. Since glass is a bad conductor of heat, the heat from inside does not reach the outside surface so quickly.
  3. Hence the outer surface does not expand thereby causing a crack in the glass.

Question 132.
Explain mechanism of thermal conduction and temperature gradient.
Answer:

  1. When one end of a metal rod is heated, the heat flows by conduction from hot end to the cold end.
    Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 32
  2. As a result, the temperature of every section of the rod starts increasing.
  3. Under this condition, the rod is said to be in a variable temperature state.
  4. After some time, the temperature at each section of the rod becomes steady i.e., does not change.
  5. Temperature of each cross-section of the rod now becomes constant though not the same. This is called steady state condition.
  6. Under steady state condition, the temperature at points within the rod decreases uniformly with distance from the hot end to the cold end.
  7. The fall of temperature with distance between the ends of the rod in the direction of flow of heat, is called temperature gradient.
    ∴ Temperature gradient = \frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{x}}
    Where, T1 = temperature of hot end
    T2 = temperature of cold end
    x = length of the rod

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 133.
State SI unit and dimensions of temperature gradient.
Answer:
S.I unit: = °C /m or K/m
Dimensions: [L-1M0T0K1]

Question 134.
State S.I. unit and dimensions of coefficient of thermal conductivity.
Answer:
SI unit of coefficient of thermal conductivity is J s-1 m-1 °C-1 or J s-1 m-1 K-1 and its dimensions are [L1M1T3K-1].

Question 135.
Explain how SI unit of coefficient of thermal conductivity be obtained as W/m °C or W/m K.
Answer:

  1. Consider equation, \frac{Q}{t}=\frac{k A\left(T_{1}-T_{2}\right)}{x}
  2. The quantity Q/t, denoted by Pcond, is the time rate of heat flow (i.e. heat flow per second) from the hotter face to the colder face, at right angles to the faces.
  3. Its SI unit is watt (W).
  4. SI unit of k can therefore be written as W m-1°C-1 or W m-1 K-1.
    [Note: Above equation, using calculus can be written as, \frac{d Q}{d t} = – kA \frac{d T}{d x}, where \frac{d T}{d x} is the temperature gradient. The negative sign indicates that heat flow is in the direction of decreasing temperature. If A = 1 m2 and \frac{d T}{d x} = 1, then \frac{d Q}{d t} = k.]

Question 136.
Define coefficient of thermal conductivity in terms of temperature gradient.
Answer:
Coefficient of thermal conductivity of a material is defined as the rate of flow of heat per unit area per unit temperature gradient when the heat flow is at right angles to the faces of a thin parallel-sided slab of material.

Question 137.
Define conduction rate.
Answer:
Conduction rate (Pcond) is the amount of energy transferred per unit time through a slab of area A and thickness x, the two sides of the slab being at temperatures T1, and T2 (T1 > T2),
and is given Pcond = \frac{Q}{t} = kA \frac{\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{x}}

Question 138.
Explain the analogy between electrical resistance and thermal resistance.
Answer:

  1. Electrical resistance is ratio of \frac{V}{I} where, V is electrical potential difference between two ends of conductor and I is current or rate flow of charge.
  2. Consider expression for conduction rate,
    Pcond = kA \frac{\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{x}}
    \frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{P}_{\mathrm{cond}}}=\frac{\mathrm{x}}{\mathrm{kA}} ……………… (1)
  3. Comparing equation (1) with \frac{V}{I}, (T1 – T2) is temperature difference between two ends and Pcond is rate of flow of heat.
  4. Ratio \frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{P}_{\text {cond }}} is called as thermal resistance (RT) of material.
  5. Using (1), thermal resistance RT = \frac{\mathrm{x}}{\mathrm{kA}}
  6. Thermal resistance depends on the material and dimensions (length / breadth) of object.

Question 139.
What is thermal resistivity? What does it depend upon?
Answer:
i. Thermal resistivity (ρT) is the reciprocal of thermal conductivity (k).
ii. It is characteristic of a material.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 140.
Complete the table.
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 33
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 34

Question 141.
Define convection.
Answer:
The process by which heat is transmitted through a substance from one point to another due to actual bodily movement of the heated particles of the substance is called convection.

Question 142.
Describe the mechanism of heat transfer by convection in liquids and gases.
Answer:

  1. Consider liquid being heated in a vessel from below.
  2. The liquid at the bottom of the vessel is heated
    first and consequently its density decreases i.e., liquid molecules at the bottom are separated farther apart.
  3. These hot molecules have high kinetic energy and rise upward to cold region while the molecules from cold region come down to take their place.
  4. Thus, each molecule at the bottom gets heated and rises then cool and descends.
  5. This action sets up the flow of liquid molecules called convection currents.
  6. The convection currents transfer heat to the entire mass of liquid via actual physical movement of the liquid molecules.
  7. Similar process takes place in case of a gas.

Question 143.
Give two applications of convection.
Answer:

  1. Heating and cooling of rooms:
    • The mechanism of heating a room by a heater is entirely based on convection.
    • The air molecules in immediate contact with the heater are heated up.
    • These air molecules acquire sufficient energy and rise upward.
    • The cool air at the top being denser moves down to take their place. This cool air in turn gets heated and moves upward.
    • In this way, convection currents are set up in the room which transfer heat to different parts of the room.
    • The same principle but in opposite direction is used to cool a room by an air-conditioner.
  2. Cooling of transformers:
    • Due to current flowing in the windings of the transformer, enormous heat is produced.
    • Therefore, transformer is always kept in a tank containing oil.
    • The oil in contact with transformer body heats up, creating convection currents.
    • The warm oil comes in contact with the cooler tank, gives heat to it and descends to the bottom. It again warms up to rise upward.
    • This process is repeated again and again. The heat of the transformer is thus carried away by convection to the cooler tank.
    • The cooler tank, in turn loses its heat by convection to the surrounding air.

Question 144.
Distinguish between free convection and forced convection.
Answer:

Free convection Forced convection
i. When a hot body is in contact with air under ordinary conditions, like air around a firewood, the air removes heat from the body by aprocess called free or natural convection. The convection process can be accelerated by employing a fan to create a rapid circulation of fresh air. This is called forced convection.
ii. Land and sea breezes are formed as a result of free convection currents in air. Heat convector, air conditioner, heat radiators in IC engine etc. operate using forced convection.

Question 145.
Define radiation.
Answer:
The transfer of heat energy from one place to another via emission of electromagnetic (EM) energy (in a straight line with the speed of light) without heating the intervening medium is called radiation.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 146.
Compare conduction, convection and radiation.
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 35
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 36

Solved Examples

Question 147.
The temperature difference between two sides of an iron plate. 2 cm thick, is 10 °C. Heat is transmitted through the plate at the rate of 600 kcal per minute per square metre at steady state. Find the thermal conductivity of iron.
Solution:
Given: \frac{\mathrm{Q}}{\mathrm{At}} = 600 kcal/min m2 = \frac{600}{60} kcal/s m2
= 10 kcal/s m2
x = 2cm = 2 × 10-2 m
T1 – T2 = 10°C
To Find.- Thermal conductivity (k)
Formula: Q = \frac{\mathrm{kA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right) \mathrm{t}}{\mathrm{x}}
Calculation: From formula.
∴ k = \frac{\mathrm{Q}}{\mathrm{At} \mathrm{t}} \frac{\mathrm{x}}{\mathrm{T}_{1}-\mathrm{T}_{2}}=\frac{10 \times 2 \times 10^{-2}}{10}
= 0.02 kcal / m s
Thermal conductivity is 0.02 kcal / m s °C.

Question 148.
Calculate the rate of loss of heat through a glass window of area 1000 cm2 and thickness of 4 mm. when temperature inside is 27 °C and outside is – 5 °C. Coefficient of thermal conductivity of glass is 0.022 cal /s cm °C.
Solution:
Given: A = 1000 cm2 1000 × 10 m2
k = 0.22 cal / s cm °C
= 0.22 × 102 cal/ m °C
x = 4mm = 0.4 × 10-2 m
T1 = 27°C, T2 = -5°C
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 37
= 1.76 × 103 cal/s = 1.76kcal / s
Rate of loss of heat is 1.76 kcal / s.

Question 149.
Heat is conducted through a copper plate at the rate of 460 cal/s-cm2. Calculate the temperature gradient when the steady state is reached. (kcopper = 92 cal/m-s °C)
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 38
Temperature gradient of the copper plate is 5°C/m.

Question 150.
Two parallel slabs of metals A and B of thickness 5 cm and 3 cm respectively are joined together. The outer face of the metal A is maintained at 100 °C and that of metal B is maintained at 40 °C. If the thermal conductivities of metal A and B are 0.045 kcal/m-s K and 0.015 kcal/m-s K respectively, find the temperature of the interface of two plates.
Solution:
For metal A:
T1 = 100 °C, T2 = θ
dx1= 5 cm = 5 × 10-2 m,
k1 = 0.045 kcal/m-s K
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 39
∴ 9(100 – T) = 5(T – 40)
∴ 900 – 9T = 5T – 200
∴ 14T = 1100
∴ T = 78.57°C
Temperature of the interlace of two plates is 78.57 °C.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 151.
What is the rate of energy loss in watt per square metre through a glass window 5 mm thick if outside temperature in -20 °C and inside temperature is 25 °C? (kglass = 1 W/m K)
Solution:
Given:
kglass = 1W/m K, T1 = 25 °C, T2 = -20 °C
T1 – T2 = 25- (-20)°C = 45 °C
X = 5 mm = 5 × 10-3 m
As one degree celsius equates to one kelvin, temperature difference of 450 C equals 45 K.
To find: Rate of energy loss per square metre \left(\frac{\mathrm{P}_{\text {cond }}}{\mathrm{A}}\right)
Formula: Pcond = \frac{Q}{t}=k A \frac{T_{1}-T_{2}}{x}
Calcula lion: From formula,
∴ The energy loss per square metre,
\frac{\mathrm{P}_{\text {oond }}}{\mathrm{A}}=\mathrm{k} \frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{x}}=\frac{1 \times 45}{5 \times 10^{-3}}
= 9 × 103 W/m2
Rate of energy loss per square metre is 9 × 103 W/m2.

Question 152.
A metal sphere cools at the rate of 1.6 °C/min when its temperature is 70 °C. At what rate will it cool when its temperature is 40 °C? The temperature of surroundings is 30 °C.
Solution:
Given: T1 = 70°C, T2 = 40 °C, T3 = 30 °C
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 40
= 0.4 (40 – 30)
= 0.4 °C/mm
Rate of cooling is 0.4 °C/mm.

Question 153.
A body cools at the rate of 0.5 °C/s when it is at 50 °C above the surrounding temperature. What is its rate of cooling when ¡t is at 30 °C above the surrounding temperature?
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 41
Divide equation (2) by (1),
\frac{\left(\frac{\mathrm{dT}}{\mathrm{dt}}\right)_{2}}{0.5}=\frac{\mathrm{C}(30)}{\mathrm{C}(50)}
\left(\frac{\mathrm{dT}}{\mathrm{dt}}\right)_{2} = 0.5 × \frac{30}{50} = 0.3 °C/s
The rate of cooling of the body at 30 °C above the surrounding temperature is 0.3 °C/s.

Apply Your Knowledge

Question 154.
A metre scale made up of aluminium (αa = 24 × 10-6 /°C) measures length of a steel rod (αs = 12 × 10-6 /°C) at room temperature as 50.00 cm. Now the temperature of the room is increased by 100 °C. What can be said about the measured length of the rod at new temperature?
Answer:
At new temperature T °C,
change in length of rod is,
∆Ls = L0s∆T) = 50.00(12 × 10-6 × 100)
= 0.06 cm.
Hence, the actual length of rod at T °C,
Ls = 50.06 cm
Due to change in temperature, along with rod, the scale will also increase in length.
For aluminium, at T °C,
∆La = L0a∆t) = 100.00 × 24 × 10-6 × 100
= 0.24 cm
∴ Length of the scale will be,
La = 100.24 cm
As, the expansion in scale is more than that in rod, the reading recorded by the scale at t°C will be less than 50 cm.

Question 155.
A mercury thermometer calibrated to measure temperature in Fahrenheit scale is kept in liquid phosphorus at 150 °F. The liquid phosphorus is then heated continuously until it reaches its boiling point measured by the thermometer to be 500 °F. Find the percentage fractional change in the density of mercury during the whole process. (γHg = 10-4/°F)
(Assume that no heat is lost to the surrounding during the process.)
Answer:
Given:
T2 = 500°F, T1 = 150°F
γHg = 10-4 /°F
As the liquid phosphorus is heated, the mercury in the thermometer also gets heated.
Due to thermal expansion,
V2 = V1(1 + γ∆t)
= V1 [1 + 10-4 × (500 – 150)]
= 1.035 V1
Now, initial density of mercury is,
ρ1 = \frac{\mathrm{m}}{\mathrm{V}_{1}}
After heating,
ρ2 = \frac{\mathrm{m}}{\mathrm{V}_{2}}=\frac{\mathrm{m}}{1.035 \mathrm{~V}_{1}}=\frac{\rho_{1}}{1.035}
⇒ ρ2 < ρ1
∴ change in density of mercury is,
\frac{\rho_{1}-\rho_{2}}{\rho_{1}}=\frac{\rho_{1}(1-0.9662)}{\rho_{1}} = 0.0338
∴ Percentage fractional change = 3.38%

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 155.
When ‘m’ g of ice is added to ‘M’g of water at 20 °C, state the conditions for m and M for which
i) temperature of the mixture remains 0° C.
ii) temperature of the mixture exceeds 0 °C. (Specific heat of water = sw = 4.2 × 103 J kg-1 °C-1, latent heat of fusion = L = 3.36 × 105 J kg-1 )
Answer:
The heat lost by water in going from 20 °C to 0°C,
Q1 = Msw ∆T = \frac{\mathrm{M}}{1000} × 4.2 × 103 × (20) = 84M J
Now, heat required to convert m g of ice into water at 0 °C,
Q2 = mL = \frac{\mathrm{M}}{1000} × 3.36 × 105 = 336m J

  1. For temperature of mixture to be 0 °C,
    Q2 > Q1
    ⇒ 336m > 84M
    ⇒ m > \frac{\mathrm{M}}{4}
  2. For temperature of mixture to exceed 0 °C,
    Q2 < Q1 ⇒ m < \frac{\mathrm{M}}{4}

Quick Review

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 42

Multiple Choice Questions

Question 1.
Heat is transferred between two (or more) systems or a system and its surrounding by virtue of
(A) temperature difference.
(B) material difference.
(C) amount of heat difference.
(D) mass difference.
Answer:
(A) temperature difference.

Question 2.
On celsius scale, the two fixed points are marked as
(A) 0°C and 232°C
(B) 32°C and 100°C
(C) 0°C and 100°C
(D) 100°C and 180°C
Answer:
(C) 0°C and 100°C

Question 3.
If the temperature in a room is 30 °C, temperature in degree fahrenheit is
(A) 22 °F
(B) 62 °F
(C) 86 °F
(D) 96 °F
Answer:
(C) 86 °F

Question 4.
If the temperature on Fahrenheit scale is 140 °F, then the same temperature on kelvin scale will be
(A) 60.15 K
(B) 213.15 K
(C) 333.15 K
(D) 413.15 K
Answer:
(C) 333.15 K

Question 5.
In the gas equation, PV = RT, V stands for volume of
(A) any amount of gas .
(B) one gram mole of gas.
(C) one gram of a gas.
(D) one litre of a gas.
Answer:
(B) one gram mole of gas.

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 6.
1 litre of an ideal gas at 27 °C is heated at constant pressure so as to attain temperature 297 °C. The final volume is approximately
(A) 1.2 litre
(B) 1.9 litre
(C) 19 litre
(D) 2.4 litre
Answer:
(B) 1.9 litre

Question 7.
How much should the pressure be increased in order to decrease the volume of a gas by 10% at a constant temperature?
(A) 7%
(B) 8%
(C) 10%
(D) 11.11%
Answer:
(D) 11.11%

Question 8.
Two rods of same material are equal in length, but one has cross-sectional area double the other. If they are heated through the same temperature then
(A) thick rod expands more.
(B) thin rod expands more.
(C) both rods will expand equally.
(D) none of these.
Answer:
(C) both rods will expand equally.

Question 9.
Two iron bars of same length with unequal radii are heated for the same rise in temperature. The linear expansion will be
(A) more in thin bar.
(B) more in thick bar.
(C) same for both.
(D) less in thick bar.
Answer:
(A) more in thin bar.

Question 10.
Which of the following has minimum coefficient of linear expansion?
(A) Gold
(B) Copper
(C) Platinum
(D) Invar steel
Answer:
(D) Invar steel

Question 11.
The coefficient of cubical expansion of a solid is the increase in volume per unit original volume at 0 °C per degree rise in _________.
(A) pressure
(B) volume
(C) temperature
(D) area
Answer:
(C) temperature

Question 12.
A disc has an area of 0.32 m2 at 20 °C, what will be its area at 100 °C? (α = 2 × 10-6 / °C)
(A) 0.12 m2
(B) 0.32 m2
(C) 0.51 m2
(D) 0.71 m2
Answer:
(B) 0.32 m2

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 13.
The coefficient of linear expansion of iron is 1.1 × 10-5 per K. An iron is 10 m long at 27 °C. Length of the rod will be decreased by 1.1 mm when the temperature of the rod changes to
(A) 0°C
(B) 10 °C
(C) 17 °C
(D) 20 °C
Answer:
(C) 17 °C

Question 14.
The length of an aluminium rod is 120 cm at 20 °C. What is its length at 80 °C, if coefficient of linear expansion of aluminium is 2.5 × 10-5/°C?
(A) 130.18 cm
(B) 120.18 cm
(C) 110.18 cm
(D) 100.18 cm
Answer:
(B) 120.18 cm

Question 15.
A metal rod having a coefficient of linear expansion of 2 × 10-5 /°C has a length of 100 cm at 20 °C. The temperature at which it is shortened by 1 mm is
(A) -40 °C
(B) -30 °C
(C) -20 °C
(D) -10 °C
Answer:
(B) -30 °C

Question 16.
Iron sheet 50 cm × 20 cm is heated through 100 °C. If a = 12 × 10-6 / °C, the change in area is
(A) 2.4 cm2
(B) 3.4 cm2
(C) 4.2 cm2
(D) 5.3 cm2
Answer:
(A) 2.4 cm2

Question 17.
A liquid with coefficient of volume expansion γ is filled in a container of a material having the coefficient of linear expansion α. If the liquid over flows on heating then
(A) γ = 3α
(B) γ < 3α (C) γ > 3α
(D) γ = 3α2
Answer:
(B) γ < 3α

Question 18.
The volume of a metal block changes by 0.18% when it is heated through 20 °C. Its coefficient at cubical expansion will be
(A) 9 × 10-5 / °C
(B) 3 × 10-5 / °C
(C) 18 × 10-5 / °C
(D) 36 × 10-5 / °C
Answer:
(A) 9 × 10-5 / °C

Question 19.
The volume of liquid is 830 m3 at 30 °C and 850 m3 at 90 °C. The coefficient of volume expansion of liquid is
(A) 2 × 10-4 per °C
(B) 8 × 10-4 per °C
(C) 4 × 10-4 per °C
(D) 2.5 × 10-4 per °C
Answer:
(C) 4 × 10-4 per °C

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 20.
The superficial expansivity is 1 / x times the cubic expansivity. The value of x is
(A) 2/3
(B) 3/2
(C) 2
(D) 3
Answer:
(B) 3/2

Question 21.
The unit of molar specific heat is
(A) JK-1 mole-1
(B) JK mole-1
(C) J-1 K-1mole-1
(D) JK-1 mole
Answer:
(A) JK-1 mole-1

Question 22.
The S.I. unit of latent heat is
(A) J-1 kg
(B) J kg-1
(C) J k-1 °C
(D) J-1 kg °C
Answer:
(B) J kg-1

Question 23.
The slowest mode of transfer of heat is
(A) conduction
(B) convection
(C) radiation
(D) specific heat
Answer:
(A) conduction

Question 24.
The quantity of heat which crosses unit area of a metal plate during conduction depends on
(A) the density of the metal.
(B) the temperature gradient perpendicular to the area.
(C) the temperature to which the metal is heated.
(D) the area of the metal plate.
Answer:
(B) the temperature gradient perpendicular to the area.

Question 25.
Which of the following is not the unit of thermal conductivity?
(A) J/m s °C
(B) K cal/m s K
(C) Watt/m °C
(D) J/m2 s °C
Answer:
(D) J/m2 s °C

Question 26.
The most desirable combination for the material of a cooking pot is
(A) high specific heat and high conductivity.
(B) low specific heat and high conductivity.
(C) high specific heat and low conductivity.
(D) low specific heat and low conductivity.
Answer:
(B) low specific heat and high conductivity.

Question 27.
While measuring thermal conductivity of a liquid, we keep the upper part hot and lower part cold, so that
(A) radiation may start.
(B) radiation may stop.
(C) convection may start.
(D) convection may be stopped.
Answer:
(D) convection may be stopped.

Question 28.
Convention currents in air in day time is from
(A) land to sea
(B) sea to land
(C) sea to sky
(D) land to land
Answer:
(B) sea to land

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 29.
One end of a metal rod one metre long is kept in ice and the other end is at 100 °C. What is temperature gradient throughout the rod?
(A) 10 °C/m
(B) 100 °C/m
(C) 50 °C/m
(D) 1 °C/m
Answer:
(B) 100 °C/m

Question 30.
__________ amount of heat is required to raise the temperature of 100 g of kerosene from 10 °C to 30 °C (Given: specific heat of kerosene is 0.51 kcal/kg °C)
(A) 0.102 kcal
(B) 1.02 kcal
(C) 10.2 kcal
(D) 102 kcal
Answer:
(B) 1.02 kcal

Question 31.
One end of copper rod is in contact with water at 100 °C and the other end in contact with ice at 0 °C. The length of the rod is 100 cm. At a point which is at a distance of 35 cm from the cold end, temperature is (assuming steady state heat flow)
(A) 35 °C
(B) 65 °C
(C) 56 °C
(D) 53 °C
Answer:
(A) 35 °C

Question 32.
In Newton’s law of cooling, the rate of fall of temperature
(A) is constant
(B) increases
(C) decreases
(D) doubles
Answer:
(C) decreases

Question 33.
The metal sphere cools at 1 °C/min, when its temperature is 50 °C. If the temperature of environment is 30 °C, its rate of cooling at 35 °C is
(A) 0.25 °C/min
(B) 0.5 °C/min
(C) 0.75 °C/min
(D) 0.4 °C/min
Answer:
(A) 0.25 °C/min

Competitive Corner

Question 1.
A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminum rod is:
Cu = 1.7 × 10-5 K-1 and αAl = 2.2 × 10-5 K-1)
(A) 88 cm
(B) 68 cm
(C) 6.8 cm
(D) 1 13.9 cm
Answer:
(B) 68 cm
Hint:
LCu αCu ∆T = LAl αAl ∆T
∴ 88 × (1.7 × 10-5) = LAl(2.2 × 10-5)
∴ LAl = \frac{88 \times 1.7}{2.2}
∴ LAl = 68 cm

Question 2.
The unit of thermal conductivity is:
(A) W m K-1
(B) W m-1 K-1
(C) JmK -1
(D) Jm-1K-1
Answer:
(B) W m-1 K-1
Hint:
Q = kA \left(\frac{\Delta \mathrm{T}}{\Delta \mathrm{x}}\right) t
Q = quantity of heat conducted.
A = area of cross section
t = time for which heat is passed
\left(\frac{\Delta \mathrm{T}}{\Delta \mathrm{x}}\right) = temperature gradient
∴ K = \frac{Q}{A t\left(\frac{\Delta T}{\Delta x}\right)}
∴ Unit of k = W m-1 K-1

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 3.
A deep rectangular pond of surface area A, containing water (density = p, specific heat capacity = s), is located in a region where the outside air temperature is at a steady value of -26°C. The thickness of the frozen ice layer in this pond, at a certain instant is x. Taking the thermal conductivity of ice as K, and its specific latent heat of fusion as L, the rate of increase of the thickness of ice layer, at this instant, would be given by
(A) 26K/ρx(L + 4s)
(B) 26K/ρx(L – 4s)
(C) 26K/(ρx2 L)
(D) 26K/(ρxL)
Answer:
(D) 26K/(ρxL)
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 43

Question 4.
An object kept in a large room having air temperature of 25°C takes 12 minutes to cool from 80°C to 70°C. The time taken to cool for the same object from 70°C to 60°C would be nearly.
(A) 15 min
(B) 10mm
(C) 12mm
(D) 20mm
Answer:
(A) 15 min
Hint:
By Newton’s law of cooling,
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 44

Question 5.
A thermally insulated vessel contains 150 g of water at 0 °C. Then the air from the vessel ispumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0 °C itself. The mass of evaporated water will be closest to :
(Latent heat of vaporization of water = 2.10 × 106 J kg-1 and Latent heat of Fusion of water = 3.36 × 105 J kg-1)
(A) 150g
(B) 20g
(C) 130g
(D) 35g
Answer:
(B) 20g
Hint:
m= 150 g = 0.15 kg
The heat required to evaporate ‘m’ grams of water,
∆Qrequired = mLv ………. ( 1)
(015 – m) is the amount of mass that converts into ice
∴ ∆Qreleased = (0.15 – m) Lf …………. (2)
Now, amount of heat required = amount of heat released
∴ From (1) and (2),
mLv = (0.15 – m)Lf
∴ m(Lf + Lv) = 0.15 Lf
∴ m = \frac{0.15 \mathrm{~L}_{\mathrm{f}}}{\mathrm{L}_{\mathrm{f}}+\mathrm{L}_{\mathrm{v}}}
∴ m = \frac{0.15 \times 3.36 \times 10^{5}}{2.10 \times 10^{6}+3.36 \times 10^{5}}
∴ m=0.0206kg ≈ 20g

Question 6.
A copper ball of mass 100 g is at a temperature T. It is dropped in a copper calorimeter of mass 100 g, filled with 170 g of water at room temperature. Subsequently, thetemperature of the system is found to be 75 °C. T is given by: (Given: room temperature = 30°C, specific heat of copper 0.1 cal/g °C)
(A) 1250°C
(B) 825°C
(C) 800°C
(D) 885°C
Answer:
(D) 885°C
Hint:
Heat lost by copper ball = Heat gained by calorimeter and water
∴mbsc∆T1 = mccc∆T2 + mwsw∆T2
∴ (100)(0.1)(T – 75) = (100)(0.1)(75 – 30) + (170)(1)(75 – 30)
10(T – 75) = 450 + 7650 = 8100
T – 75 = 810
T = 885 °C

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 7.
Coefficient of linear expansion of brass and steel rods are α1 and α2. Lengths of brass and steel rods are l1 and l2 respectively. If (l2 – l1) is maintained same at all temperatures, which one of the following relations holds good?
(A) α12l2 = α22l1
(B) α1l1 = α2l2
(C) α1l2 = α2l1
(D) α1l22 = α2l12
Answer:
(B) α1l1 = α2l2
Hint:
∆L = L(1 + α∆t)
i.e. ∆l2 = l2(1 + α2∆t)
and ∆l1 =11(1 + α1∆t)
It is given,
l2– l1 = ∆tl2 – ∆ll1
∴ l2 – l1 = l2 (1 + α2∆t) – l1 (1+ α1∆t)
= l2 + l2α2∆t – l1 – l1α1∆t
∴ – l2 + l2 + l2α2∆t = -l1 + l1 + l1α1∆t
∴ l2α2∆t = l1α1∆t
i.e., l2α2 = l1α1

Question 8.
A pendulum clock loses 12 s a day if the temperature is 40 °C and gains 4 s a day if the temperature is 20 °C. The temperature at which the clock will show correct time, and the coefficient of linear expansion (a) of the metal of the pendulum shaft are respectively:
(A) 60 πC, a = 1.85 × 10-4/πC
(B) 30 πC, a = 1.85 × 10-3/πC
(C) 55 πC, a = 1.85 × 10-2/πC
(D) 25 πC, a = 1.85 × 10-5/πC
Answer:
(D) 25 πC, a = 1.85 × 10-5/πC
Hint:
Period of pendulum, T = 2π\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}
∴ T ∝ \sqrt{\mathrm{L}}
But, L = L0 (1 + α∆t)
∴ T ∝ \sqrt{\mathrm{L}_{0}(1+\alpha \Delta \mathrm{t})}
As L0 is constant,
⇒ T ∝ (1 + α ∆t)
Calculating fractional change in time period of pendulum, \frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{1}{2}(\alpha \Delta \mathrm{t})
For the given pendulum,
T = 24 × 60 × 60 = 864000 s
When t1 = 40 °C, ∆T = 12 s,
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 45

Question 9.
A piece of ice falls from a height h so that it melts completely. Only one — quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is [Latent heat of ice is 3.4 × 105 J/kg and g = 10 N/kg]
(A) 136 km
(B) 68km
(C) 34km
(D) 544km
Answer:
(A) 136 km
Hint:
When the piece of ice falls from the height h, it possesses potential energy, mgh.
This P.E. is converted to heat energy.
∴ Q = mgh
But only \frac{1^{\text {th }}}{4} of it is absorbed by ice which is used to change the state.
\frac{\mathrm{mgh}}{4} = mL
\frac{10 \times \mathrm{h}}{4} = 3.4 × 105
∴ h = 13.6 × 104 m = 136km

Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter

Question 10.
A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton’s law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be
(A) T
(B) \frac{7}{4} T
(C) \frac{3}{2} T
(D) \frac{4}{3} T
Answer:
(C) \frac{3}{2} T
Hint:
By Newton’s law of cooling,
Maharashtra Board Class 11 Physics Important Questions Chapter 7 Thermal Properties of Matter 46

Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids

Balbharti Maharashtra State Board 11th Physics Important Questions Chapter 6 Mechanical Properties of Solids Important Questions and Answers.

Maharashtra State Board 11th Physics Important Questions Chapter 6 Mechanical Properties of Solids

Question 1.
Explain the equilibrium state of solids at a given temperature.
Answer:

  1. Solids are made up of atoms or a group of atoms placed in a definite geometric arrangement.
  2. This arrangement is decided by nature so that the resultant force acting on each constituent due to others is zero. This is the equilibrium state of a solid at room temperature.
  3. This equilibrium arrangement does not change with time but it can only change when an external stimulus, like compressive force is applied to a solid from all sides.
  4. The constituents vibrate about their equilibrium positions even at very low temperature but cannot leave their fixed positions.
  5. As a result, the solids possess a definite shape and size.

Question 2.
Explain the effects of applied force on a rigid body.
Answer:

  1. When an external force is applied to a solid, the constituents are slightly displaced and restoring forces are developed in it.
  2. These restoring forces try to bring the constituents back to their equilibrium positions so that the solid can regain its shape.
  3. When the deforming forces are removed, the inter-atomic forces tend to restore the original positions of the molecules and thus the body regains its original shape and size.

Question 3.
Explain the concept of deforming force with the help of examples.
Answer:

  1. When a force (within specific limit) is applied to a solid (which is not free to move), the size or shape or both change due to changes in the relative positions of molecules. Such a force is called deforming force.
  2. The larger the deforming force on a body, the larger is its deformation.
  3. Deformation could be in the form of change in length of a wire, change in volume of an object or change in shape of a body.
  4. Examples:
    • When a deforming force such as stretching, is applied to a rubber band, it gets deformed (elongated) but when the force is removed, it regains its original length.
    • When a similar force is applied to a dough or a clay, it also gets deformed but it does not regain its original shape and size after removal of the deforming force.

Question 4.
Define plasticity.
Answer:
If a body does not regain its original shape and size and retains its altered shape or size upon removal of the deforming force, it is called a plastic body and the property is called plasticity.

Question 5.
When is a body said to be perfectly elastic? Give an example for perfectly elastic body and perfectly plastic body.
Answer:

  1. If a body regains its original shape and size completely and instantaneously upon removal of the deforming force, then it is said to be perfectly elastic.
    • There is no solid which is perfectly elastic or perfectly plastic,
    • The best example of a near perfectly elastic body is quartz fibre and that of a plastic body is putty.

Question 6.
State SI unit and dimensions of strain.
Answer:
Strain is the ratio of two similar quantities. Hence strain is a dimensionless physical quantity and it has no units.

Question 7.
State and explain longitudinal stress (Tensile stress and Compressive stress).
Answer:
i. Stress produced by a deforming force acting along the length of a body or a rod is called longitudinal stress.

ii. Tensile stress: Consider a force F is applied along a length of a wire, or perpendicular to its cross-section A of a wire (or along its length).

Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 1

[Note: Elongation of wire ∆l is exaggerated for explanation.]
This produces an elongation in the wire and the length of the wire increases, then
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 2

iii. Compressive stress: When a rod is pushed from two ends with equal and opposite forces.
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 3
[Note: Compression of wire ∆l is exaggerated for explanation.]
This restoring force per unit area is called compressive stress.
Compressive stress = \frac{|\overrightarrow{\mathrm{F}}|}{\mathrm{A}}

Question 8.
State and explain longitudinal strain (Tensile strain or Linear strain).
Answer:
The strain produced by a tensile deforming force is called longitudinal strain (tensile strain or linear strain,).
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 4
where, L = Original length,
∆l = Change in length.

Question 9.
State and explain volume stress / hydraulic stress.
Answer:
When a deforming force acting on a body produces change in its volume, the stress is called volume stress.
Volume stress/hydraulic stress:
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 5
[Note: Change in size is exaggerated for explanation.]
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 6

  1. Let \vec{F} be a force acting perpendicular to the entire surface of the body.
  2. It acts normally and uniformly all over the surface area A of the body.
  3. Such a stress which produces change in size but no change in shape is called volume stress.
    Volume stress = \frac{|\overrightarrow{\mathrm{F}}|}{\mathrm{A}}
  4. Volume stress produces change in size without change in shape of body, hence it is also called as hydraulic or hydrostatic volume stress.

Question 10.
Explain volume strain.
Answer:

  1. A deforming force acting perpendicular to the entire surface of a body produces a volume strain.
  2. Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 7
    where ∆V = change in volume,
    V = original volume.

Question 11.
Define and explain shearing stress.
Answer:
The restoring force per unit area developed due to the applied tangential force is called shearing stress or tangential stress.
Shearing stress:

  1. When a deforming force acting on a body produces change in the shape of a body shearing stress is produced.
  2. Consider ABCD as a front face of a cube, a tangential force is applied to the cube so that the bottom of the cube is fixed and only the top surface is slightly displaced.
    Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 8

Question 12.
Explain shearing strain.
Answer:

  1. The relative displacement of the bottom face and the top face of the cube is called shearing strain.
  2. Shearing strain = \frac{\Delta l}{\mathrm{~L}} = tan θ
    where, ∆l = displaced length,
    L = Original length.
  3. When ∆l is very small,
    tan θ ≈ θ and shearing strain = θ

Question 13.
State and explain Hooke’s law.
Answer:
Statement: Within elastic limit, stress is directly proportional to strain.
Explanation:

  1. According to Hooke’s law,
    Stress-Strain
    Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 9
    This constant of proportionality is called modulus of elasticity.
  2. Modulus of elasticity of a material is the slope of stress-strain curve in elastic deformation region and depends on the nature of the material.
  3. The graph of strain (on X-axis) and stress (on Y-axis) within elastic limit is shown in the figure.
    Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 10

Question 14.
Define elastic limit.
Answer:
The maximum value of stress upto which stress is directly proportional to strain is called the elastic limit.

Question 15.
Define modulus of elasticity.
Answer:
The modulus of elasticity of a material is the ratio of stress to the corresponding strain.

Question 16.
State different types of modulus of elasticity.
Answer:

  1. Young’s modulus (Y): It is the modulus of elasticity related to change in length of an object like a metal wire, rod, beam, etc., due to the applied deforming force.
  2. Bulk modulus (K): It is the modulus of elasticity related to change in volume of an object due to applied deforming force.
  3. Shear modulus or Modulus of rigidity (η): The modulus of elasticity related to change in shape of an object is called modulus of rigidity.

Question 17.
Explain the usefulness of Young’s modulus.
Answer:

  1. Young’s modulus indicates the resistance of an elastic solid to elongation or compression.
  2. Young’s modulus of a material is useful for characterization of an object subjected to compression or tension.

Question 18.
Within elastic limit, prove that Young’s modulus of material of wire is the stress required to double the length of wire.
Answer:

(i) Let, L = Initial length of wire
2 L = Final length of wire
∴ Increase in length = ∆l = 2L – L = L

(ii) Longitudinal strain of wire = \frac{\Delta l}{\mathrm{~L}}=\frac{\mathrm{L}}{\mathrm{L}}=1

(iii)
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 11
∴ Y = Longitudinal stress

(iv) Hence, Young’s modulus of material of wire is the stress required to double the length of wire.

Question 19.
What is bulk modulus? Derive an expression for bulk modulus.
Answer:
Definition:
Bulk modulus is defined as the ratio of volume stress to volume strain.
It is denoted by ‘K’.
Unit: N/m2 or Pa in SI system
Dimensions: [L-1M1T-2]
Expression for bulk modulus:

(i) If a sphere made from rubber is completely immersed in a liquid, it will be uniformly compressed from all sides.
Let, F = Compressive force,
dP = Change in pressure,
dV = Change in volume,
V = Original volume.

(ii) Volume stress = \frac{|\overrightarrow{\mathrm{F}}|}{\mathrm{A}} = dP

Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 12

(iii) The negative sign indicates that there is a decrease in volume.
The magnitude of the volume strain is \frac{\mathrm{dV}}{\mathrm{V}}

Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 13

Question 20.
Explain the usefulness of bulk modulus.
Answer:

  1. Bulk modulus indicates the resistance of gases, liquids or solids to change their volume.
  2. Materials with small bulk modulus and large compressibility are easier to compress.

Question 21.
State few applications of bulk modulus.
Answer:

  1. When a balloon is filled with air at high pressure, its walls experience a force from within. It tries to expand the balloon and change its size without changing shape. When the volume stress exceeds the limit of bulk elasticity, the balloon explodes.
  2. A gas cylinder explodes when the pressure inside it exceeds the limit of bulk elasticity of its material.
  3. A submarine when submerged under water is under volume stress. The depth it can reach within water depends upon its limit of bulk elasticity.

Question 22.
Define compressibility. State its unit and dimensions.
Answer:

  1. The reciprocal of bulk modulus of elasticity is called compressibility of the material.
    Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 14
  2. Compressibility is the fractional decrease in volume, (-dV/V) per unit increase in pressure.
    Compressibility = \frac{-\mathrm{dV}}{\mathrm{V} \mathrm{dP}}
  3. Unit: m2/N or Pa-1 in SI system.
  4. Dimensions: [L1M-1T2]

Question 23.
What is modulus of rigidity? Derive an expression for it.
Answer:
Definition: It is defined (is the ratio of shear stress to shear strain within elastic limit.
It is denoted by ‘η’.
Unit: N/m2 or Pa in SI system.
Dimension: [L-1M1T-2]

Expression for modulus of rigidity:

Consider a solid cube as shown in the figure.

Let, F = Tangential force
A = Cross sectional area
∆l = Relative displaced length
l = Original length
θ = Shear strain
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 15
[Note: Displacement of upper surface is exaggerated for explanation.]
The forces applied on the block is subjected to a shear stress,
Shearing stress = F/A
The comer angle which changes by a small amount θ (expressed in radian) is given by,
Shearing strain = \frac{\Delta l}{l} ≈ θ
From definition,
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 16

Question 24.
What does modulus of rigidity indicate?
Answer:
Modulus of rigidity indicates resistance offered by solid to change in its shape.

Question 25.
Explain the change of diameter of a wire when it is stretched and compressed.
Answer:
i. When a wire is fixed at one end and a force is applied at its free end so that the wire gets stretched, length of the wire increases and at the same time, its diameter decreases, i.e., the wire becomes longer and thinner as shown in figure.
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 17
[Note: Linear expansion ∆l is exaggerated far explanation.]

ii. If equal and opposite forces are applied to an object along its length inwards, the object gets compressed. There is a decrease in dimensions along its length and at the same time there is an increase in its dimensions perpendicular to its length. When length of the wire decreases, its diameter increases.
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 18

[Note: Compression of wire ∆l is exaggerated for explanation.]

Question 26.
Derive expression for Poisson’s ratio.
Answer:
i. Let,
L = original length
l = increase/decrease in length
D = original diameter
d = change in diameter

ii. The ratio of change in dimensions to original dimensions in the direction of the applied force is called linear strain.
Linear strain = \frac{l}{\mathrm{~L}} …. (1)

iii. The ratio of change in dimensions to original dimensions in a direction perpendicular to the applied force is called lateral strain.
Lateral strain = \frac{\mathrm{d}}{\mathrm{D}} ….(2)

iv. Poisson’s ration,
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 19

Question 27.
A wire of length 20 m and area of cross section 1.25 × 10-4 m2 is subjected to a load of 2.5 kg. (1 kg wt = 9.8 N). The elongation produced in wire is 1 × 10-4 m. Calculate Young’s modulus of the material.
Solution:
L = 20 m, A = 1.25 × 10-4m2,
F = mg = 2.5 × 9.8 N, l = 10-4 m
Formula Y = \frac{\mathrm{FL}}{\mathrm{Al}}
To find: Young’s modulus (Y)
Calculation: From formula,
Y = \frac{2.5 \times 9.8 \times 20}{1.25 \times 10^{-4} \times 10^{-4}} = 3.92 × 1010Nm-2
Answer: The Young’s modulus of the material is 3.92 × 1010 Nm-2.

Question 28.
A wire of diameter 0.5 mm and length 2 m is stretched by applying a force of 2 kg wt. Calculate the increase in length of the wire, (g = 9.8 m/s2, Y = 9 × 1010 N/m2)
Solution:
Given:
L = 2 m, F = 2 kg wt, d = 0.5 mm = 5 × 10-4 m,
∴ r = \frac{\mathrm{d}}{2} = 2.5 × 10-4 m.
Y = 9 × 1010 N/m2, g = 9.8 m/s2
To find: Increase in length (l)
Formula: Y = \frac{\mathrm{FL}}{\mathrm{Al}}=\frac{\mathrm{MgL}}{\pi \mathrm{r}^{2} l}
Calculation:
From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 20
Answer:
The increase in length of the wire is 2.218 × 10-3 m.

Question 29.
A brass wire of length 4.5 m with cross-section area of 3 × 10-5 m2 and a copper wire of length 5.0 m with cross section area 4 × 10-5 m2 are stretched by the same load. The same elongation is produced in both the wires. Find the ratio of Young’s modulus of brass and copper.
Solution:
LB = 4.5 m, AB = 3 × 10-5 m2
LC = 5 m, AC = 4 × 10-5 m2 lB = C, FB = FC
To find: Ratio of Young’s modulus \left(\frac{Y_{B}}{Y_{C}}\right)
Formula: Y = \frac{\mathrm{FL}}{\mathrm{Al}}
Calculation: For brass,
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 21
= 1.2
Answer:
The ratio of Young’s modulus of brass and copper is 1.2 : 1.

Question 30.
The length of wire increases by 9 mm when weight of 2.5 kg is hung from the free end of wire. If all conditions are kept the same and the radius of wire is made thrice the original radius, find the increase in length.
Solution:
Given; l1 = 9mm = 9 × 10-3m,
M = 2.5 kg, r2 = 3r1,
Y1 = Y2 = Y (material is same)
To find: Increase in length (l2)
Formula: Y = \frac{\mathrm{FL}}{\mathrm{Al}}
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 22
Answer:
The longitudinal strain produced in 1st wire is

Question 31.
Two wires of diameter 0.25 cm, one made of steel and the other made of brass are loaded as shown in the figure. The unloaded length of steel wire is 1.5 m and that of brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.(Ys = 2.0 × 1011 Nm-2, YB = 0.91 × 1011 Nm-2) (NCERT)
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 23
Solution:
Given: D = 0.25 cm = 0.25 × 10-2 m,
LS = 1.5 m, LB = 1 m,
YS = 2.0 × 1011 Nm-2,
YB = 0.91 × 1011 Nm-2
To find: Elongations of brass wire (lB)
Elongations of steel wire (lS)

Formula: Y = \frac{\mathrm{FL}}{\mathrm{Al}}

Calculation: Since, A = \frac{\pi \mathrm{D}^{2}}{4}
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 24
Answer:
The elongation of the steel wire is 1.5 × 10-4 m and that of brass wires is 1.32 × 10-4 m.

Question 32.
One end of steel wire is fixed to a ceiling and load of 2.5 kg is attached to the free end of the wire. Another identical wire is attached to the bottom of load and another load of 2.0 kg, is attached to the lower end of this wire as shown in the figure. Compute the longitudinal strain produced in both the wires, if the cross-sectional area of wires is 10-4m2, (Ysteel = 20 × 1010N/m2)
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 25
Solution:
Given: M1 = 2.5 kg, M2 = 2kg, A = 10-4m2, Ysteel = 20 × 1010 N/m2, L1 = L2 = L
To find: Longitudinal strain of 1st wire (Strain1).
Longitudinal strain of 2nd wire (Strain2)
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 26
Answer:
The longitudinal strain produced in 1st wire is 1.225 × 10-6 and in 2nd wire is 2.205 × 10-6

Question 33.
A steel wire having cross-sectional area 2 mm2 is stretched by 10 N. Find the lateral strain produced in the wire. (Given: Y for steel = 2 × 1011 N/m2, Poisson’s ratio σ = 0.29)
Solution:
Given: A = 2 mm2 = 2 × 10-6 m2,
F = 10 N, Ystee; = 2 × 1011 N/m2, σ = 0.29

To find: Lateral strain
Formulae:
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 27
Calculation: From formula (i),
longitudinal stress = \frac{10}{2 \times 10^{-6}}
= 5 × 106 N/m2
From formula (ii),
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 28
From formula (iii),
lateral strain = σ × longitudinal strain
= 0.29 × 2.5 × 10-5
∴ lateral strain = 7.25 × 10-6
Answer:
Lateral strain produced in the wire is 7.25 × 10-6.

Question 34.
A brass wire of radius 1 mm is loaded by a mass of 31.42 kg. What would be the decrease in its radius? (Y = 9 × 1010 N/m2, Poisson’s ratio σ = 0.36)
Solution:
Given: R = 1 mm = 1 × 10-3 m, M = 31.42 kg, Y = 9 × 1010 N/m2, σ = 0.36
To find: Decrease in radius (r)

Formulae:

i. Y = \frac{\mathrm{FL}}{\mathrm{Al}}
ii. σ = \frac{\mathrm{Lr}}{l \mathrm{R}}

Calculation: From formula (i),
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 29
Answer:
The decrease in radius of the brass wire would be 3.92 × 10-7 m

Question 35.
A metal cube of side 1 m is subjected to a force. The force acts normally on the whole surface of cube and its volume changes by 1.5 × 10-5 m3. The bulk modulus of metal is 6.6 × 1010 N/m2. Calculate the change in pressure.
Solution:
Given: L = 1 m, dV = 1.5 × 10-5 m3,
K = 6.6 × 1010 N/m2.
To find: Change in pressure (dP)
Formula: K = V\frac{\mathrm{dP}}{\mathrm{dV}}
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 30
Answer:
The change in pressure is 9.9 × 105 N/m2.

Question 36.
Determine the volume contraction of solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 × 106 P.a. (Bulk modulus of copper = 140 × 109 pa)
Solution:
Given: L = 10 cm =0.1 m, ∆P = 7 × 106 Pa, K = 140 × 109 pa
To find: Volume contraction (dV)
Formula: K = V × \frac{\mathrm{dP}}{\mathrm{dV}}
Calculation: From formula,
dV = \mathrm{L}^{3} \times \frac{\mathrm{dP}}{\mathrm{K}} = (0.1)3 × \frac{7 \times 10^{6}}{140 \times 10^{9}}
∴ dV = 5 × 10-8 m3
Answer:
The volume contraction of solid copper cube is 5 × 10-8 m3

Question 37.
Calculate the modulus of rigidity of a metal, if a metal cube of side 40 cm is subjected to a shearing force of 2000 N. The upper surface is displaced through 0.5 cm with respect to the bottom. Calculate the modulus of rigidity of the metal.
Solution:
Given: L = 40 cm = 0.4 m,
F = 2000 N = 2 × 103N
l = 0.5 cm = 0.005 m, A = L2 = 0.16 m2
To find: Modulus of rigidity (η)

Formulae:

i. θ = \frac{l}{\mathrm{~L}}
ii. η = \frac{\mathrm{F}}{\mathrm{A} \theta}

Calculation:

From formula (i),
θ = \frac{0.005}{0.4} = 0.0125
From formula (ii),
η = \frac{2 \times 10^{3}}{0.16 \times 0.0125} = 1 × 106 N/m2
Answer:
The modulus of rigidity of the metal cube is 1 × 106 N/m2.

Question 38.
A piece of copper having a rectangular cross-section of 15.2 mm × 19.1 mm is pulled in tension with 44500 N forces producing only elastic deformation. Calculate the resulting strain. (Rigidity modulus of copper = 42 × 109 N m-2)
Solution:
Given: A = 15.2 × 19.14 × 10-6 m2,
F = 44500 N, η = 42 × 109 N m-2
To find: Strain (θ)
Formula: η = \frac{\mathrm{F}}{\mathrm{A} \theta}

Calculation:
From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 31
Answer:
The strain produced in the piece of copper is 3.64 × 10-3

Question 39.
A copper metal cube has each side of length 1 m. The bottom edge of cube is fixed and tangential force 4.2 × 108 N is applied to top surface. Calculate the lateral displacement of the top surface, if modulus of rigidity of copper is 14 × 1010 N/m2.
Solution:
Given: L = h = 1 m, F = 4.2 × 108 N, η = 1.4 × 1011 N/m2
To find: Lateral displacement (x)
Formula: η = \frac{\mathrm{F}}{\mathrm{A} / \theta} = \frac{\mathrm{Fh}}{\mathrm{Ax}}
Calculation: From formula,
x = \frac{\mathrm{Fh}}{\mathrm{A\eta}}
∴ x = \frac{4.2 \times 10^{8} \times 1}{(1 \times 1) \times 1.4 \times 10^{11}} = 3 × 10-3 m
∴ x = 3 mm
Answer:
The lateral displacement of top is 3 mm.

Question 40.
The area of the upper face of a rectangular block is 0.5 m × 0.5 m and the lower face is fixed. The height of the block is 1 cm. A shearing force applied at the top face produces a displacement of 0.0 15 mm. Find the strain and shearing force. (Modulus of rigidity: η = 4.5 × 1010 N/m2)
Solution:
Given: A = 0.5 m × 0.5 m = 0.25 m2,
h = 1 cm = 10-2m,
x = 0.015 mm = 15 × 10-6m
η = 4.5 × 1010 N/m2
To find: Strain (θ). Shearing force (F)

Formulae:

i. θ = \frac{\mathrm{x}}{\mathrm{h}}
ii. F = ηAθ

Calculations:

Using formula (i),
θ = \frac{15 \times 10^{-6}}{10^{-2}} = 1.5 × 10-3
Using formula (ii),
F = 4.5 × 1010 × 0.25 × 1.5 × 10-3
= 1.688 × 107 N
Answer:
Shearing force is 1.688 × 107 N and strain is 1.5 × 10-3

Question 41.
Explain the behaviour of metal wire under increasing load.
Answer:
Consider a metal wire suspended vertically from a rigid support and stretched by applying load to its lower end. The load is gradually increased in small steps until the wire breaks. The elongation produced in the wire is measured during each step. Stress and strain are noted for each load and a graph is drawn by taking tensile strain along X-axis and tensile stress along Y-axis. It is a stress-strain curve as shown in the figure.
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 32

  1. Proportional limit: The initial part of the graph is a straight line OA. This is the region in which Hooke’s law is obeyed and stress is directly proportional to stain. The straight line portion ends at A. The stress at this point is called proportional limit.
  2. Yield point: If the load is further increased till point B is reached, stress and strain are no longer proportional and Hooke’s law is not valid. If the load is gradually removed starting at any point between O and B. The curve is retracted until the wire regains its original length. The change is reversible. The material of the wire shows elastic behaviour in the region OB. Point B is called the yield point. It is also known as the elastic limit.
  3. Permanent Set: When the stress is increased beyond point B, the strain continues to increase. If the load is removed at any point beyond B, for example (at C), the material does not regain its original length. It follows the line CE. Length of the wire when there is no stress is greater than the original length. The deformation is irreversible and the material has acquired a permanent set.
  4. Fracture point: Further increase in load causes a large increase in strain for relatively small increase in stress, until a point D is reached at which fracture takes place. The material shows plastic flow or plastic deformation from point B to point D. The material does not regain its original state when the stress is removed. The deformation is called plastic deformation.

Question 42.
Stress-strain curve for two materials A and B are shown in the figure. The graphs are drawn to the same scale.

  1. Which material has greater Young’s modulus?
  2. Which of the two is the stronger material? (NCERT)

Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 33
Answer:

  1. For a given strain, stress for A is more than that of B. Hence, Young’s modulus (= stress/strain) is greater for A than that of B.
  2. Material A is stronger than B because A can bear greater stress before the breaking of the wire.

Question 43.
Figure shows the stress-strain curve for a given material. What are

  1. Young’s modulus and
  2. approximate yield strength for this material? (NCERT)

Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 34
Answer:

  1. The graph, implies stress of 150 × 106 N m-2 corresponds to a strain of 0.002. Therefore, Young’s modulus is,
    Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 35
  2. The yield strength for the material is less than 300 × 106 N m-2, i.e.. 3 × 108 N m-2 and greater than 2.5 × 108 N m-2.

Question 44.
Explain the following terms:

  1. Ductile
  2. Malleable

Answer:

  1. Metals such as copper, aluminium, wrought iron, etc. have large plastic range of extension. They lengthen considerably and undergo plastic deformation till they break. They are called ductile.
  2. Metals such as gold, silver which can be hammered into thin sheets are called malleable.

Question 45.
Define strain energy.
Answer:
The elastic potential energy gained by a wire during elongation b a stretching force is called as strain energy.

Question 46.
A steel wire is acted upon by a load of 10 N. Calculate the extension produced in the wire, if the strain energy stored in the wire is 1.1 × 10-3 J.
Solution:
Given: F = 10 N, Strain energy =1.1 × 10-3 J,
To find: Extension (l)
Formula: W = \frac{1}{2} × F × l
Calculation:
From formula,
l = \frac{2 \mathrm{~W}}{\mathrm{~F}} = \frac{2 \times 1.1 \times 10^{-3}}{10} = 2.2 × 10-4 m.
Answer:
The extension produced in the wire is 2.2 × 10-4 m.

Question 47.
Calculate the strain energy per unit volume in a brass wire of length 3 m and area of cross-section 0.6 mm2 when it is stretched by 3 mm and a force of 6 kg-wt is applied to its free end.
Solution:
Given: L = 3 m, F = 6 kg wt = 6 × 9.8N = 58.8N, A = 0.6 mm2 = 0.6 × 10-6 m2, l = 3 mm = 3 × 10-3 m
To find: Strain energy per unit volume (u)

Formulae:

i. Stress = \frac{F}{A}
ii. Strain = \frac{l}{L}
iii. u = \frac{1}{2} × Stress × Strain

Calculation:

From formula (i),
Stress = \frac{F}{A} = \frac{58.8}{0.6 \times 10^{-6}} = 98 × 106 N/m2
From formula (ii),
Strain = \frac{l}{L} = \frac{3 \times 10^{-3}}{3} = 10-3
From formula (iii),
u = \frac{1}{2} × Stress × Strain
= \frac{1}{2} × 98 × 106 × 10-3
u = 49 × 103 J/m3
Answer:
Strain energy per unit volume in the brass wire is 49 × 103 J/m3

Question 48.
A steel wire of diameter 1 × 10-3 m is stretched by a force of 20 N. Calculate the strain energy per unit volume. (Ysteel = 2 × 1011 N/m2)
Solution:
Given: d = 1 × 10-3 m, r = 5 × 10-4 m, ysteel = 2 × 1011 N/m2
To find: Strain energy per unit volume
Formula: Strain energy per unit volume
= \frac{1}{2} × \frac{\text { (stress) }^{2}}{\mathrm{Y}}
Calculation:
From formula.
Strain energy per unit volume
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 36
Answer:
The strain energy per unit volume of the steel wire is 1621 J.

Question 49.
A uniform steel wire of length 3 m and area of cross section 2 mm2 is extended through 3 mm. Calculate the energy stored in the wire, if the elastic limit is not exceeded. (Ysteel = 20 × 1010 N/m2)
Solution:
Given: L = 3 m, A = 2 mm2 = 2 × 10-6 m2,
l = 3 mm = 3 × 10-3 m,
Ysteel = 20 × 1010 N/m2
To find: Energy stored (U)
Formula: W = \frac{1}{2} × F × l
Calculation: Since, Y = \frac{\mathrm{FL}}{\mathrm{Al}}
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 37
Answer:
The energy stored in the steel wire is 0.6 J.

Question 50.
Explain the following terms:
i. Hardness
ii. Strength
iii. Toughness
Answer:

i. Hardness:

  1. Hardness is the property of a material which enables it to resist plastic deformation.
  2. Hard materials have little ductility and they are brittle to some extent.
  3. The term hardness also refers to stiffness or resistance to bending, scratching, abrasion or cutting.
  4. It is the property of a material which gives it the ability to resist permanent deformation when a load is applied to it.
  5. The greater the hardness, greater is the resistance to deformation.
  6. Hardness of material is different from its strength and toughness.
  7. The most well known example for hard material is diamond, while metal with very low hardness is aluminium.

ii. Strength:

  1. If a force is applied to a body, it produces deformation in it.
  2. Higher is the force required for deformation, the stronger is the material, i.e., the material has more strength.
  3. Steel has high strength whereas plasticine clay is not strong because it gets easily deformed even by a small force.

iii. Toughness:

  1. Toughness is the ability of a material to resist fracturing when a force is applied to it.
  2. Plasticine clay is relatively tough as it can be stretched and deformed due to applied force without breaking.

Question 51.
Explain the concept of frictional force.
Answer:

  1. Whenever the surface of one body slides over another, each body exerts a certain amount of force on other body.
  2. These forces are tangential to the surfaces. The force on each body is opposite to the direction of motion between two bodies.
  3. It prevents or opposes the relative motion between two bodies.
  4. It is common experience that an object placed on any surface does not move easily when a small force is applied to it.
  5. This is because of certain force of opposition acting between the surface of the object and the surface on which it is placed.
  6. To initiate any motion between pair of surfaces, we need a certain minimum force. Also, after the motion begins, it is constantly opposed by some natural force.
  7. This mechanical force between two solid surfaces in contact with each other is called as frictional force.

Question 52.
Explain few examples of friction.
Answer:

  1. A rolling ball comes to rest after covering a finite distance on playground because of friction.
  2. Our foot ware is provided with designs at the bottom of its sole so as to produce force of opposition to avoid slipping. It is difficult to walk without such opposing force. When we try to walk fast on polished flooring at home with soap water spread on it. There is a possibility of slipping due to lack of force of friction.
  3. Relative motion between solids and fluids (i.e. liquids and gases) is also opposed naturally by friction, eg.: a boat on the surface of water experiences opposition to its motion.

Question 53.
Explain the origin of friction.
Answer:

  1. If smooth surfaces are observed under powerful microscope, many irregularities and projections are observed.
  2. Friction arises due to interlocking of these irregularities between two surfaces in contact.
  3. The surfaces can be made extremely smooth by polishing to avoid irregularities but then case also, friction does not decrease but may increase.
  4. Hence the interlocking of irregularities is not the real cause of friction.
  5. According to modem theory, cause of friction is the force of attraction between molecules of two surfaces in actual contact in addition to the. force due to the interlocking between the two surfaces.
  6. When one body is in contact with another body, the real microscopic area in contact is very small due to irregularities in contact.
    Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 38
  7. Due to small area, pressures at points of contact is very high. Hence there is strong force of attraction between the surfaces in contact.
  8. When the surfaces in contact become more and more smooth, the actual area of contact goes on increasing.
  9. Due to this, the force of attraction between the molecules increases and hence the friction also increases.

Question 54.
State the following terms:

  1. Cohesive force
  2. Adhesive force

Answer:

  1. When two Surfaces are of the same material, the force of attraction between them is called cohesive force.
  2. When two surfaces are of different materials, the force of attraction between them is called adhesive force.

Question 55.
Explain the concept of static friction.
Answer:

  1. Consider a wooden block placed on a horizontal surface as shown in the figure and small horizontal force F is applied to it.
    Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 39
  2. The block does not move with this force as it cannot overcome the frictional force between the block and horizontal surface.
  3. In this case the force of static friction is equal to F and balances it.
  4. The frictional force which balances applied force when the body is static is called force of static friction. In other words, static friction prevents sliding motion.
  5. If we keep increasing F, a stage will come
    • For F < Fmax, the force of static friction is equal to F.
    • when for F = Fmax, the object will start moving.
    • For F ≥ Fmax, the kinetic friction comes into play.
  6. Static friction opposes impending motion i.e. the motion that would take place in absence of frictional force under the applied force.

Question 56.
Define limiting force of friction.
Answer:
Just before the body starts sliding over another body, the value of frictional force is maximum, it is called as limiting force of friction.

Question 57.
Explain the concept of kinetic friction.
Answer:

  1. Once the sliding of block on the surface starts the force of friction decreases.
  2. The force required to keep the body sliding steadily is thus less than the force required to just start its sliding.
  3. The force of friction that comes into play when a body is in steady state of motion over another surface is called kinetic fòrce of friction.
  4. Friction between two surfaces in contact when one body is actually sliding over the other body, is called kinetic friction or dynamic friction.

Question 58.
Why ball bearings are used in machines?
Answer:

  1. For same pair of surfaces, the force of static friction is greater than the force of kinetic friction while the force of kinetic friction is greater than force of rolling friction.
  2. As ball bearing undergo rolling friction and rolling friction is the minimum, ball bearings are used to reduce friction in parts of machines to increase its efficiency.

Question 59.
The coefficient of static friction between a block of mass 0.25 kg and a horizontal surface is 0.4. Find the horizontal force applied to it.
Solution:
Given: μs = 0.4, m = 0.25 kg, g = 9.8 m/s2
To find: Force (FL)
Formula: FL = μsN = μs(mg)
Calculation: From formula,
FL = 0.4 × 0.25 × 9.8 = 0.98 N
Answer:
The horizontal force applied to it is 0.98 N.

Question 60.
Calculate the force required to move a block of mass 20 kg resting on a horizontal surface, if μs = 0.3 and g = 9.8 m/s2.
Solution:
Given: m = 20 kg, μs = 0.3, g = 9.8 m/s2
To find. Force required (F)
Formula: FS = μsN = μsmg
Calculation: From formula,
FS = 3 × 20 × 9.8 = 58.8N
Answer:
The force required to move the block is 58.8 N.

Question 61.
A block of mass 40 kg resting on a horizontal surface just begins to slide when a horizontal force of 120 N is applied to it. Once the motion starts, It can be maintained by a force of 80 N. Determine the coefficients of static friction and kinetic friction (g = 9.8 m/s2)
Solution:
Given: FL= 120N, Fk = 80N, m = 40 kg, g = 9.8 m/s2

To find:

i. Coefficient of static friction (μs)
ii. Coefficient of kinetic friction (μk)

Formulae:

i. μs = \frac{\mathrm{F}_{\mathrm{L}}}{\mathrm{N}}
ii. μk = \frac{\mathrm{F}_{\mathrm{k}}}{\mathrm{N}}

Calculation:

From formula (i) we get.
N = mg = 40 × 9.8 = 392 N
∴ μs = \frac{F_{L}}{N} = \frac{120}{392} = 0.306
From formula (ii) we get,
∴ μk = \frac{F_{k}}{N} = \frac{80}{392} = 0.204
Answer:

  1. The coefficient of static friction is 0.306.
  2. The coefficient of kinetic friction is 0.204.

Question 62.
A 20 kg metal block is placed on a horizontal surface. The block just begins to slide when horizontal force of 100 N is applied to it. Calculate the coefficient of static friction. If coefficient of kinetic friction is 0.4, then find minimum force to maintain its uniform motion.
Solution:
Given: m = 20 kg, FL = 100 N, μk = 0.4

To find:

i. Coefficient of static friction (μs)
ii. Minimum force required (Fk)

Formulae:

i. μs = \frac{F_{L}}{N} = \frac{\mathrm{F}_{\mathrm{L}}}{\mathrm{mg}}
ii. μs = \frac{F_{k}}{N}

Calculation:

From formula (i),
μs = \frac{100}{20 \times 9.8} = 0.5102
From formula (ii),
Fk = μkN = μk × mg = 0.4 × 20 × 9.8
∴ Fk = 78.4 N
Answer:

  1. The coefficient of static friction is 0.5102.
  2. The minimum force required is 78.4 N.

Question 63.
The Mariana trench is located in the Pacific Ocean and at one place it is nearly 11 km beneath the surface of water. The water pressure at the bottom of the trench is about 1.1 × 108 Pa. A steel ball of initial volume 0.32 m3 is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom? (K = 1.6 × 1011 N/m2)
Answer:
Given: V = 0.32 m3, K = 1.6 × 1011 N/m2,
PW= 1.1 × 108 Pa, Patm = 1.01 × 105 Pa
∴ dP = PW – Patm = 1.1 × 108 – 1.01 × 105 ≈ 1.1 × 108 Pa
As, bulk modulus is given as,
K = V × \frac{d P}{d V}
∴ dV = \frac{\mathrm{V} \times \mathrm{dP}}{\mathrm{K}} = \frac{\left(1.1 \times 10^{8}\right) \times 0.32}{1.6 \times 10^{11}}
∴ dV = 2.2 × 10-4 m3
The change in the volume of the ball when it reaches the bottom will be 2.2 × 10-4 m3.

Question 64.
Two spheres A and B having same volume are dropped from same height in ocean. Sphere A is made up of brass and sphere B is made up of steel. Will there be same change in volume of spheres at a certain depth inside water? What will be the ratio of change in volumes of the two spheres at this depth?
Answer:

  1. Brass and copper have different elastic moduli. Hence, there won’t be same change in the volume of spheres at a certain depth inside water.
  2. As two spheres are dropped from same height and are at same depth in water pressure exerted on them remains same.
    ∴ dPA = dPB = dP
    VA = VB = V
  3. If dVA and dVB be the change in volume of two spheres A and B then,
    dVA = \frac{\mathrm{V} \mathrm{dP}}{\mathrm{K}_{\mathrm{A}}} and dVB = \frac{\mathrm{V} \mathrm{dP}}{\mathrm{K}_{\mathrm{B}}}
  4. Ratio of change in volume,
    Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 40
    where, KA and KB are bulk modulus of material of spheres A and B respectively.

Question 65.
What is the basis of deciding the thickness of metallic ropes used in crane to lift the heavy weight?
Answer:

  1. The thickness of the metallic ropes used in cranes is decided on the basis of the elastic limit of the material of the rope and the factor of safety.
  2. To lift a load upto 104 kg, the rope is made for a factor of safety of 10.
  3. It should not break even when a load of (original load × factor of safety = 104 × 10) 105 kgf i.e., 105 × 9.8 N is applied on it.
  4. If ‘r’ is the radius of the rope, then maximum stress = \frac{10^{5}}{\pi r^{2}}.
  5. The maximum stress (ultimate stress) should not exceed the breaking stress (5 to 20 × 108 N/m2) as well as elastic limit of steel Ys(30 × 107 N/m2).
    Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 41
  6. In order to have flexibility, the rope is made up of large number of thin wires twisted together.

Question 66.
Multiple choice questions

Which one of the following substances possesses the highest elasticity?
(A) Rubber
(B) Glass
(C) Steel
(D) Copper
Answer:
(C) Steel

Question 1.
S.I unit of stress is
(A) Newton/ metre
(B) Newton/ metre2
(C) Newton2/metre
(D) Newton/metre3
Answer:
(B) Newton/ metre2

Question 2.
A wire is stretched to double of its length. The strain is
(A) 2
(B) 1
(C) zero
(D) 0.5
Answer:
(B) 1

Question 3.
A and B are two steel wires and the radius of A is twice that of B. If they are stretched by the same load, then the stress on B is ____.
(A) four times that of A
(B) two times that of A
(C) three times that of A
(D) same as that of A
Answer:
(A) four times that of A

Question 4.
Two wires of the same material have radii rA and rB respectively. The radius of wire A is twice the radius of wire B. If they are stretched by same load then stress on wire B is ___
(A) equal to that of A
(B) half that of A.
(C) two times that of A.
(D) four times that of A.
Answer:
(D) four times that of A.

Question 5.
The length of a wire increases by 1% by a load of 2 kg wt. The linear strain produced in the wire will be
(A) 0.02
(B) 0.001
(C) 0.01
(D) 0.002
Answer:
(C) 0.01

Question 6.
A wire of length ‘L’, radius ‘r’ when stretched with a force ‘F’ changes in length by l’. What will be the change in length of a wire of same material having length ‘2L’ radius ‘2r and stretched by a force ‘2F’?
(A) l/2
(B) l
(C) 2l
(D) 4l
Answer:
(B) l

Question 7.
A force of 100 N produces a change of 0.1% in a length of wire of area of cross section 1 mm2. Young’s modulus of the wire is ____
(A) 105 N/m2
(B) 109 N/m2
(C) 1011 N/m2
(D) 1012 N/m2
Answer:
(C) 1011 N/m2

Question 8.
A copper wire (Y = 1 × 1011 N/m2) of length 6 m and a steel wire (Y = 2 × 1011 N/m2) of length 4 m each of cross-section 10-5 m2 are fastened end to end and stretched by a tension of 100 N. The elongation produced in the copper wire is
(A) 0.2 mm
(B) 0.4 mm
(C) 0.6 mm
(D) 0.8 mm
Answer:
(C) 0.6 mm

Question 9.
When a force is applied to the free end of a metal wire, metal wire undergoes
(A) longitudinal and lateral extension.
(B) longitudinal extension and lateral contraction.
(C) longitudinal contraction and lateral extension.
(D) longitudinal and lateral contraction.
Answer:
(B) longitudinal extension and lateral contraction.

Question 10.
A force of 1 N doubles the length of a cord having cross-sectional area 1 mm2. The Young’s modulus of the material of cord is
(A) 1 N m-2
(B) 0.5 × 106 N m-2
(C) 106 N m-2
(D) 2 × 106 N m-2
Answer:
(C) 106 N m-2

Question 11.
In equilibrium the tensile stress to which a wire of radius r is subjected by attaching a mass ‘m’ is ____.
(A) \frac{\mathrm{mg}}{\pi \mathrm{r}}
(B) \frac{\mathrm{mg}}{2 \pi \mathrm{r}}
(C) \frac{\mathrm{mg}}{\pi \mathrm{r}^{2}}
(D) \frac{\mathrm{mg}}{2 \pi \mathrm{r}^{2}}
Answer:
(C) \frac{\mathrm{mg}}{\pi \mathrm{r}^{2}}

Question 12.
When load is applied to a wire, the extension is 3 mm, the extension in the wire of same length but half the radius by the same load is
(A) 0.75 mm
(B) 6 mm
(C) 1.5 mm
(D) 12.0 mm
Answer:
(D) 12.0 mm

Question 13.
The S.I. unit of compressibility is ____.
(A) \frac{\mathrm{m}^{2}}{\mathrm{~N}}
(B) Nm2
(C) \frac{\mathrm{N}}{\mathrm{m}^{2}}
(D) \frac{\mathrm{kg}}{\mathrm{m}^{3}}
Answer:
(A) \frac{\mathrm{m}^{2}}{\mathrm{~N}}

Question 14.
When the pressure applied to one litre of a liquid is increased by 2 × 106 N/m2. Its volume decreases by 1 cm3. The bulk modulus of the liquid is
(A) 2 × 109 N/m2
(B) 2 × 103 dyne/cm2
(C) 2 × 103 N/m2
(D) 0.2 × 109 N/m2
Answer:
(A) 2 × 109 N/m2

Question 15.
A cube of aluminium of each side 0.1 m is subjected to a shearing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be
(A) 0.02
(B) 0.1
(C) 0.005
(D) 0.002
Answer:
(D) 0.002

Question 16.
A wire has Poisson’s ratio of 0.5. It is stretched by an external force to produce a longitudinal strain of 2 × 10-3. If the original diameter was 2 mm, the final diameter after stretching is
(A) 2.002 mm
(B) 1.998 mm
(C) 0.98 mm
(D) 1.999 mm
Answer:
(B) 1.998 mm

Question 17.
The compressibility of a substance is the reciprocal of ___.
(A) Young’s modulus
(B) Bulk modulus
(C) Modulus of rigidity
(D) Poisson’s ratio
Answer:
(B) Bulk modulus

Question 18.
For which of the following is the modulus of rigidity highest?
(A) Aluminium
(B) Quartz
(C) Rubber
(D) Water
Answer:
(B) Quartz

Question 19.
An elongation of 0.2% in a wire of cross-section 10-4 m2 causes a tension of 1000 N. Then its Young’s modulus is
(A) 6 × 108 N/m2
(B) 5 × 109 N/m2
(C) 108 N/m2
(D) 107 N/m2
Answer:
(B) 5 × 109 N/m2

Question 20.
Within the elastic limit, the slope of graph between stress against strain gives ____
(A) compressibility
(B) Poisson’s ratio
(C) modulus of elasticity
(D) extension
Answer:
(C) modulus of elasticity

Question 21.
Solids which break or rupture before the elastic limits are called
(A) brittle
(B) ductile
(C) malleable
(D) elastic
Answer:
(A) brittle

Question 22.
Substances which break just after their elastic limit is reached are ___.
(A) ductile
(B) brittle
(C) malleable
(D) plastic
Answer:
(B) brittle

Question 23.
Which of the following substances is ductile?
(A) glass
(B) high carbon steel
(C) Steel
(D) copper
Answer:
(D) copper

Question 24.
The Young’s modulus of a material is 1011 Nm-2 and its Poisson’s ratio is 0.2. The modulus of rigidity of the material is
(A) 0.42 × 1011 N/m2
(B) 0.42 × 1014 N/m2
(C) 0.42 × 1016 N/m2
(D) 0.42 × 1018 N/m2
Answer:
(A) 0.42 × 1011 N/m2

Question 25.
Two pieces of wire A and B of the same material have their lengths in the ratio 1:2, and their diameters are in the ratio 2:1. If they are stretched by the same force, their elongations will be in the ratio
(A) 2 : 1
(B) 1 : 4
(C) 1 : 8
(D) 8 : 1
Answer:
(C) 1 : 8

Question 26.
Young’s modulus of material of wire is ‘Y’ and strain energy per unit volume is ‘E’, then the strain is
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 42
Answer:
(C) \sqrt{\frac{2 \mathrm{E}}{\mathrm{Y}}}

Question 27.
Strain energy per unit volume is given by
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 43
Answer:
(A) \frac{1}{2} \times \frac{(\text { stress })^{2}}{\mathrm{Y}}

Question 28.
The strain energy per unit volume of the wire under increasing load is
(A) \frac{1}{2} × (stress)2 × strain
(B) \frac{1}{2} × stress × (strain)2
(C) 0.5 × stress × strain
(D) 0.5 × (strain)2 × \frac{1}{Y}
Answer:
(C) 0.5 × stress × strain

Question 29.
The energy stored per unit volume of a strained wire is
(A) \frac{1}{2} × (load) × (extension)
(B) \frac{1}{2} × \frac{Y}{(\text { strain })^{2}}
(C) \frac{1}{2} × Y × (strain)2
(D) Stress × strain
Answer:
(C) \frac{1}{2} × Y × (strain)2

Question 30.
If work done in stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of same material, but with double the radius and half the length by 1 mm in joule is
(A) 1/4
(B) 4
(C) 8
(D) 16
Answer:
(D) 16

Question 31.
When the load on a wire is slowly increased from 3 to 5 kg wt, the elongation increases from 0.61 to 1.02 mm. The work done during the extension of wire is
(A) 0.16 J
(B) 0.016 J
(C) 1.6 J
(D) 16 J
Answer:
(B) 0.016 J

Question 32.
A body lies on a table. Its weight is balanced by the ___.
(A) frictional force
(B) normal force
(C) force causing motion on the body
(D) surface of the table
Answer:
(B) normal force

Question 33.
The friction that exists between the surface of two bodies in contact when one body is sliding over the other, is called ___.
(A) rolling friction
(B) friction
(C) kinetic friction
(D) static friction.
Answer:
(C) kinetic friction

Question 34.
Limiting force of static friction does NOT depend on
(A) actual area of contact.
(B) geometrical area of contact.
(C) interlocking between surfaces in contact.
(D) intermolecular forces of attraction between molecules of the two surfaces.
Answer:
(C) interlocking between surfaces in contact.

Question 35.
In case of coefficient of static friction (µs), kinetic friction (µk) and rolling friction (µr), which of the following relation is true
(A) µs > µk > µr
(B) µs > µr > µk
(C) µr > µs > µk
(D) µr > µk > µs
Answer:
(A) µs > µk > µr

Question 36.
A body of weight 50 N is placed on a smooth surface. If the force required to move the body on the surface is 30 N, the coefficient of friction is
(A) 0.6
(B) 0.4
(C) 0.3
(D) 0.8
Answer:
(A) 0.6

Question 37.
A wooden block of 50 kg is at rest on the table. A force of 70 N is required to just slide the block. The coefficient of static friction is
(A) \frac{6}{7}
(B) \frac{5}{7}
(C) \frac{7}{35}
(D) \frac{1}{7}
Answer:
(D) \frac{1}{7}

Question 38.
When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + l). The elastic potential energy stored in the extended wire is:
(A) \frac{1}{2}Mgl
(B) \frac{1}{2}MgL
(C) Mgl
(D) MgL
Answer:
(A) \frac{1}{2}Mgl
Hint: elastic potential energy: \frac{1}{2} × F × L = \frac{1}{2}Mgl

Question 67.
A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1 π ms-2, What will be the tensile stress that would be developed
(A) 6.2 × 106 N m-2
(B) 5.2 × 106 N m-2
(C) 3.1 × 106 N m-2
(D) 4.8 × 106 N m-2
Answer:
(C) 3.1 × 106 N m-2
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 44

Question 68.
A boy’s catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms-1. Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:
(A) 106 N m-2
(B) 104 N m-2
(C) 108 Nm-2
(D) 103 N m-2
Answer:
(A) 106 N m-2
Hint: d = 6 mm = 0.006 m, l = 42 cm = 0.42 m, ∆l = 20 cm = 0.2 m, m = 0.02 kg, v = 20 m/s
Energy stored in the catapult,
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 45

Question 69.
The stress-strain curves are drawn for two different materials X and Y. It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y. We can say that materials X and Y are likely to be (respectively),
(A) Plastic and ductile
(B) Ductile and brittle
(C) Brittle and ductile
(D) Brittle and plastic
Answer:
(C) Brittle and ductile
Hint: Ductile materials have a fracture strength lower than the ultimate Tensile strength (i.e., the points are far apart.) whereas in brittle materials, the fracture strength is equivalent to ultimate tensile strength (i.e., the points are close.)
∴ Material X is brittle and Y is ductile in nature.

Question 70.
The compressibility of water is ‘o’ per unit atmospheric pressure. The decrease in its volume ‘V’ due to atmospheric pressure ‘P’ will be
(A) \frac{\sigma \mathrm{V}}{\mathrm{P}}
(B) \frac{\sigma P}{\mathrm{~V}}
(C) σPV
(D) \frac{\sigma}{\mathrm{PV}}
Answer:
(C) σPV

Question 71.
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by ∆l on applying a force F, how much force is needed to stretch the second wire by the same amount?
(A) 9 F
(B) 6 F
(C) 4 F
(D) F
Answer:
(A) 9 F
Hint: As material is same, Young’s modulus of two wires is same.
Also, volume of both wires is same.
V1 = V2
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 46

Question 72.
A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \left(\frac{\mathrm{dr}}{\mathrm{r}}\right),is:
where negative sign indicates volume decreases with increase in pressure.
(A) \frac{\mathrm{mg}}{\mathbf{3} \mathrm{Ka}}
(B) \frac{\mathrm{mg}}{\mathrm{Ka}}
(C) \frac{\mathrm{Ka}}{\mathrm{mg}}
(D) \frac{\mathrm{Ka}}{3 \mathrm{mg}}
Answer:
(A) \frac{\mathrm{mg}}{\mathbf{3} \mathrm{Ka}}
Hint:
Bulk modulus is given as,
K = \left(\frac{-\mathrm{dP}}{\mathrm{dV} / \mathrm{V}}\right)
where negative sign indicates volume decreases with increase in pressure.
∴ Fractional decrease in volume will be,
\frac{\mathrm{dV}}{\mathrm{V}} = \frac{\mathrm{dP}}{\mathrm{K}}
If area of cross-section of cylinder is a, then,
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 47

Question 73.
Two metal wires ‘P’ and ‘Q’ of same length and material are stretched by same load. Their masses are in the ratio m1 : m2. The ratio of elongations of wire ‘P’ to that of’Q’ is
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 48
Answer:
(C) m2 : m1
Hint:
Maharashtra Board Class 11 Physics Important Questions Chapter 6 Mechanical Properties of Solids 49

Question 74.
The increase in energy of a metal bar of length ‘L’ and cross-sectional area ‘A’ when compressed with a load ‘M’ along its length is (Y = Young’s modulus of the material of metal bar)
(A) \frac{\mathrm{FL}}{2 \mathrm{AY}}
(B) \frac{\mathbf{F}^{2} \mathbf{L}}{\mathbf{2 A Y}}
(C) \frac{\mathrm{FL}}{\mathrm{AY}}
(D) \frac{F^{2} L^{2}}{2 A Y}
Answer:
(B) \frac{\mathbf{F}^{2} \mathbf{L}}{\mathbf{2 A Y}}
Hint:
U = \frac{1}{2} × F × l
= \frac{1}{2} × F × \frac{\mathrm{FL}}{\mathrm{AY}} = \frac{\mathrm{F}^{2} \mathrm{~L}}{2 \mathrm{AY}}

Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases

Balbharti Maharashtra State Board 12th Biology Important Questions Chapter 10 Human Health and Diseases Important Questions and Answers.

Maharashtra State Board 12th Biology Important Questions Chapter 10 Human Health and Diseases

Multiple Choice Questions

Question 1.
Infectious stage of Plasmodium is …………………
(a) trophozoite
(b) sporozoite
(c) cryptozoite
(d) metacercaria
Answer:
(b) sporozoite

Question 2.
After birth, antibodies are transferred from mother to infant through …………………
(a) colostrum
(b) placenta
(c) blood
(d) tissue fluid
Answer:
(a) colostrum

Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases

Question 3.
Which cells give rise to T-lymphocytes?
(a) Thymocytes
(b) Bone marrow cells
(c) Erythrocytes
(d) Leucocytes
Answer:
(a) Thymocytes

Question 4.
Where is antigen D is present?
(a) On Rhesus factor
(b) On the surface of RBCs
(c) On A-antigen
(d) On AB-antigen
Answer:
(b) On the surface of RBCs

Question 5.
Erythroblastosis foetalis is caused when mother is …………………
(a) Rh +ve
(b) with antibody ‘a’
(c) Rh -ve
(d) with antibody ‘b’
Answer:
(c) Rh -ve

Question 6.
Which of the following is NOT a parasitic vector insect?
(a) Mosquito
(b) Housefly
(c) Honey bee
(d) Head louse
Answer:
(c) Honey bee

Question 7.
Which is the proper sequence in the developmental stages of Plasmodium?
(a) Merozoites → Sporozoite → Trophozoites → Schizonts
(b) Trophozoites → Merozoites → Sporozoite → Schizonts
(c) Sporozoite → Merozoites → Trophozoites → Schizonts
(d) Schizonts → Merozoites → Sporozoite → Trophozoites.
Answer:
(c) Sporozoite → Merozoites → Trophozoites → Schizonts

Question 8.
There is no vaccination on this disease till today.
(a) Typhoid
(b) Tuberculosis
(c) Polio
(d) AIDS
Answer:
(d) AIDS

Question 9.
Charas, hashish, ganja are obtained from …………………
(a) Papaver somnijerum
(b) Erythroxylum coca
(c) Atropa belladorta
(d) Cannabis sativa
Answer:
(d) Cannabis sativa

Question 10.
………………. Plant is used to obtain cocaine alkaloid.
(a) Marijuana
(b) Papaver somntferum
(c) Cannabis sativa
(d) Coca
Answer:
(d) Coca

Question 11.
………………… fish is released in the waterbody to prevent the spread of Malaria and Filaria.
(a) Pomfret
(b) Tilapia
(c) Gambusia
(d) Gold fish
Answer:
(c) Gambusia

Question 12.
The carcinogen that can cause vaginal cancer is …………………
(a) Vinyl chloride
(b) Diethylstilboestrol
(c) Mustard gas
(d) Cadmium oxide
Answer:
(b) Diethylstilboestrol

Question 13.
Prostate cancer can be caused due to exposure to …………………
(a) cadmium oxide
(b) mustard gas
(c) asbestos
(d) Nickel and chromium compounds
Answer:
(a) cadmium oxide

Question 14.
Choose the correct definition of health …………………
(a) Health is not contracting any disorder or disease.
(b) State of complete physical, mental and social well-being.
(c) Health is complete absence of any disease.
(d) Health is feeling good all the time.
Answer:
(b) State of complete physical, mental and social well-being

Question 15.
The interval between infection and appearance of disease symptoms is called …………………
(a) inoculation
(b) penetration
(c) infection period
(d) incubation period
Answer:
(d) incubation period

Question 16.
What is injected in vaccination ?
(a) Half killed pathogen
(b) Dead pathogens
(c) Live pathogens
(d) Readymade antibodies
Answer:
(a) Half killed pathogen

Question 17.
Who among the following is considered as father of immunology ?
(a) Ferdinand Kohn
(b) Robert Koch
(c) Louis Pasteur
(d) Edward Jenner
Answer:
(d) Edward Jenner

Question 18.
Who coined the term antibiotics ?
(a) Charles Darwin
(b) Louis Pasteur
(c) Alexander Fleming
(d) Selman Waksman
Answer:
(d) Selman Waksman

Question 19.
Who coined the term antibody?
(a) Selman Waksman
(b) Alexander Fleming
(c) Paul Ehrlich
(d) Edward Jenner
Answer:
(c) Paul Ehrlich

Question 20.
Widal test is used for the diagnosis of …………………
(a) Malaria
(b) Typhoid
(c) Diabetes mellitus
(d) HIV/AIDS
Answer:
(b) Typhoid

Question 21.
Which bacterial genus out of the following is the common pathogen causing pneumonia ?
(a) Streptococcus sps
(b) Lactobacillus sps
(c) Pseudomonas sps
(d) Salmonella sps
Answer:
(a) Streptococcus sps

Question 22.
Given below are some statements. Which among them are symptoms of pneumonia ?
(i) Greenish, yellow sputum coughed out.
(ii) Hepatomegaly and hypoglycemia.
(iii) High fever with shaking chills.
(iv) Thickening of skin and underlying tissues.
(v) Stabbing chest pain with shortness of breath.
(vi) Mood swings and joint pains along with nausea and vomiting.
(a) (i), (ii), (iii), (iv)
(b) (i), (iii), (v), (vi)
(c) (i), (ii), (iv), (vi)
(d) (ii), (iii), (iv), (v)
Answer:
(b) (i), (hi), (v), (vi)

Question 23.
Which of the following is not the common way to prevent common cold ?
(a) Using hand sanitizers
(b) Blowing nose in open
(c) Staying away from people suffering from cold
(d) Sipping warm water
Answer:
(b) Blowing nose in open

Question 24.
Common cold is not cured by antibiotics because it is …………………
(a) caused by a virus
(b) caused by a Gram-positive bacterium
(c) caused by a Gram-negative bacterium
(d) not an infectious disease
Answer:
(a) caused by a virus

Question 25.
Motile zygote of Plasmodium occurs in …………………
(a) gut of female Anopheles
(b) salivary glands of Anopheles
(c) Human RBCs
(d) Human liver
Answer:
(a) gut of female Anopheles

Question 26.
Haemozoin is …………………
(a) a precursor of haemoglobin
(b) a toxin from Streptococcus
(c) a toxin from Plasmodium
(d) a toxin from Hemophilus
Answer:
(c) a toxin from Plasmodium

Question 27.
Vaccination against malaria is not possible because …………………
(a) they produce antibodies and antitoxins
(b) they do not produce antibodies and antitoxins
(c) antibodies resistant to vaccines are produced
(d) none of these
Answer:
(b) they do not produce antibodies and antitoxins

Question 28.
The active form of Entamoeba histolytica feeds upon …………………
(a) blood only
(b) erythrocytes, mucosa and submucosa of colon
(c) mucosa and submucosa of colon only
(d) food in intestine
Answer:
(b) erythrocytes, mucosa and submucosa of colon

Question 29.
Eating unwashed and raw green leafy vegetables grown along the railway tracks in Mumbai may cause …………………
(a) malaria
(b) influenza
(c) amoebic colitis
(d) ringworm
Answer:
(c) amoebic colitis

Question 30.
Which method of water purification can terminate amoebae ?
(a) Chlorination
(b) Sedimentation
(c) Filtration
(d) Boiling
Answer:
(d) Boiling

Question 31.
Which of the following measures should be taken to control amoebic dysentery ?
(A) Using insecticidal sprays to kill flies.
(B) Not allowing stagnant water to be accumulated over a long time.
(C) To avoid eating uncovered food.
(D) Drinking only boiled water.
(E) Eating plenty of fruits.
(a) (A) (C) (D)
(b) (A) (B) (D)
(c) (B) (C) (E)
(d) (A) (B) (E)
Answer:
(a) (A) (C) (D)

Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases

Question 32.
Which of the following should be avoided for endemic spread of amoebiasis ?
(a) Cleaning bathroom taps and toilet seats with disinfectants.
(b) Washing hands and using hand sanitizers.
(c) Proper sewage disposal and treatment.
(d) Eating uncovered roadside food.
Answer:
(d) Eating uncovered roadside food.

Question 33.
Name the disease in which the genital organs are grossly affected due to infective helminth.
(a) Ascariasis
(b) Ring worm
(c) Scabies
(d) Filariasis
Answer:
(d) Filariasis

Question 34.
Find the odd organism:
(a) Wuchereria bancrofti
(b) Brugia malayi
(c) Brugia timori
(d) Ascaris lumbricoides
Answer:
(d) Ascaris lumhricoides

Question 35.
When is hydrocele formed in a man ?
(a) When testis are not functioning properly.
(b) When scrotum is infected with filarial worms.
(c) When testis are injured due to accident.
(d) When there is water accumulation in testis.
Answer:
(b) When scrotum is infected with filarial worms

Question 36.
Which medicine is used for eradicating microfilariae from endemic areas ?
(a) Diethyle carbamacine
(b) Mebendazole
(c) Albendazole
(d) Rimfampcin
Answer:
(a) Diethyle carbamacine

Question 37.
Which of the following fungi are causative organisms of ringworm ?
(a) Microsporum
(b) Candida
(c) Thrush
(d) Tinea pedis
Answer:
(a) Microsporum

Question 38.
On which material present on the outer skin surfaces of the human body does the fungus causing infections feed on ?
(a) Melanin
(b) Keratin
(c) Lignin
(d) Suberin
Answer:
(b) Keratin

Question 39.
Which of the following statements is correct ?
(a) Fungus grows well on dry skin.
(b) Fungus cannot survive on the outside of the hair shafts.
(c) Fungus thrives well on the warm and moist skin.
(d) Nails can never show fungal infections.
Answer:
(c) Fungus thrives well on the warm and moist skin.

Question 40.
Which of the following pair is viral diseases ?
(a) Common cold, AIDS
(b) Dysentery, Common cold
(c) Typhoid, Tuberculosis
(d) Ringworm, AIDS
Answer:
(a) Common cold, AIDS

Question 41.
Which one of the following glands is often referred in relation with AIDS ?
(a) Thymus
(b) Adrenal
(c) Thyroid
(d) Pancreas
Answer:
(a) Thymus

Question 42.
The first patient of AIDS was detected in India in …………………
(a) 1980
(b) 1986
(c) 1990
(d) 1996
Answer:
(b) 1986

Question 43.
Why is it said that for AIDS prevention is the only cure ?
(a) AIDS does not have any cure, once it is contracted.
(b) By prevention AIDS cannot be cured.
(c) AIDS can be cured by proper medication and vaccination.
(d) Only prevention helps as there is no cure for AIDS.
Answer:
(d) Only prevention helps as there is no cure for AIDS.

Question 44.
After a person is detected to be having AIDS by ELISA test, which is the next confirmatory test ?
(a) Western blot
(b) Southern blot
(c) PCR
(d) Northern blot
Answer:
(a) Western blot

Question 45.
What is full form of ELISA ?
(a) Enzyme Linked Inductive Assay
(b) Enzyme Linked Iron Sorbent Assay
(c) Enzyme Linked Immunosorbent Assay
(d) None of the above
Answer:
(c) Enzyme Linked Immunosorbent Assay

Question 46.
The possible ways of transmission of AIDS are …………………
(A) Intimate sexual contact
(B) Hugging and kissing
(C) Blood transfusion without properly checking it
(D) Eating from the same plate
(E) Sharing bed linen
(F) Transplacental infection from infected mother
(G) Sharing same tattoo gun and syringes
(a) (A), (C), (F), (G)
(b) (B), (D), (E), (G)
(c) (C), (D), (E), (F)
(d) (A), (B), (C), (D)
Answer:
(a) (A), (C), (F), (G)

Question 47.
Which one of the following statements is correct ?
(a) Benign tumours show the property of metastasis.
(b) Heroin accelerates body functions.
(c) Malignant tumours may exhibit metastasis.
(d) Patients who have undergone surgery are given cannabinoids to relieve pain.
Answer:
(c) Malignant tumours may exhibit metastasis.

Question 48.
Heroin or smack is chemically …………………
(a) diclofenac
(b) diacetyl morphine
(c) benzodiazepine
(d) amphetamines
Answer:
(b) diacetyl morphine

Question 49.
Ecstasy is a drug that is used in most of the Rev parties which is chemically a derivative of …………………
(a) Barbiturates
(b) Amphetamines
(c) Catecholamine
(d) Morphine
Answer:
(b) Amphetamines

Question 50.
From which plant is charas obtained?
(a) Cannabis sativa
(b) Erythroxylum coca
(c) Papaver somniferum
(d) Atropa belladonna
Answer:
(a) Cannabis sativa

Question 51.
Opium is obtained from the latex of the unripe fruits of …………………
(a) Cannabis sativa
(b) Thea siensis
(c) Papaver somniferum
(d) Erythroxylon coca
Answer:
(c) Papaver somniferum

Question 52.
Use of Cannabis products results in …………………
(a) depressed brain activity and feeling of calmness
(b) suppressed brain function and relief of pain
(c) stimulation of nervous system, increased alertness and activity
(d) alteration in perception, thoughts and feelings
Answer:
(d) alteration in perception, thoughts and feelings

Question 53.
Marijuana, ganja and LSD are …………………
(a) narcotics
(b) stimulants
(c) hallucinogens
(d) all of these
Answer:
(c) hallucinogens

Question 54.
What is the source of LSD ?
(a) Poppy seeds
(b) Datura plant
(c) Sugar
(d) Claviceps purpurea
Answer:
(d) Claviceps purpurea

Question 55.
Narcotics are …………………
(a) amphetamines and caffeine
(b) morphine and heroine
(c) LSD and cocaine
(d) barbiturates and benzodiazepine
Answer:
(b) morphine and heroine

Question 56.
Which is an incorrectly matched pair ?
(a) LSD – Ergot fungus
(b) Heroin – Opium
(c) Amphetamines – Depressant
(d) Benzodiazepine – Calmpose tablets
Answer:
(c) Amphetamines – Depressant

Question 57.
Choose the incorrect statement
(a) The excessive use of anabolic steroids cause severe acne.
(b) In both the sexes there is increased aggressiveness and mood swings, due to steroids.
(c) In females, anabolic steroids cause breast enlargement.
(d) In males, anabolic steroids cause enlargement of prostate gland.
Answer:
(c) In females, anabolic steroids cause breast enlargement.

Question 58.
Who are the first ones to note the danger signs of drug or alcohol abuse in the adolescents ?
(a) Alert parents and teachers
(b) Neighbours
(c) Relatives
(d) Doctors
Answer:
(a) Alert parents and teachers

Question 59.
Who can give professional help for the deaddiction?
(a) Highly qualified psychiatrist
(b) Parents
(c) Teachers
(d) Friends
Answer:
(a) Highly qualified psychiatrist

Match the columns

Question 1.

Column I Column II
(a) Metchnikoff (i) ABO Blood group system
(b) Fleming (ii) Concept of immunity
(c) Edward Jenner (iii) Phagocytic cells
(d) Karl Lands teiner (iv) Lysozyme

Answer:

Column I Column II
(a) Metchnikoff (iii) Phagocytic cells
(b) Fleming (iv) Lysozyme
(c) Edward Jenner (ii) Concept of immunity
(d) Karl Lands teiner (i) ABO Blood group system

Question 2.

Disease Vector species
(a) Dengue (i) Anopheles
(b) Malaria (ii) Housefly
(c) Filaria (iii) Culex
(d) Typhoid (iv) Aedes

Answer:

Disease Vector species
(a) Dengue (iv) Aedes
(b) Malaria (i) Anopheles
(c) Filaria (iii) Culex
(d) Typhoid (ii) Housefly

Classify the following to form Column B as per the category given in Column A

Question 1.
Benzyl penicillin, Chloromycetin, Mebendazole, Levamisole, Pyrimethamine Ampicillin, Ty21a vaccine, Sulfadoxine.

Column A (Disease) Column B (Treatment)
(1) Pneumonia ————–
(2) Malaria ————–
(3) Ascariasis ————–
(4) Typhoid ————–

Answer:

Column A (Disease) Column B (Treatment)
(1) Pneumonia Benzyl penicillin, Ampicillin
(2) Malaria Pyrimethamine, Sulfadoxine
(3) Ascariasis Mebendazole, Levamisole
(4) Typhoid Chloromycetin, Ty21a vaccine

Question 2.
Lung cancer, Pituitary, Spleen, Skin cancer, Cancer of adipose tissue, lymph nodes, Adrenal, Bone tumour.

Column (A Type of cancer) Column B (Organs affected)
(1) Carcinoma ————–
(2) Sarcoma ————–
(3) Lymphoma ————–
(4) Adenocarcinoma ————–

Answer:

Column (A Type of cancer) Column B (Organs affected)
(1) Carcinoma Lung cancer, Skin cancer
(2) Sarcoma Cancer of adipose tissue, Bone tumour
(3) Lymphoma Spleen, Lymph nodes
(4) Adenocarcinoma Pituitary, Adrenal

Very Short Answer Questions

Question 1.
By which process T-cells and B-cells are produced?
Answer:
T-cells and B-cells are produced from the stem cells called haemocytoblasts, in bone marrow of adults and in liver of the foetus, by the process of haematopoiesis and in the bone marrow in adult.

Question 2.
What is a hinge?
Answer:
Hinge is the region of Y-shaped structure, holding arms and stem of antibody where four polypeptide chains of antibody are held together by disulfide bonds (-s-s-) to form a ‘Y’-shaped structure.

Question 3.
What is epitope?
Answer:
Epitope is antigenic determinant, which is present on antigens.

Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases

Question 4.
What is paratope?
Answer:
Paratope is antigen binding site that is present on the antibodies.

Question 5.
Which antigen is present in Rh +ve person?
Answer:
Antigen D is present in Rh +ve person.

Question 6.
Give the role of flushing action of lachrymal secretions.
Answer:
The conjunctiva is freed from foreign particles by the flushing action of lachrymal secretions.

Question 7.
What happens when lachrymal secretion is absent in eyes?
Answer:
Eyes become susceptible to infection when lachrymal secretion is absent.

Question 8.
In tears which antibacterial substance is present?
Answer:
Lysozyme is the antibacterial substance present in the tears.

Question 9.
Which kind of immunity is provided by vaccination?
Answer:
Artificial acquired active and passive immunity is provided by vaccination.

Question 10.
Who was Edward Jenner?
Answer:
Edward Jenner was the British scientist who developed cowpox vaccine for the protection against small pox virus.

Question 11.
Mrunmayi is called universal blood acceptor. What is her blood group?
Answer:
Blood group of Mrunmayi is AB.

Question 12.
What are antigens?
Answer:
Different foreign substances that invade the body and are capable of stimulating an immune response are called antigens.

Question 13.
In which animal Rh factor was discovered at first?
Answer:
Rh factor was first discovered in Rhesus monkey for the first time.

Question 14.
What is elephantiasis?
Answer:
Elephantiasis is one of the symptoms of lymphatic filariasis, in which there is thickening of skin and underlying tissues due to presence of malarial parasite.

Question 15.
What is dermatophytosis ?
Answer:
Dermatophytosis is a clinical condition in which fungal infection of skin occur in humans, pets and cattle which is commonly called as ringworm.

Question 16.
What is sporozoite?
Answer:
Sporozoite is a developmental stage of Plasmodium produced by rupture of oocyst. Sporozoite can enter the bloodstream in human body and then infect hepatocytes or liver cells, where they multiply into merozoites.

Question 17.
Why does male mosquito not spread Malaria?
Answer:
Male mosquito feed only on plant sap and not blood of human beings; therefore it does not spread Malaria.

Question 18.
Where does Plasmodium reproduce asexually?
Answer:
Plasmodium reproduce asexually in the liver cells and red blood cells of infected human being.

Question 19.
Where does Plasmodium reproduce sexually?
Answer:
Plasmodium undergoes sexual reproduction by the process of fertilization and development in the intestine of mosquito.

Question 20.
Which fish can be used for mosquito control?
Answer:
Gambusia fish can be used for mosquito control.

Question 21.
What is arthralgia?
Answer:
Arthralgia means joint pains.

Question 22.
What do you mean by hepatomegaly?
Answer:
Hepatomegaly means enlargement of liver.

Question 23.
Which organism yields LSD?
Answer:
Ergot fungus, Claviceps purpurea yield LSD.

Question 24.
Enlist various types of barriers which prevent entry of foreign agents into the body.
Answer:

  1. Epithelial surface
  2. Antimicrobial substances in blood and tissues
  3. Cellular factors in innate immunity
  4. Fever
  5. Acute phase proteins (APPs).

Question 25.
Which is the gastro-intestinal disease by which 15% Indian population is affected?
Answer:
Amoebiasis or amoebic dysentery is the gastro-intestinal disease by which 15% Indian population is affected.

Question 26.
What are the anti-helminthic drugs which are used in treatment of Ascariasis?
Answer:
Anti-helminthic drugs like Piperazine, Mebendazole, Levamisole, Pyrantel are used against Ascaris lumbricoidies.

Question 27.
Which are the diseases that can be avoided by eradication of mosquitoes in your area?
Answer:
Malaria, dengue, chikungunya and filariasis or elephantiasis can be avoided by eradication of mosquitoes.

Define the following

Question 1.
Serology
Answer:
A branch of immunology which deals with the study of antigen-antibody interactions is called serology.

Question 2.
Hygiene
Answer:
Hygiene is the science of health, which aims at preserving, maintaining and improving the health of an individual or the community as a whole.

Question 3.
Disease
Answer:
Disease is a condition of disrupted or deranged functioning of one or more organs or systems of the body caused due to infection, detective diet or heredity.

Question 4.
Immune system
Answer:
The system which protects us from various infectious agents is called immune system.

Question 5.
Resistance
Answer:
Resistance is an ability to ward off damage or disease through our defence mechanism.

Question 6.
Immunity
Answer:
The immunity is defined as the general ability of a body to recognize and neutralize or destroy and eliminate foreign substances or resist a particular infection or disease.

Question 7.
Antibody
Answer:
The protective chemicals produced by immune cells in response to antigens is called antibodies.

Question 8.
Opsonisation
Answer:
The process of coating of bacteria to facilitate their subsequent phagocytosis by macrophages is called opsonisation.

Question 9.
Pathogen
Answer:
Pathogen are living agents such as viruses, ricketssia, bacteria, fungi, protozoans, helminth and certain insect larvae which are capable of causing diseases.

Question 10.
Parasite
Answer:
An organism that lives in or on another organism called host and takes its nourishment from it (host) is called parasite.

Question 11.
Pathogenicity
Answer:
The ability of an organism to enter a host and cause a disease is called pathogenicity.

Question 12.
Infectious disease
Answer:
The disease which is transmitted from infected person to another healthy person either directly or indirectly is called infectious disease or communicable disease.

Question 13.
Non-infectious disease
Answer:
The disease that cannot be transmitted from one infected person to another healthy person, either directly or indirectly is called non infectious or non-communicable disease.

Question 14.
Innate immunity
Answer:
Innate immunity is defined as the resistance to infections that an individual possesses due to his or her genetic make-up and thus it is inborn defence mechanism present naturally in the body.

Question 15.
Acquired immunity
Answer:
The resistance developed during lifetime is called acquired immunity.

Question 16.
APP proteins
Answer:
APP proteins or acute phase proteins are certain collection of plasma proteins which are suddenly increased by the infection caused after injury.

Question 17.
Incubation period
Answer:
Incubation period is the time interval from the invasion of a pathogen to the development of clinical manifestations or symptoms.

Name the following

Question 1.
Name the cell that produces lymphokines.
Answer:
Helper T-cells

Question 2.
Blood group systems in human beings.
Answer:
ABO, Rh, Duffy, Kidd, Lewis, P MNS, Bombay blood group.

Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases

Question 3.
Types of sarcoma.
Answer:

  1. Osteosarcoma (bone)
  2. Myosarcoma (muscle)
  3. Chondrosarcoma (cartilage)
  4. Liposarcoma (adipose tissue)

Question 4.
Therapies used for treatment of cancer.
Answer:

  1. Chemotherapy
  2. Radiotherapy
  3. Surgery
  4. Immunotherapy
  5. Supportive therapy

Question 5.
Name the term for the transmission of HIV from pregnant mother to foetus.
Answer:
Transplacental.

Question 6.
Factors that maintain good health.
Answer:

  1. Balanced diet
  2. Personal hygiene
  3. Regular exercise
  4. Right attitude of mind
  5. Good habits.

Question 7.
Two examples of ascaricides.
Answer:
Mebendazole and Albendazole, etc.

Question 8.
Two vaccines for typhoid.
Answer:

  1. Oral Ty21a
  2. Injectable Typhoid polysaccharide vaccine or Typhium vi/ Typherix.

Question 9.
Parasites causing lymphatic filariasis.
Answer:

  1. Wuchereria bancrojti
  2. Brugiamalayi
  3. Brugia timori.

Question 10.
Parasites causing Subcutaneous Filariasis.
Answer:

  1. Loa loa
  2. Mansonella spp.

Question 11.
Name the scientists who discovered AB blood group?
Answer:
Decastallo and Sturti

Distinguish between the following

Question 1.
Inborn immunity and acquired immunity.
Answer:

Inborn Immunity Acquired Immunity
1. Inborn immunity or innate immunity is also called natural immunity. 1. Acquired immunity is also called adaptive immunity.
2. Innate immunity is present right from the birth. 2. Acquired immunity is not present at birth, but is acquired during lifetime of the individual.
3. Inborn immunity does not depend upon the previous exposure to a pathogen or foreign substance. 3. Acquired immunity always depends upon the previous exposure to a pathogen or foreign substance.
4. It is non-specific immunity as it can offer resistance to any pathogen. 4. It is specific immunity as it can offer resistance only to a particular pathogen.
5. Innate immunity consists of various types of barriers for defence against the pathogens. 5. Acquired immunity consists of various types of cells which are able to produce antibodies.
6. Inborn immunity shows immediate effect in the body. 6. Acquired immunity requires several days to become activated.
7. Inborn immunity is seen in all animals. 7. Acquired immunity is seen only in vertebrates.
8. Inborn immunity is genetic in nature and is heritable. 8. Acquired immunity is non-genetic in nature and is non-heritable.

Question 2.
Communicable and non-communicable diseases.
Answer:

Communicable diseases Non-communicable diseases
1. Diseases transmitted from infected person to healthy person are called communicable or infectious diseases. 1. Diseases that are not passed from one person to other are non-communicable or non-infectious diseases.
2. Communicable diseases spread through pathogens. 2. Non-communicable diseases do not spread through pathogens.
3. Communicable diseases are not inherited from parental generation to offspring. 3. Non-communicable diseases like cancer can be from parental generation to offspring.
4. Vectors play the major role in spreading disease from one person to another. 4. Caused due to allergy, illness, malnutrition or abnormalities in cell proliferation, changes in lifestyle, environment play a significant role.
5. Treated by conventional methods using antibiotics and other drugs. 5. Treated conservatively for a long time or surgically.
6. Diseases are acute which develop suddenly due to infections.

E.g. Pneumonia, Tuberculosis, AIDS, Typhoid, Cholera, Malaria.

6. Diseases are chronic which develop and persist for a long time.
E.g. Cancer, Rickets, Allergies, Kwashiorkor, Diabetes, Heart disease, etc.

Question 3.
Ascariasis and Filariasis.
Answer:

Ascariasis Filariasis
1. Only one species Ascaris lumbricoid.es cause ascariasis. 1. There are many species of nematode that can cause filariasis.
2. Ascaris causes the infection of alimentary canal. 2. Wuchereria bancrofti causes the infection of lymphatic system.
3. Ascaris does not cause swellings of upper and lower limbs. 3. Filariasis cause swellings of extremities.
4. Ascaris is caused due to faeco-oral transmission. 4. Filariasis is caused due to vector transmission (Culex mosquito).
5. Medicines for treatment of Ascariasis are Piperazine, Mebendazole, Levamisole, Pyrantel. 5. Medicines for treatment of filariasis are diethyl- carbamazine citrate.

Short answer questions

Question 1.
Despite constant exposure to variety of pathogens, why do most of us remain healthy?
Answer:

  1. All human beings are exposed to various foreign bodies, including infectious agents like bacteria, viruses, etc. which are called pathogens.
  2. But human body can resist almost all types of these pathogens.
  3. For this purpose, there is immune system which protects us from various infectious agents.
  4. There is resistance and prevention of the damage or disease, through our defence mechanisms.
  5. Thus, despite constant exposure to variety of pathogens, most of us remain healthy.

Question 2.
What are the unique features of acquired immunity?
Answer:
Following are the unique features of acquired immunity:

  1. Specificity : Production of specific antibody or T-lymphocyte against a particular antigen/ pathogen is called specificity.
  2. Diversity : Ability to recognize vast variety of diverse pathogens or foreign molecules by immunity is called diversity.
  3. Discrimination between self and non¬self : Acquired immunity can differentiate between own body cells (self) and foreign (non-self) molecules.
  4. Memory : The first immune response upon encounter of a specific foreign agent and its elimination is retained as a memory. This results in quicker and stronger immune response when the same pathogen is encountered again.

Question 3.
Describe the polypeptide chains seen in the structure of an antibody.
Answer:

  1. There are four polypeptide chains which make the antibody.
  2. There are two heavy or H-chains and two light or L-chains.
  3. Each chain has two distinct regions, the variable region and the constant region.
  4. Variable regions carry the antigen binding site or paratope.
  5. This part of antibody recognizes and bindsto the specific antigen to form an antigen- antibody complex.

Question 4.
Which are the antimicrobial substances in blood and tissues?
Answer:

  1. There are more than 30 serum proteins, circulating in the blood in an inactive state, which forms the complement system.
  2. ‘Complement cascade’ is activated by presence of pathogens and thus they eliminate pathogens.
  3. Cells which are affected by viruses secrete interferons which are a class of cytokines. These soluble proteins attack the pathogens.
  4. Some leucocytes stimulate other cells to protect themselves from viral infection.

Question 5.
Is developing fever a bad sign or a good action? Explain.
Answer:

  1. Fever is the innate immunity mechanism. When there is fever, the body rises.
  2. This is in response to infection in a natural way.
  3. Developing fever is a natural defence mechanism.
  4. Fever helps to accelerate the physiological processes by which the invading pathogens are destroyed.
  5. Fever stimulates the production of interferon and helps in recovery from viral infections.
  6. Taking all these points into consideration, getting fever is a good action that innate immunity is working properly, however, entry of pathogen in the body causing illness is a bad sign.

Question 6.
With the help of a chart explain the compatibility of human blood groups.
Answer:
Different types of blood groups:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 1

  1. Person with blood group A can donate blood to persons having blood group A or AB and receive blood from A or O.
  2. Person with blood group B can donate blood to persons having blood group B or AB and receive blood from B or O.
  3. Person with blood group O can donate blood to all the persons having blood group either A, B, AB or O, because blood group O is universal donor. But can receive blood only from person having blood group O.
  4. Person with blood group AB can donate blood to only AB but can receive blood from all the persons having blood group either, A, B, O or AB because AB is universal recipient.

Question 7.
The blood group of Krutika is O Rh +ve. What would be the possible blood groups of her parents?
Answer:

  1. Krutika has O blood group, therefore her genotype is I°I°.
  2. Her parents can be of following combinations.
  3. They may be having blood group A or B with heterozygous genotype respectively, i.e. IAI° and IBI°. If both of them are heterozygous, having either A or B blood group, Krutika can be of O type.
  4. Other possibility is both the parents have to be O.
  5. For being Rh positive, her at least one parent should be Rh positive. Rh negative is a recessive phenotype and hence needs double dose of these genes.

Question 8.
Can a person with blood group O Rh+ve donate blood to a patient with blood group O Rh-ve? Why?
Answer:
No. blood group O may be common to both donor and recipient but their Rh factor is different. A person with RH+ve blood cannot donate to a patient with Rh-ve blood group. In Rh+ve blood there is antigen D. This antigen D when enters the body of recipient, there are production of anti-RH antibodies in his or her body. These anitibodies with cause agglutination of the Rh +ve blood which will be given to the patient. This agglutination will cause clots inside the vital organ of the recipient and the death may follow.

Question 9.
Why do we suffer from common cold repetitively in our life, but other viral diseases like Influenza or Small pox only once?
Answer:
Influenza infection causes production of antibodies in our body, once the virus attacks us. Therefore, second encounter with the virus may not cause effect. But in case of common cold, large number of different virus families are responsible for developing infection of common cold. Many a times different allergens are also inducing agents for common cold. Thus we may suffer from common cold again and again.

Question 10.
What are the symptoms of pneumonia?
Answer:

  1. Main symptoms of infectious pneumonia are cough producing greenish or yellow sputum or phlegm and a high fever with chills.
  2. Shortness of breath, stabbing chest pain, coughing up blood, headaches, sweaty and clammy skin, loss of appetite, fatigue, blueness of the skin, nausea, vomiting, mood swings and joint pains or muscle aches are some other symptoms.

Question 11.
What is the diagnosis and treatment of filariasis? How can we control this disease ?
Answer:
I. Diagnosis and Treatment : For the patient, diethyl-carbamazine citrate is the drug used for twice a day for three weeks. Thereafter for five days every six months the same treatment is repeated. This becomes effective against filarial worms.

II. Prevention and Control:

  1. Mosquito eradication should be done for controlling filariasis.
  2. In the areas with mosquitoes, avoid mosquito bite by using mosquito nets and insect repellents.

Question 12.
What are the signs and symptoms of filariasis?
Answer:
Signs and symptoms of filariasis:

  1. As the lymphatic drainage does not take place, there is oedema with thickening of skin and underlying tissue.
  2. Extremities like legs, arms, breasts, scrotum, etc. are affected by nematode causing lymphatic filariasis, i. e. Wuchereria bancrofti.
  3. Lymph vessels and lymph nodes are enlarged and swollen.
  4. Elephantiasis is seen in which limbs are swollen like legs of elephant.
  5. Lymphoedema, i.e. accumulation of lymph fluid is seen in tissue causing swelling.
  6. Hydrocele condition develops in which testis are enlarged due to accumulation of lymphatic fluid in testis.

Question 13.
What are the various ways in which mosquitoes can be eradicated from any area?
Answer:
Eradication of mosquitoes:

  1. Removal of all stagnant water pools around the houses.
  2. If such water bodies are there, they should be sprayed with insecticides.
  3. But better option which is eco-friendly is releasing mosquito eating fish like Gambusia or Tilapia.
  4. Use of mosquito repellent plants like Citronella. Use of coils and repellent creams.
  5. Fumigation of the area to kill the mosquito.
  6. Aedes sps. breed in man-made containers, especially plastic and cement tanks. Care should therefore be taken to dispose such containers properly. Water should not be accumulated in them.

Question 14.
What precautions will you take if you are travelling in an area which has lot of mosquitoes?
Answer:

  1. Avoiding areas where mosquitoes are in more concentration.
  2. Carrying mosquito repellent creams or coils.
  3. Use of mosquito nets and other fumigation devices.
  4. Wearing full clothing in light colours.
  5. Staying indoors when mosquitoes are swarming, especially in the evening.
  6. Taking anti-malarial pills as a precautionary measure.

Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases

Question 15.
Deaddiction may be difficult but not impossible. Collect information about NGOs, working in the field of deaddiction.
Answer:
There are many NGOs that work in the field of deaddiction. In different cities, there are different organizations. Even the central Government has started helpline number 1800-11-0031 for those drug and alcohol addicts who need help to come out of these addictions. Muktangan in Pune is one such reputed organization which does the great work in the field of deaddiction.

Question 16.
What are the most common warning signs of drug and alcohol abuse among youth ?
Answer:
The most warning signs of addictions are as follows:

  1. Drop in academic performance, absenteeism from school or college.
  2. No interest in personal hygiene and hobbies.
  3. Withdrawal from the society, increased tendency of isolation and depression.
  4. Aggressive and rebellious behaviour resulting into strained relationships with family and friends.
  5. Fatigue and change in sleeping and eating habits.
  6. Fluctuations in weight, appetite, deteriorating health, etc.

Question 17.
What are the preventive measures for malaria?
Answer:
Preventive measures of malaria :

  1. Transmission of malarial parasite can be reduced by preventing mosquito bites. Therefore, mosquitoes should be controlled or totally eradicated.
  2. This can be done by using of mosquito nets and insect repellents.
  3. Mosquito control measures such as spraying insecticides inside houses and draining stagnant water where mosquitoes lay their eggs.
  4. The mosquito larvae can be eradicated by releasing Gambusia fish which can feed upon these larvae.
  5. Vaccine against malaria is also under preparation.

Question 18.
How does Entamoeba histolytica causes amoebiosis ?
Answer:

  1. Amoebiosis is spread through ingestion of the cyst form of Entamoeba histolytica. This is a commensal organism.
  2. Cyst is a semi-dormant and hardy structure found in faeces of infected person.
  3. Non-encysted amoebae are called trophozoites. The trophozoites die quickly after leaving the body but may also be present in faeces.
  4. Trophozoites are rarely the source of new infections.
  5. The infection may remain asymptomatic for many days as Amoeba can remain latent in the gastrointestinal tract.

Question 19.
Describe the signs and symptoms of amoebiasis.
Answer:
Amoebiasis shows following common symptoms:

  1. Diarrhoea, flatulence, stool with mucus and abdominal pains (cramps) are common.
  2. Stool sticky with mucus and blood.
  3. Amoebae form cysts in the liver, in such case there is hepatomegaly, i.e. enlargement of liver.
  4. Liver shows amoebic liver abscess accompanied with fever and pain in right side of the abdomen.

Question 20.
How can amoebiasis be prevented?
Answer:
Prevention of amoebiasis is to be done at two levels, viz. at home and at endemic level.
1. Prevention of the spread of amoebiasis at the home level:

  • Washing hands with soap and water after using the toilet or changing a baby’s diaper and before handling and eating food.
  • Cleaning bathrooms and toilets properly with germicides.
  • Avoiding raw vegetables when in endemic areas where they are grown in soil fertilized by human faeces.
  • Boiling and purifying the drinking water.

2. Prevention of the spread of amoebiasis at endemic level:

  • Avoiding consumption of street foods especially in public places.
  • Following good sanitary practice, as well as using proper sewage disposal or treatment.
  • E. histolytica cysts are usually resistant to chlorination; therefore sedimentation and filtration of water supplies are necessary to reduce the incidence of infection.
  • Avoiding shared towels or face washers.

Question 21.
Describe the symptoms of ascariasis.
Answer:

  1. After infection by Ascaris lumbricoides, there is appearance of eggs in stools in 60 – 70 days.
  2. In larval ascariasis, symptoms are seen in 4-16 days after infection.
  3. The final symptoms are gastrointestinal discomfort, colic and vomiting, fever and appearance of live worms in faeces.
  4. Some patients may have pulmonary symptoms. Inflammation of alveolar walls is seen. This is known as pneumonitis.
  5. Some may show neurological disorders during migration of the larvae.
  6. Loss of appetite which reflects in weight loss.
  7. A bolus of worms may obstruct the intestine.
  8. Larvae that migrate may also cause eosinophilia, i.e. increase in number of eosinophils.

Question 22.
What are the preventive measures against ascariasis?
Answer:

  1. Prevention of ascariasis can be done by adopting the following measures :
  2. Use of proper toilet facilities.
  3. Safe disposal of excreta.
  4. Protection of food from dirt and soil.
  5. Washing of vegetables before cooking and avoiding eating raw, unwashed vegetables and fruits.
  6. Hand washing and use of safe food. Observing personal hygiene.
  7. Use of pharmaceutical drugs such as Mebendazole and Albendazole can kill Ascaris.

Question 23.
Discuss the clinical manifestation of AIDS.
Answer:
There are four stages of clinical manifestations or symptoms of AIDS.

  1. Stage I : This is initial infection with the virus and formation of antibodies, usually 2-8 weeks after initial infection.
  2. Stage II : In this stage the person is asymptomatic carrier. Incubation takes place with a period ranging for 6 months to 10 years.
  3. Stage III : This is called AIDS related complex (ARC). In this stage, one or more of the following clinical signs are seen. E.g. Recurrent fever for longer than one month, fatigue, unexplained diarrhoea, night sweats, shortness of breath, loss of more than 10 per cent body weight, etc.
  4. Stage IV : This is the end stage in which patient shows full blown AIDS. Thus it is called the end stage of HIV infection. Life threatening opportunistic infections (like pneumonia, tuberculosis, Kaposi sarcoma, etc.) are easily caught during this period.

Question 24.
Through which modes HIV infection does not spread?
Answer:

  1. HIV does not spread through casual contact such as hugging, etc.
  2. Insect bite such as mosquito bites does not transmit HIV.
  3. Participation in sports is not the mode by which HIV transmits.
  4. Contact between articles used by AIDS patient, a hand shake with him or her does not transmit HIV
  5. HIV infections do not occur through swimming pool or by sharing clothes, utensils, etc.

Question 25.
Write about laboratory diagnosis and treatment of AIDS.
Answer:
I. Laboratory diagnosis :

  1. There are two tests for diagnosis of AIDS.
  2. First test is ELISA (Enzyme-Linked Immunosorbent Assay) which is used to detect the HIV antibodies.
  3. The second confirmatory test is Western Blot, which is used to weed out any false positive results. It is a highly specific test.
  4. It is based on detecting specific antibody to viral core protein and envelope glycoprotein.

II. Treatment of AIDS:

  1. AIDS cannot be cured.
  2. Antiretroviral drugs are used to reduce the viral load and prolong the life of HIV patient. E.g. Antiretroviral therapy (ART) uses drugs such as TDF (tenofovir), EFV (Efavirenz), Lamivudine (3TC), etc.

Question 26.
Describe the structure of HIV with a suitable diagram.
Answer:

  1. Human Immunodeficiency Virus or HIV is spherical and 100 to 140 nm in diameter.
  2. It has centrally located two ss RNA molecules along with reverse transcriptase enzymes.
  3. There are coverings of two layers of proteins. The outer layer formed by matrix protein (pi7) while in inner layer is of capsid protein (p24).
  4. An additional layer of lipids is seen over the matrix protein layers. This layer is impregnated with glycoprotein GP120 and GP41.
    Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 2

Question 27.
What are the modes of transmission of HIV or AIDS?
Answer:
The transmission of HIV occurs through following routes:

  1. Sexual relations, mainly unsafe sexual contact including oral, vaginal and anal sex.
  2. Through blood and blood products either by blood transfusions or sharing needles and syringes.
  3. Transplacental From pregnant mother to her foetus through placenta. Nursing mother can also transmit HIV to her baby through lactation.
  4. Spreading the virus is very rare in case of accidental needle injury, artificial insemination with infected donated semen and transplantation with infected organs.
  5. HIV is seen in urine, tears, saliva, breast milk and vaginal secretions but unless these body fluids enter the injuries and wounds, transmission is not easy.

Question 28.
What are the measures of prevention and control of AIDS ?
Answer:

  1. Preventive measures : AIDS has no cure, hence prevention is the best choice. The
    following steps help in preventing this dreadful disease.
  2. High risk group people should be educated about HIV transmission. They should never donate blood.
  3. Use of disposable needles and syringes should be done with proper disposal.
  4. Risky sexual habits should be avoided.
  5. Tooth brushes, razors, other articles that can become contaminated with blood should not be shared.
  6. Blood should be screened before receiving it.
  7. Routine screening of blood and semen donors, organ donors (kidney, liver, lung, cornea), and patients undergoing haemodialysis must be done.
  8. Pregnant women or those women who are contemplating pregnancy should be regularly screened.

Question 29.
Explain the ill-effects of opioids and cannabinoids on health.
OR
What are harmful effects of drug abuse?
Answer:

  1. Opioids bind to specific opioid receptors which are present in central nervous system and gastrointestinal tract. Some opioids e.g. heroin act like depressants and slow down all the body functions.
  2. Cannabinoids have the capacity to interact with receptors present in the brain. Inhalation or ingestion of cannabinoids such as marijuana, hashish, charas and ganja have adverse effect on cardiovascular system.
  3. Cannabinoid like LSD causes hallucinations.
  4. All these substances are addictive and hence cause adverse effects on the body and health.

Question 30.
Give the adverse effects of opioids, cannabinoids and morphine on human health.
Answer:
1. Opioids:

  • Opioids bind to specific opioid receptors present in the central nervous system and in gastrointestinal tract.
  • They are depressants and slow down the body functions.

2. Cannabinoids:

  • Cannabinoids interact with receptors in the brain.
  • They affect cardiovascular system of the body.

3. Morphine:

  • Morphine is an effective sedative and pain killer when used for medicinal purpose.
  • When abused it affects physical, physiological and psychological functions.

Give reasons

Question 1.
Vaccines are safe.
Answer:
During their manufacture, vaccines are rigorously tested. Many rounds of study, examination and research are carried out before they are used for general public. Extensive research and evidences are gathered to check their safety. Sometimes, some vaccines produce side effects but these are rare and mild. Hence vaccines are considered to be safe.

Question 2.
Innate immunity is also known as non-specific immunity.
Answer:
Innate immunity is non-specific because it does not depend on previous exposure to foreign substances. It is inborn capacity of the body to resist the pathogen that causes the disease. It is natural immunity and hence it remains non-specific, trying to protect the body in case of any invasion of foreign body.

Question 3.
Vaccination is important for preventing pneumonia.
Answer:
Vaccinations for pneumonia are available against Haemophilus influenzae and Streptococcus pneumoniae. If given earlier in life, they reduce the chances of catching pneumococcal infections. The deaths can be prevented which are common due to lung infections. Since it is a common and chronic j disease for all age groups, for the prevention one must take vaccination.

Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases

Question 4.
Common cold is the most frequent ! infectious disease in humans.
Answer:
Common cold is caused by virus which is abundantly present in congested city environments. The upper respiratory tract is infected due to these rhinoviruses and corona viruses. Average adult contracts such infections 2 to 4 times in a year while children capture it 6 to 12 times in a year. Therefore, it is said to be the most frequent infectious disease of human beings.

Question 5.
Typhoid is food and water-borne disease.
Answer:
Typhoid is caused due to Salmonella typhi which isa Gram-negative bacterium, transmitted from a patient or carrier to another healthy person through contaminated food or water. Flying insects, mostly houseflies transmit the bacteria from faeces to the food. Poor hygienic habits and improper public sanitation system spreads typhoid. Therefore, it is said to be food and water-borne disease.

Question 6.
Malignant tumour is more dangerous than benign tumour.
Answer:
Malignant tumour cells can show metastasis and hence can spread far and wide in the body, affecting other healthy cells and tissues. They are difficult to cure by any therapy as one does not know exact location of the cancerous cells. They also produce variety of symptoms depending on their i location. On the contrary, benign tumours can be treated surgically. Since they are covered by a cyst like membrane, the cancerous cells do not spread from them. Thus malignant tumour can be lethal as against the benign tumour.

Question 7.
Prevention is better than cure for AIDS.
Answer:
Till this time, there is no preventive vaccination for AIDS. There is also no cure for AIDS. The medicines are also costly and may not give complete cure. The only way to remain away from AIDS is the complete awareness about it. Thus it should be prevented by not allowing HIV to enter our body. Once HIV finds the entrance, the cure is impossible. Therefore, it is said that prevention is better them cure for AIDS.

Write short notes

Question 1.
Cellular factors in innate immunity.
Answer:

  1. Phagocytic cells ingest and destroy the pathogens.
  2. This is natural defence against the invasion of pathogenic microorganisms and other foreign particles in blood and tissues.
  3. Phagocytic cells are of two types, viz. microphages and macrophages. They can remove foreign particles that enter the body.
  4. Natural killer (NK) cells is a class of lymphocytes which carry out important and non-specific defence against viral infections and tumours.

Question 2.
Acute phase proteins (APPs).
Answer:

  1. Acute phase proteins are involved in innate immune mechanism.
  2. When there is an infection or injury, it leads to a sudden increase in concentration of certain plasma proteins, which are called acute phase proteins or APPs.
  3. These include C Reactive Protein (CRP), Mannose binding protein, Alpha-1-acid glycoprotein, Serum Amyloid P etc.
  4. APPs enhance host resistance, prevent tissue injury and promote repair of inflammatory lesions.

Question 3.
Rh factor.
Answer:
Rh factor:

  1. Rh factor is the term adapted from Rhesus monkey.
  2. In rhesus monkey, there is antigen D on the surface of their RBCs.
  3. Landsteiner and Wiener discovered this antigen and termed it as Rh factor.
  4. Persons having Rh factor or D antigen are called Rh positive while those lacking D antigen or Rh factor are called Rh negative.

Question 4.
Erythroblastosis foetalis.
Answer:

  1. Erythroblastosis foetalis is condition in which there is destruction of the erythrocytes of the foetus. It is the haemolytic disease of the newborn (HDN).
  2. This is caused in foetus, if mother is Rh -ve and father is Rh +ve. Rh +ve is the dominant allele, the foetus becomes Rh +ve, when its father is RH +ve.
  3. Rh +ve blood groups have D antigen which induces a strong immunogenic response when introduced into Rh -ve individuals.
  4. During foetal life, there is connection between mother and foetus through placenta, therefore Rh +ve antigen D from the foetus enters maternal circulation.
  5. This triggers formation of anti-Rh antibodies in mother. Subsequently Rh+ve foetus receives anti-Rh antibodies produced by mother.
  6. This causes agglutination reaction resulting into haemolysis in foetus. In order to prevent HDN, Rh -ve mother is injected with the anti-Rh antibody during all her pregnancies if her husband is Rh +ve.

Question 5.
Common cold.
Answer:

  1. The common cold (nasopharyngitis or rhinopharyngitis) is a viral infectious disease of the upper respiratory system. The causative organisms are rhinoviruses and coronaviruses.
  2. Symptoms include cough, sore throat, runny nose and fever.
  3. There is no known treatment, however, symptoms usually resolve spontaneously in 7 to 10 days.
  4. The best prevention for the common cold is to stay away from infected people and places where infected individuals have been.
  5. Hand washing with plain soap and water is recommended. Also alcohol-based hand sanitizers provide very little protection.

Question 6.
Life cycle of Plasmodium.
Answer:

  1. Anopheles Female mosquito which is a carrier carries sporozoites. When it bites the human, these sporozoites enter human circulation.
  2. Sporozoites undergo asexual reproduction through fission or schizogony in the liver cells or erythrocytes of the human.
  3. It forms merozoites. The cells formed within erythrocytes function as gametocytes. They undergo gamogony.
  4. Upon biting such person, the gametocytes enter into female Anopheles, fertilization occurs in its gut.
  5. Diploid zygote transforms into oocyst. Oocyst forms large number of haploid sporozoites through meiosis (sporogony).
  6. Sporozoites migrate to salivary glands and are ready to infect new human host.
  7. Again Sporozoite → Merozoite → Trophozoite → Schizont sequence is carried on for plasmodial stages in human body.
  8. The sexual life cycle of Plasmodium occurs in mosquito body which acts as a vector. While its asexual phase takes place in human body.

Question 7.
Pneumonia.
Answer:

  1. Pneumonia is an inflammatory condition of alveoli in the lungs causing formation of fluid in the lungs. This condition is called consolidation and exudation.
  2. Causes of pneumonia are infection due to bacteria, viruses, fungi or parasites, chemical burns or physical injury to the lungs.
  3. Influenza virus, adenovirus, para influenza and Respiratory Syncytial Virus (RSV) are some viruses that can cause pneumonia. Bacteria like Streptococcus pneumoniae and fungal pathogens e.g. Pneumocystis jirovecii and Pneumocystis carinii can also spread infection of pneumonia. Chemical burns of physical injury to lungs also cause similar infection.
  4. Main symptoms of infectious pneumonia are cough producing greenish or yellow sputum or phlegm and a high fever with chills.
  5. Shortness of breath or dyspnea, stabbing chest pain, coughing up blood, headaches, sweaty and clammy skin, loss of appetite, fatigue, blueness of the skin, nausea, vomiting, mood swings and joint pains or muscle aches are some other symptoms.
  6. Preventive vaccination against pneumonia is available. Medicines such as Benzyl penicillin, Ampicillin and Chloramphenicol are effective to prevent pneumonia.

Question 8.
Ringworm.
Answer:

  1. Ringworm or Dermatophytosis is a clinical condition caused by Trichophyton and Microsporum fungal infection of the skin. This infection is seen in humans and pets.
  2. Dermatophytes are the fungi that feed on keratin. Keratin is the material found in the outer layer of skin, hair and nails.
  3. These fungi attack various parts of the body. Infections on the body forms enlarged raised red rings. These patches have intense itching. Infection on the skin of the feet may cause athlete’s foot and jock itch.
  4. When the nails are infected it causes onychomycosis. During this the nails thicken, discolour and finally crumble and fall off.
  5. Prevention of ringworm infection is to be done by avoiding sharing of clothing, sports equipment, towels or sheets. Clothes should be washed in hot water with fungicidal soap after suspected exposure to ringworm. One should not walk barefoot but use appropriate footwear.
  6. Diagnosis of ringworm is done by physical examination and treatment is done with uses drugs like nystatin, fluconazole, itraconazole, etc.

Question 9.
Dengue.
Answer:

  1. Dengue is a viral disease causing high fever. It is a painful, debilitating vector-borne disease.
  2. There are four closely related dengue viruses that cause infection.
  3. Vector of Dengue virus is female Aedes mosquito. The mosquito takes up the dengue virus when it sucks blood of a person suffering from dengue.
  4. The spread of dengue is not directly from one person to another person.

Question 10.
Performance enhancers.
Answer:

  1. Performance enhancers are certain drugs used by sportspersons to enhance their performance during competitions.
  2. Narcotic analgesics, anabolic steroids, diuretics and certain hormones are misused by such sportspersons to increase muscle strength and bulk. It also promotes aggressiveness and improve overall performance.
  3. Use of anabolic steroids cause side effects.
  4. Females show masculinization, increased aggressiveness, mood swings, depression, abnormal menstrual cycles, excessive hair growth on the face and body, enlargement of clitoris, deepening of voice.
  5. Males show acne, increased aggressiveness, mood swings, depression, and reduction of size of the testicles, decreased sperm production, kidney and liver dysfunction, breast enlargement, premature baldness, enlargement of the prostate gland.
  6. These effects may be permanent with prolonged use. Using such drugs is illegal and punishable.

Chart Based Questions

Question 1.
Complete the chart of ABO blood group system and answer the questions given below:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 3
Questions:
(i) Which blood group from the above table is called universal acceptor?
(ii) Which blood group from the above table is called universal donor?
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 4
(i) Blood group AB is called universal acceptor.
(ii) Blood group O is called universal donor.

Question 2.
Complete the table

Plasmodium species Incubation period Pattern of fever
———— ————– High fever after 48 hours.
————– 28 days ————–
————– 17 days ————-
———— ————- High fever at irregular intervals between 22 to 48 hours.

Answer:

Plasmodium species Incubation period Pattern of fever
P. vivax 14 days High fever after 48 hours.
P. malariae 28 days High fever after 72 hours interval
P. ovale 17 days High fever after 48 hours interval
P. falciparum 12 days High fever at irregular intervals between 22 to 48 hours.

Question 3.
Complete the following table
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 5
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 6

Question 4.
Complete the following table:

Carcinogen Organ affected
N-nitrosodimethlene ————–
Aflatoxin ———-
————– Vagina
————– Urinary bladder
————– Prostate
————– Skin and lungs

Answer:

Carcinogen Organ affected
N-nitrosodimethlene Lungs
Aflatoxin Liver
Diethylstilboestrol Vagina
2-naphthylamine and 4-aminobiphenyl Urinary bladder
Cadmium oxide Prostate
Soot, coal tar (2-4 benzopyrene) Skin and lungs

Diagram Based Questions

Question 1.
Label the given diagram
Img 7Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 7
Answer:

  1. Antigen binding site.
  2. Variable region of heavy chain
  3. Varible region of light chain
  4. Constant region of light chain
  5. Constant region of heavy chain
  6. Disulphide bond
  7. Hinge
  8. Light chain
  9. Heavy chain

Question 2.
Observe the given diagram and answer the following questions:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 8
(1) What is I and II in the above diagram?
Answer:
I is a virus which is trying to cause infection, II are two antigen molecules which are trying to attack the virus.

(2) What structures are responsible for antigen and antibody complex? Identify them in the above diagram.
Answer:
(a) is epitope which is antigen determinant and
(b) is a paratope which is part of the antibody. Epitope and paratope are specific to each other and hence they form a complex.

(3) What is the study of antigen-antibody interactions called?
Answer:
The study of antigen-antibody interactions is called serology.

Question 3.
Fill in the blanks after observing the diagram.
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 9
On the right side of the diagram, the stages of plasmodium are passed in the body of ……………….. Whereas on the left side of the diagram, those take place in the body of ………………, ………………. is the stage that is dormant in the liver of human host. From this ………………… and then ………………… is the stage in the erythrocytes, which rupture and gives rise to …………….. Microgamete and macrogamete fuse with each other to form …………………… which later gives rise to ookinete which forms ………………… This enters the salivary glands of mosquito …………………. phase of Plasmodium occurs in mosquito body, whereas …………………… phase is in human body.
Answer:
On the right side of the diagram, the stages of plasmodium are passed in the body of human. Whereas on the left side of the diagram, those take place in the body of mosquito. Hypnozoite is the stage that is dormant in the liver of human host. From this schizont and then merozoites Trophozoite is the stage in the erythrocytes, which rupture and gives rise to gamerocyte. Microgamete and macrogamete fuse with each other to form zygote which later gives rise to ookinete which forms sporozoites. This enters the salivary glands of mosquito. Sexual phase of Plasmodium occurs in mosquito body, whereas asexual phase is in human body.

Question 4.
Observe the given diagram and answer the following questions
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 10
(1) Enlist the stages of Entamoeba histolytica you see in the above diagram.
Answer:
Trophozoite, pre-cystic form, cyst, binucleate cyst, quadrinucleate cyst, Metacycstic amoeba, amoebulae are the different stage of Entamoeba histolytica that are seen in the above diagram.

(2) Where are these stages passed?
Answer:
These stages are passed in the lumen of intestine of the host human being.

(3) How does Entamoeba come out of the body of the host?
Answer:
Encysted Entamoeba pass out with the faecal matter of the host.

Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases

Question 5.
Observe the given diagram and answer the following questions:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 11

(1) In life cycle of Ascaris at what stage do they enter the human body?
Answer:
When there is development of infective larva inside the egg of Ascaris, it enters the human body.

(2) How do they enter the human body and through which organ do they enter?
Answer:
Ascaris eggs are deposited in the faeces. They mix in the soil, if faeces is exposed in open. From there, it can enter into nearby water body or it may contaminate vegetables or other food stuffs. Such unhygienic food or unclean hands pass these eggs in the body of human through the mouth.

(3) What are the vital organs affected by the Ascaris during its development within the body of host human ?
Answer:
Ascaris can affect trachea, lungs, heart, brain and eyes too.

(4) In which organ do they copulate and produce fertilized eggs?
Answer:
Adult male and female copulate in the intestine of the host human.

Question 6.
Observe the given diagram and answer the following questions:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 12

(1) In which host stage II is completed?
Answer:
Stage II is completed in human.

(2) What happens in step 1 and step 2?
Answer:
Humans are infected at step 1 when mosquito bites human and larvae enter blood stream. In step 2 adult Wuchereria worms are formed in lymphatics.

(3) Describe the events in step 3.
Answer:
Mosquito carries the blood as it bites the human in step 4 and ingests microfilariae in human blood. Later the microfilariae start growing in the midgut of mosquito.

(4) In which host stage I is completed?
Answer:
Stage I is completed in mosquito.

Question 7.
Sketch and label the diagram of pathogen that causes typhoid.
Answer:
Pathogen of typhoid is Salmonella typhi.
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 13

Question 8.
Sketch and label disease causing agents of pneumonia.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 14

Question 9.
Sketch and label benign and malignant tumours.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 15

Question 10.
Sketch and label structure of HIV.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 16

Long answer questions

Question 1.
Describe different ways in which epithelial surface offers the innate immunity.
Answer:

  1. Skin and mucous covering, when intact protects the body against the invasion by pathogens. The healthy skin has bactericidal activity due to the salts present in drying sweat.
  2. Sebaceous glands in the skin produce secretions and long chain of fatty acids. These are bactericidal and fungicidal.
  3. Respiratory tract is provided with mucosa which prevents entry of microorganisms to a large extent.
  4. The inhaled particles are arrested through hair in the nasal passage. The particles that pass beyond nasal passage are caught by mucus lining the epithelium. They are swept back to pharynx. Then they are either swallowed or coughed out.
  5. The cough reflex is an important defence mechanism of respiratory tract.
  6. There is saliva in the mouth which has inhibitory effect on microorganisms. Gastric secretions has acidity and hence microorganisms are destroyed in stomach.
  7. The flushing action of urine eliminates bacteria from the urethra. Semen too has antibacterial substances, e.g. Spermine and zinc.

Question 2.
Explain ABO blood group system in human being with a suitable chart.
Answer:

  1. In ABO system, the blood groups are determined by the antigen present on the surface of red blood cells.
  2. The blood groups are of four types, viz. A. B, AB and O.
  3. In person with blood group A there is antigen ‘A’ on the surface of their red blood cells (RBCs) and antibodies ‘b’ in their plasma.
  4. In person with blood group B there is antigen ‘B’ on the surface of their red blood cells (RBCs) and antibodies ‘a’ in their plasma.
  5. In person with blood group AB there are both antigens ‘A’ and ‘B’ on the surface of their RBCs and no antibodies in their plasma.
  6. In person with blood group ‘O’ there are no antigens ‘A’ and ‘B’ on the surface of their RBCs but have both ‘a’ and ‘b’ antibodies in their plasma.
  7. During blood transfusion compatibility of blood has to be taken into consideration.
  8. Person with ‘O’ blood group is called universal donor while the person with ‘AB’ blood group is called universal recipient. Individuals with blood group O can donate blood to anyone, while those individuals with blood group AB can receive blood from any person.
    Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases 17

Question 3.
What are the main causes of cancer?
Answer:
Causes of Cancer : Following carcinogenic factors are responsible for causing cancer.

  1. Chemicals : Many induce development of cancer. E.g. nicotine, caffeine, polycyclic hydrocarbons and products of combustion of coal and oil. Sex hormone and steroids, if given or secreted in excess, can cause cancer. E.g. Breast cancer.
  2. Radiation : Radiations such as X-rays, gamma-rays, cosmic rays, ultra-violet rays are carcinogenic.
  3. Viruses : Virus possessing oncogenes (v-onc genes) are carcinogenic. E.g. EBV (Epstein-barr virus), HPV (Human papiloma virus) are oncogenic viruses.
  4. Oncogenes : Cellular oncogenes (c-onc genes) or proto-oncogenes can cause cancer. They are present in normal cells but if activated they lead to oncogenic transformation of cells.
  5. Addiction : Addictive substances like cigarette smoke, tobacco lead to cancer of mouth, lips and lungs. Alcohol can cause cancer of oesophagus, stomach, intestine and liver. Drugs like marijuana or anaerobic steroids can also cause cancer.

Maharashtra Board Class 12 Biology Important Questions Chapter 10 Human Health and Diseases

Question 4.
What are the different ways of treating cancer?
Answer:
Cancer treatment consists of combination of a number of therapies which are follows:
(1) Chemotherapy : Chemotherapy means giving certain anticancer drugs. These drugs check cell division by inhibiting DNA synthesis. But these are more toxic to cancerous cell than to normal cells. Chemotherapy shows side effects such as hair loss or anaemia.

(2) Radiotherapy : In addition to chemotherapy, radiations are given. The cancer cells are bombarded with the radiations from radioactive materials such as cobalt, iridium and iodine. The X-rays, gamma rays and charge particles are used to destroy the cancerous tissue or cells. They cause minimum damage to the surrounding normal tissue or cells.

(3) Surgery : Entire cancerous tissue or cells are removed surgically. E.g. breast tumour or uterine tumour. After removing the cancerous tissue, additionally other treatments are also given.

(4) Immunotherapy : For tackling with tumour, patients are given biological response modifiers such as a-interferon which activates their immune system to destroy the tumour.

(5) Supportive therapy : With supportive therapy, patient’s quality of life is increased. To treat symptoms of cancer and side effects of cancer treatments, this therapy is used. This therapy varies depending upon condition of individual patient.

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Balbharti Maharashtra State Board 12th Biology Important Questions Chapter 9 Control and Co-ordination Important Questions and Answers.

Maharashtra State Board 12th Biology Important Questions Chapter 9 Control and Co-ordination

Multiple choice questions

Question 1.
The supporting cells that produce myelin sheath in the CNS are ……………….
(a) Oligodendrocytes
(b) Satellite cells
(c) Astrocytes
(d) Schwann cells
Answer:
(a) Oligodendrocytes

Question 2.
Human brain develops to its full size at an age of year/s.
(a) 1
(b) 6
(c) 12
(d) 18
Answer:
(b) 6

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 3.
Telencephalon is the other name of ……………….
(a) pons varolii
(b) medulla oblongata
(c) cerebrum
(d) cerebellum
Answer:
(c) cerebrum

Question 4.
Olfactory tracts merge in olfactory area of lobe.
(a) Frontal
(b) Parietal
(c) Occipital
(d) Temporal
Answer:
(d) Temporal

Question 5.
………………. is the largest commissure of the human brain.
(a) Corpora striata
(b) Corpora quadrigemina
(c) Habencular commissure
(d) Corpus callosum
Answer:
(d) Corpus callosum

Question 6.
Grey matter of the brain shows large collection of ……………….
(a) dendrons
(b) cytons
(c) axons
(d) synapsis
Answer:
(b) cytons

Question 7.
Masses of grey matter in white matter of the cerebrum are called ……………….
(a) corpora striata
(b) corpus callosum
(c) paracoel
(d) basal ganglia
Answer:
(d) basal ganglia

Question 8.
Parietal and temporal lobes of cerebrum are separated by sulcus.
(a) lateral
(b) parieto occipital
(c) central
(d) median longitudinal
Answer:
(a) lateral

Question 9.
……………… area is motor speech area
(a) Acoustic
(b) Wernike’s
(c) Somato sensory
(d) Broca’s
Answer:
(d) Broca’s

Question 10.
Maxillary nerve is a branch of nerve.
(a) Occulomotor
(b) Trochlear
(c) Trigeminal
(d) Facial
Answer:
(c) Trigeminal

Question 11.
Spinal accessory is the cranial nerve.
(a) IV
(b) VI
(c) IX
(d) XI
Answer:
(d) XI

Question 12.
Rotation of eye ball is controlled by ……………….
(a) Optic nerve
(b) Pathetic nerve
(c) Auditory nerve
(d) Hypoglossal nerve
Answer:
(b) Pathetic nerve

Question 13.
The spinal nerves emerge out of vertebral column through ……………….
(a) intervertebral foramina
(b) neural canal
(c) central canal
(d) foramen magnum
Answer:
(a) intervertebral foramina

Question 14.
The neuro transmitter is removed by an enzyme called ……………….
(a) noradrenaline
(b) acetylcholine
(c) hyaluronidase
(d) cholinesterase
Answer:
(d) cholinesterase

Question 15.
The reflex action originates in ……………….
(a) sensory neuron
(b) motor neuron
(c) receptor organ
(d) effector organ
Answer:
(c) receptor organ

Question 16.
Cytons of neurons are located in dorsal root ganglion.
(a) afferent
(b) efferent
(c) adjustor
(d) association
Answer:
(a) afferent

Question 17.
Wall of carotid arteries contain ……………….
(a) thermoreceptors
(b) mechanoreceptors
(c) baroreceptors
(d) statoacoustic receptors
Answer:
(c) baroreceptors

Question 18.
The electronegativity inside the membrane is due to ……………….
(a) less anions than cations
(b) less cations than anions
(c) bicarbonates
(d) carbonates
Answer:
(b) less cations than anions

Question 19.
The neuro transmitters stimulate ……………….
(a) presynaptic membrane
(b) cyton
(c) axon terminals
(d) postsynaptic membrane
Answer:
(d) postsynaptic membrane

Question 20.
………………. is an extero-receptor.
(a) Thermoreceptor
(b) Baroreceptor
(c) Proprioreceptor
(d) Enteroreceptor
Answer:
(a) Thermoreceptor

Question 21.
The are described as windows for brain.
(a) sensory neurons
(b) motor neurons
(c) effectors
(d) sense organs
Answer:
(d) sense organs

Question 22.
Otolith organ is formed of ……………….
(a) cochlea and vestibule
(b) sacculus and utriculus
(c) semicircular canals
(d) ear ossicles
Answer:
(b) sacculus and utriculus

Question 23.
Olfactory bulbs are extensions of brain’s ……………….
(a) cerebrum
(b) limbic system
(c) RAS
(d) pons varolii
Answer:
(b) limbic system

Question 24.
Gustatory senses are noted by ……………….
(a) retina
(b) skin
(c) nose
(d) tongue
Answer:
(d) tongue

Question 25.
………………. is attached to the eardrum.
(a) Malleus
(b) Incus
(c) Stapes
(d) Cochlea
Answer:
(a) Malleus

Question 26.
Eustachian tube is present in ……………….
(a) external ear
(b) internal ear
(c) heart
(d) middle ear
Answer:
(d) middle ear

Question 27.
The internal ear is a fluid filled structure called ……………….
(a) cochlea
(b) vestibule
(c) labyrinth
(d) otolith
Answer:
(c) labyrinth

Question 28.
The space within cochlea is known as ……………….
(a) scala vestibule
(b) scala tympani
(c) aqueous chamber
(d) scala media
Answer:
(d) scala media

Question 29.
Thermoregulatory centre in the body is ……………….
(a) hypothalamus
(b) cerebellum
(c) spinal cord
(d) pituitary
Answer:
(a) hypothalamus

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 30.
Which of the following is a sensory nerve?
(a) Vagus
(b) Auditory
(c) Facial
(d) Lumbar
Answer:
(b) Auditory

Question 31.
Chemical transmission in synapse occurs due to ……………….
(a) cholesterol
(b) ADH
(c) acetylcholine
(d) cholinesterase
Answer:
(c) acetylcholine

Question 32.
Voluntary muscular coordination is under the control of ……………….
(a) medulla
(b) pons
(c) hypothalamus
(d) cerebrum
Answer:
(d) cerebrum

Question 33.
All involuntary vital activities are under the control of ……………….
(a) medulla oblongata
(b) cerebellum
(c) cerebral hemispheres
(d) pons Varolii
Answer:
(a) medulla oblongata

Question 34.
Cerebellum is controlling centre for ……………….
(a) muscular strength
(b) memory
(c) equilibrium
(d) muscular coordination
Answer:
(c) equilibrium

Question 35.
Which receptors are present in the retina?
(a) Chemoreceptors
(b) Thermoreceptors
(c) Photoreceptors
(d) Baroreceptors
Answer:
(c) Photoreceptors

Question 36.
Breathing is controlled by ……………….
(a) trachea
(b) medulla oblongata
(c) lungs
(d) hypothalamus
Answer:
(b) medulla oblongata

Question 37.
Corpus callosum is a nerve fibre bridge which connects ……………….
(a) two cerebral hemispheres
(b) cerebrum and cerebellum
(c) cerebellum and medulla
(d) midbrain and hindbrain
Answer:
(a) two cerebral hemispheres

Question 38.
Centre for thirst and hunger are located in ……………….
(a) cerebrum
(b) cerebellum
(c) hypothalamus
(d) medulla
Answer:
(c) hypothalamus

Question 39.
Gyri in the brain are present in ……………….
(a) cerebral cortex
(b) olfactory lobes
(c) medulla oblongata
(d) hypothalamus
Answer:
(a) cerebral cortex

Question 40.
Which of the following is a structure of mesencephalon?
(a) Inferior colliculi
(b) Thalamus
(c) Cerebellum
(d) Pons varolii
Answer:
(a) Inferior colliculi

Question 41.
Third ventricle lies in ……………….
(a) midbrain
(b) forebrain
(c) cerebellum
(d) medulla oblongata
Answer:
(b) forebrain

Question 42.
Medulla oblongata encloses ……………….
(a) third ventricle
(b) fourth ventricle
(c) first ventricle
(d) second ventricle
Answer:
(b) fourth ventricle

Question 43.
Loss of memory may result from injury to the ……………….
(a) corpora quadrigemina
(b) pons varolii
(c) cerebellum
(d) cerebrum
Answer:
(d) cerebrum

Question 44.
Terminal non-nervous part of spinal cord is ……………….
(a) funiculus
(b) filum terminale
(c) cauda equina
(d) conus terminalis
Answer:
(b) filum terminale

Question 45.
Which part of the pituitary is neurohaemal organ?
(a) Pars distalis
(b) Infundibulum
(c) Pars nervosa
(d) Pars intermedia
Answer:
(c) Pars nervosa

Question 46.
Development of secondary sexual characteristics in female is under the control of ……………….
(a) growth hormone
(b) TSH
(c) estrogen
(d) progesterone
Answer:
(c) estrogen

Question 47.
Hypersecretion of STH in children causes ……………….
(a) cretinism
(b) gigantism
(c) dwarfism
(d) myxoedema
Answer:
(b) gigantism

Question 48.
Milk secretion in lactating woman is controlled by ……………….
(a) LH
(b) prolactin
(c) relaxin
(d) oestrogen
Answer:
(b) prolactin

Question 49.
ADH is secreted by
(a) adrenal gland
(b) thyroid
(c) hypothalamus
(d) pancreas
Answer:
(c) hypothalamus

Question 50.
BMR is increased by the administration of ……………….
(a) insulin
(b) GH
(c) thyroxine
(d) testosterone
Answer:
(c) thyroxine

Question 51.
The largest endocrine gland in the body is ……………….
(a) pituitary
(b) adrenal
(c) liver
(d) thyroid
Answer:
(d) thyroid

Question 52.
Diabetes insipidus is caused by the deficiency of ……………….
(a) calcitonin
(b) oxytocin
(c) atrial natriuretic factor
(d) vasopressin
Answer:
(d) vasopressin

Question 53.
Simple goitre is caused by the deficiency of ……………….
(a) TSH
(b) thyrocalcitonin
(c) thyroxine
(d) iodine
Answer:
(d) iodine

Question 54.
Exopthalmic goitre is also known as ……………….
(a) Grave’s disease
(b) Gull’s disease
(c) Simple goitre
(d) Cushing’s disease
Answer:
(a) Grave’s disease

Question 55.
Cushing’s syndrome is developed due to ……………….
(a) hyposecretion of ACTH
(b) hypersecretion of corticoids
(c) hyposecretion of thyroxine
(d) hypersecretion of thyroxine
Answer:
(b) hypersecretion of corticoids

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 56.
Pituitary gland is under the control of ……………….
(a) thyroid
(b) adrenal
(c) pineal
(d) hypothalamus
Answer:
(d) hypothalamus

Question 57.
FSH is secreted by ……………….
(a) pituitary gland
(b) thyroid gland
(c) ovary
(d) adrenal gland
Answer:
(a) pituitary gland

Question 58.
ICSH stimulates ……………….
(a) ovary
(b) Leydig cells
(c) seminiferous tubules
(d) kidney
Answer:
(b) Leydig cells

Question 59.
Which of the following secrete LH ?
(a) Pituitary
(b) Thyroid
(c) Ovary
(d) Adrenal
Answer:
(a) pituitary

Question 60.
TSH regulates secretion.
(a) thyroxine
(b) MSH
(c) androgens
(d) insulin
Answer:
(a) thyroxine

Question 61.
Deficiency of thyroxine in adults cause ……………….
(a) cretinism
(b) myxoedema
(c) diabetes
(d) Cushing’s disease
Answer:
(b) myxoedema

Question 62.
Osmotic pressure and blood pressure are maintained by ……………….
(a) glucocorticoids
(b) aldosterone
(c) TRF
(d) MSH
Answer:
(b) aldosterone

Question 63.
Hormone secreted by corpus luteum is ……………….
(a) aldosterone
(b) progesterone
(c) testosterone
(d) cortisol
Answer:
(b) progesterone

Question 64.
………………. is also called hypophyseal stalk.
(a) Infundibulum
(b) Median eminence
(c) Pars intermedia
(d) Sphenoid bone
Answer:
(a) infundibulum

Question 65.
………………. is like a collar around hypophyseal stalk.
(a) Pars distalis
(b) Pars nervosa
(c) Pars intermedia
(d) Pars tuberalis
Answer:
(d) Pars tuberalis

Question 66.
Herring bodies are the parts of ……………….
(a) hypothalamo-hypophyseal tracts
(b) pituicytes
(c) hypothalamo-hypophyseal portal system
(d) pituitary cleft
Answer:
(a) hypothalamo-hypophyseal tracts

Question 67.
Corticotropin is the other name of ……………….
(a) ACTH
(b) STH
(c) Aldosterone
(d) ADH
Answer:
(a) ACTH

Question 68.
Adrenal failure leads to ……………….
(a) Acromegaly
(b) Simmond’s disease
(c) Midget
(d) Addison’s disease
Answer:
(d) Addison’s disease

Question 69.
Prolactin inhibiting factor is secreted by ……………….
(a) Hypophysis
(b) Hypothalamus
(c) Thyroid
(d) Mammary glands
Answer:
(b) Hypothalamus

Question 70.
Which one of the following is not applicable to prolactin ?
(a) Mammotropin
(b) Lactogenic hormone
(c) Somatotropin
(d) Luteotropin
Answer:
(c) Somatotropin

Question 71.
………………. is a gonadotropic hormone.
(a) STH
(b) LTH
(c) ACTH
(d) FSH
Answer:
(d) FSH

Question 72.
Rhythmic integrated contractions of jejunum are controlled by ……………….
(a) coherin
(b) insulin
(c) glucagon
(d) ADH
Answer:
(a) coherin

Question 73.
Thyroid gland is derived from of embryo.
(a) ectoderm
(b) mesoderm
(c) endoderm
(d) ecto-endoderm
Answer:
(c) endoderm

Question 74.
Deficiency of thyroxine in infants causes ……………….
(a) Cretinism
(b) Grave’s disease
(c) Myxoedema
(d) Exophthalmos
Answer:
(a) Cretinism .

Question 75.
………………. is a hypercalcemic hormone.
(a) PTH
(b) TCT
(c) Thyroxine
(d) ACTH
Answer:
(a) PTH

Question 76.
………………. is a middle layer of adrenal cortex.
(a) Zona fasciculata
(b) Zona pellicida
(c) Zona glomerulosa
(d) Zona reticularis
Answer:
(a) Zona fasciculata

Question 77.
Decrease in the blood calcium level is ……………….
(a) hyperglycemia
(b) hypercalcemia
(c) hypoglycemia
(d) hypocalcemia
Answer:
(d) hypocalcemia

Question 78.
………………. stimulates RBC production.
(a) Aldosterone
(b) Cortisol
(c) Epinephrine
(d) Parathormone
Answer:
(b) Cortisol

Question 79.
Chemicals which are released at the synaptic junction are called ……………….
(a) hormones
(b) neurotransmitters
(c) cerebrospinal fluid
(d) lymph
Answer:
(b) neurotransmitters

Question 80.
Potential difference across resting membrane is negatively charged. This is due to differential distribution of the following ions.
(a) Na+ and K+ ions
(b) Ca++ and Cl ions
(c) Ca++ and Mg++ ions
(d) Mg++ and Cl ions
Answer:
(a) Na+ and K+ ions

Question 81.
Which of the following is not involved in Knee-jerk reflex?
(a) Muscle spindle
(b) Motor neuron
(c) Brain
(d) Inter neurons
Answer:
(c) Brain

Question 82.
An area in the brain which is associated with strong emotions is ……………….
(a) Cerebral cortex
(b) Cerebellum
(c) Limbic system
(d) Medulla
Answer:
(c) Limbic system

Question 83.
Which is the vitamin present in Rhodopsin?
(a) Vitamin A
(b) Vitamin B
(c) Vitamin C
(d) Vitamin D
Answer:
(a) Vitamin A

Question 84.
Wax gland present in the ear canal is modified ……………….
(a) Sweat gland
(b) Vestibular gland
(c) Cowper’s gland
(d) Sebaceous gland
Answer:
(d) Sebaceous gland

Question 85.
The part of internal ear responsible for hearing is ……………….
(a) cochlea
(b) semicircular canal
(c) utriculus
(d) sacculus
Answer:
(a) cochlea

Question 86.
The organ of corti is a structure present in ……………….
(a) external ear
(b) middle ear
(c) semi circular canal
(d) cochlea
Answer:
(d) cochlea

Question 87.
Select the right match of endocrine gland and their hormones among the options given below.
A. Pineal i. Epinephrine
B. Thyroid ii. Melatonin
C. Ovary iii. Estrogen
D. Adrenal medulla iv. Tetraiodothyronine
(a) A-iv, B-ii, C-iii, D-i
(b) A-ii, B-iv, C-i, D-iii
(c) A-iv, B-ii, C-i, D-iii
(d) A-ii, B-iv, C-iii, D-i
Answer:
(d) A-ii, B-iv, C-iii, D-i

Question 88.
Listed below are the hormones of anterior pituitary origin. Tick the wrong entry.
(a) Growth hormone
(b) FSH
(c) Oxytocin
(d) ACTH
Answer:
(c) Oxytocin

Question 89.
Mary is about to face an interview. But during the first five minutes before the interview she experiences sweating, increased rate of heartbeat, respiration, etc. Which hormone is responsible for her restlessness?
(a) Estrogen and progesterone
(b) Oxytocin and vasopressin
(c) Adrenaline and noradrenaline
(d) Insulin and glucagon
Answer:
(c) Adrenaline and noradrenaline

Question 90.
The steroid responsible for balance of water and electrolytes in our body is ……………….
(a) Insulin
(b) Melatonin
(c) Testosterone
(d) Aldosterone
Answer:
(d) Aldosterone

Question 91.
Thymosin is responsible for ……………….
(a) raising the blood sugar level
(b) raising the blood calcium level
(c) increased production of T lymphocytes
(d) decrease in blood RBC
Answer:
(c) increased production of T lymphocytes

Question 92.
In the mechanism of action of a protein hormone, one of the second messengers is ……………….
(a) Cyclic AMP
(b) Insulin
(c) T3
(d) Gastrin
Answer:
(a) Cyclic AMP

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 93.
Leydig cells produce a group of hormones called ……………….
(a) androgens
(b) estrogen
(c) aldosterone
(d) gonadotropins
Answer:
(a) androgens

Question 94.
Corpus luteum secretes a hormone called ……………….
(a) prolactin
(b) progesterone
(c) aldosterone
(d) testosterone
Answer:
(b) progesterone

Question 95.
Cortisol is secreted from ……………….
(a) pancreas
(b) thyroid
(c) adrenal
(d) thymus
Answer:
(c) adrenal

Question 96.
A hormone responsible for normal sleep – wake cycle is ……………….
(a) epinephrine
(b) gastrin
(c) melatonin
(d) insulin
Answer:
(c) melatonin

Question 97.
Match the pairs and choose the correct answer among the following options.
A. Epinephrine
i. Increase in muscle growth
B. Testosterone
ii. Decrease in blood pressure
C. Glucagon
iii. Decrease in liver glycogen content
D. Atrial natriuretic factor
iv. Increase in heartbeat
(a) A-ii, B-i, C-iii, D-iv
(b) A-iv, B-i, C-iii, D-ii
(c) A-i, B-ii, C-iii, D-iv
(d) A-i, B-iv, C-ii, D-iii
Answer:
(b) A-iv, B-i, C-iii, D-ii

Question 98.
Blood calcium level is a resultant of how much dietary calcium is absorbed, how much calcium is lost in the urine, how much bone dissolves releasing calcium into the blood and how much calcium from blood enters tissues. Several factors play an important role in these processes. Mark the one which has no role.
(a) Vitamin D
(b) Parathyroid hormone
(c) Thyrocalcitonin
(d) Thymosin
Answer:
(d) Thymosin

Question 99.
All the following tissues in mammals except one consists of a central ‘medullary’ region surrounded by a cortical region. Mark the wrong entry.
(a) Ovary
(b) Adrenal
(c) Liver
(d) Kidney
Answer:
(c) Liver

Match the columns

Question 1.
Match the hormones with their source

Column A Column B
(1) Glucagon (i) Neurohypophysis
(2) Adrenaline (ii) Islets of Langerhans
(3) Somato tropins (iii) Adenohypophysis
(4) ADH (iv) Medulla

Answer:

Column A Column B
(1) Glucagon (ii) Islets of Langerhans
(2) Adrenaline (iv) Medulla
(3) Somato tropins (iii) Adenohypophysis
(4) ADH (i) Neurohypophysis

Question 2.
Match the layer of adrenal with its hormone.

Column A (Layers of adrenal cortex) Column B (Hormones)
(1) Zona glomerulosa (A) Cortisols
(2) Zona fasciculata (B) Androgens
(3) Zona reticularis (C) Aldosterone

Answer:

Column A (Layers of adrenal cortex) Column B (Hormones)
(1) Zona glomerulosa (C) Aldosterone
(2) Zona fasciculata (A) Cortisols
(3) Zona reticularis (B) Androgens

Question 3.
Match the disorder with the gland associated with it.

Column A (Disorder) Column B (Associated Gland)
(1) Addison’s disease (A) Hypothalamus
(2) Grave’s disease (B) Pituitary
(3) Diabetes insipidus (C) Thyroid
(4) Acromegaly (D) Adrenal

Answer:

Column A (Disorder) Column B (Associated Gland)
(1) Addison’s disease (D) Adrenal
(2) Grave’s disease (C) Thyroid
(3) Diabetes insipidus (A) Hypothalamus
(4) Acromegaly (B) Pituitary

Classify the following to form Column B as per the category given in Column A

Question 1.

Column A Column B
(1) Forebrain ————–
(2) Midbrain ————–
(3) Hindbrain ————–

Answer:

Column A Column B
(1) Forebrain Olfactory lobes, Corpus callosum
(2) Midbrain Superior colliculi, Iter
(3) Hindbrain Pons varolii, Vermis

Question 2.
Types of nerves
Occulomotor, Facial, Optic, Vagus, Abducens, Vestibulocochlear

Column A Column B
(1) Sensory ————–
(2) Motor ————–
(3) Mixed ————–

Answer:

Column A Column B
(1) Sensory Optic, Vestibulocochlear
(2) Motor Occulomotor, Abducens
(3) Mixed Facial, Vagus

Question 3.
Hormones
Estrogen, Glucagon, Epinephrine, Relaxin, Somatostatin, Nor-Adrenalin

Column A Column B
(1) Ovary ————
(2) Pancreas ————
(3) Adrenal Medulla ————

Answer:

Column A Column B
(1) Ovary Estrogen, Relaxin
(2) Pancreas Glucagon, Somatostatin
(3) Adrenal Medulla Epinephrine, Nor-Adrenaline

Question 4.
Disorders
Dwarfism, Myxoedema, Addison’s disease, Cushing’s disease, Gigantism, Goitre

Column A Column B
(1) Pituitary ————
(2) Thyroid ————
(3) Adrenal Cortex ————

Answer:

Column A Column B
(1) Pituitary Dwarfism, Gigantism
(2) Thyroid Myxoedema, Goitre
(3) Adrenal Cortex Addison’s disease, Cushing’s disease

Very short answer questions

Question 1.
What is the need for the control and coordination in multicellular animals?
Answer:
Multicellular animals need control and coordination to maintain constancy of internal environment, i.e. homeostasis.

Question 2.
How do plants carry out control and coordination?
Answer:
Plants carry out control and coordination by sending chemical signals and bringing about various types of movements.

Question 3.
What is the type of nervous system of Earthworm?
Answer:
Earthworm is an annelid having ventral, ganglionated nervous system. It consists mainly of nerve ring, nerve cord and peripheral segmentally arranged nerves.

Question 4.
What kind of nervous system is seen in Hydra, earthworm and cockroach?
Answer:
In Hydra, the nervous system is in the form of nerve net, while in earthworm and cockroach the nervous system is ganglionated.

Question 5.
What is a gland?
Answer:
An organized collection of secretory epithelial cells capable of producing of some secretion is called a gland.

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 6.
What do you mean by discrete endocrine glands ?
Answer:
The glands which are exclusively endocrine in function are discrete endocrine glands.

Question 7.
What is genu and splenium?
Answer:
Genu is anterior and splenium is posterior fold of corpus callosum.

Question 8.
Which is the largest basal nucleus of brain ?
Answer:
Corpus striatum is the largest basal nucleus of the brain.

Question 9.
What is EEG?
Answer:
EEG is electro encephalography. It is used to detect the electrical changes taking place in the brain.

Question 10.
Mention the major sulci present in the cerebral hemispheres.
Answer:
The sulci present in the cerebral hemisphere are – central sulcus, parieto-occipital sulcus and lateral sulcus.

Question 11.
What is the difference in ‘tract’ and ‘nerve’?
Answer:
A bundle of axons within CNS is called a ‘tract’ while the one outside the CNS is called ‘nerve’.

Question 12.
What is a choroid plexus? State its locations.
Answer:
Network of blood capillaries associated with the brain is called choroid plexus, which are anterior choroid plexus present on the roof of epithalamus and posterior choroid plexus located on the roof of medulla oblongata.

Question 13.
What is a synapse ?
Answer:
The interconnection between two neurons or neuron with motor organ is called synapse.

Question 14.
What is a polarised membrane?
Answer:
The cell membrane of a neuron at resting stage is called polarised membrane. In such membrane, the outer side of the cell membrane is more electropositive due to more Na+ ions.

Question 15.
What is summation effect?
Answer:
Many weak stimuli given in a quick succession may produce a response due to summation or additive effect of stimuli, which is known as summation effect.

Question 16.
What is synaptic delay?
Answer:
The time required for a nerve impulse to cross a synapse during transmission of a nerve impulse is called synaptic delay, which is about 0.3-0.5 milliseconds.

Question 17.
What is refractory period?
Answer:
The time interval between two consecutive nerve impulses is called refractory period, during which a nerve cannot be stimulated. Nerve is stimulated only after completion of this period.

Question 18.
What is a synaptic cleft?
Answer:
Small intercellular space between two successive neurons which is about 20¬30 nm in width, is called synaptic cleft.

Question 19.
What is synaptic transmission?
Answer:
The process by which the impulse from the pre-synaptic neuron is conducted to the post-synaptic neuron or cell is called synaptic transmission.

Question 20.
What is a pre-synaptic neuron?
Answer:
The neuron carrying an impulse to the synapse is the pre-synaptic neuron.

Question 21.
What is transmission terminal and generator region?
Answer:
The pre-synaptic membrane of a neuron is transmission terminal while the post- synaptic membrane is called generation region.

Question 22.
What is synaptic fatigue?
Answer:
The synaptic fatigue is the time lag or halting of the transmission of nerve impulse, temporarily at synapse due to exhaustion of its neurotransmitter.

Question 23.
What is the width of synaptic cleft?
Answer:
The width of synaptic cleft is about 20-30 nm.

Question 24.
How much is the resting potential of axon?
Answer:
The resting potential of axon is -70 mV.

Question 25.
How does Na+ – K+ pump work?
Answer:
During repolarisation of certain part of a nerve, Na+ – K+ Pump, pumps out 3 Na+ ions for every 2 K+ ions they pump into the cell.

Question 26.
What is blood-brain barrier?
Answer:
The barrier that keeps a check on passage of ions and large molecules from the blood to the brain tissue is called blood-brain barrier. Endothelial cells lining the blood capillaries help in this process along with the astrocytes.

Question 27.
Enlist meninges of human brain.
Answer:
Dura mater, arachnoid mater or membrane and pia mater are the meninges of human brain.

Question 28.
What is the source of CSF?
Answer:
CSF is secreted by the choroid plexuses of brain and ependymal cells lining the ventricles of brain and central canal of spinal cord.

Question 29.
What is the function of tympanic membrane?
Answer:
Tympanic membrane vibrates on receiving the sound waves and then transfers the vibrations to malleus, the first of the three ear ossicles.

Question 30.
Mention the role of semicircular canals in ear.
Answer:
Semicircular canals help in balancing the equilibrium of the body.

Question 31.
What is the cause for diabetes insipidus?
Answer:
Diabetes insipidus is caused by the deficiency of ADH.

Question 32.
Give role of Parathormone.
Answer:
Parathormone regulates the calcium balance in the body. It increases blood calcium level by increasing reabsorption of calcium from bones.

Question 33.
What is meningitis?
Answer:
Infection of meninges is called meningitis.

Question 34.
Where is general motor area located? What is the function of this area?
Answer:
General motor area is located on precentral gyrus of frontal lobe. It is concerned with all motor activities.

Question 35.
What is the role of Wernicke’s area?
Answer:
Wernicke’s area is the sensory speech area responsible for understanding and formulating written and spoken language.

Question 36.
What is the location of Wernicke’s area?
Answer:
Wernicke’s area is located in the area of contact between temporal, parietal and occipital lobes of cerebrum.

Question 37.
What is the role of Broca’s area?
Answer:
The role of Broca’s area which is the motor speech area that translates thoughts into speech and controls movement of tongue, lips and vocal cords.

Question 38.
What is the location of Broca’s area?
Answer:
Broca’s area is present in the frontal lobe of cerebrum.

Question 39.
Which areas are present in the post central gyrus?
Answer:
General sensory areas concerned with sensation of temperature, touch, pressure, pain and speech are present in the post central gyrus.

Question 40.
Which areas are located on temporal lobe?
Answer:
The areas concerned with sense of taste, sense of hearing and sense of smell are located on temporal lobe.

Question 41.
What is the main function of occipital lobe?
Answer:
Occipital lobe carries sensory visual area which is concerned with the sense of sight. Association visual area is concerned with perception, analysis and storing of information obtained by sight.

Question 42.
What is neuroendocrine system?
Answer:
Neuroendocrine system is an integrated and coordinated system consisting of nervous and endocrine system which brings about the coordination of the body.

Question 43.
What is the quantity of cerebrospinal fluid in adult human being?
Answer:
Cerebrospinal fluid is about 120 ml in adult human being.

Question 44.
How many neurons are present in the brain?
Answer:
There are about 30,000 million neurons in the brain.

Question 45.
Which part of the brain forms 80-85% of the brain?
Answer:
Cerebrum forms 80-85% of the brain.

Question 46.
Which sense is poorly developed in human beings and what is the reason for this?
Answer:
Sense of smell is poorly developed in human beings and it is due to less developed olfactory lobes.

Question 47.
Where are lateral ventricles situated and what is its roof called?
Answer:
Lateral ventricles are the cavities filled with cerebrospinal fluid, present inside the cerebrum and its roof is called pallium.

Question 48.
What is foramen of Monro?
Answer:
Foramen of Monro is a narrow opening that connects lateral ventricle present in cerebrum with third ventricle present in diencephalon.

Question 49.
What is the roof and floor of diencephalon called respectively?
Answer:
Roof of diencephalon is epithalamus and floor of diencephalon is hypothalamus.

Question 50.
Which hormones are produced from pineal gland? Name their functions.
Answer:
Serotonin and melatonin are hormones of pineal gland which are concerned with metabolic activities and regulation of biological rhythm respectively.

Question 51.
What is Habenular commissure?
Answer:
Habenular commissure connects the lateral walls of diencephalon or thalami with each other.

Question 52.
What structure is present on the anterior side of the hypothalamus?
Answer:
Optic chiasma or crossing of two optic nerves is seen on the anterior side of the hypothalamus.

Question 53.
Name the parts of corpora quadrigemina and give their functions.
Answer:
The upper two lobes of corpora quadrigemina are called superior colliculi which receive impulse from optic nerves while the lower two lobes are called inferior colliculi which receive auditory stimuli. Both colliculi control and coordinate head movements.

Question 54.
What is arbour vitae?
Answer:
Arbor vitae is white, branching tree-like processes of white matter that are sent into grey cortex of cerebellum.

Question 55.
Which cranial nerve is called a dentist nerve?
Answer:
Trigeminal, the Vth cranial nerve is called a dentist nerve.

Question 56.
What is central canal?
Answer:
Central canal is the narrow central cavity present inside the spinal cord.

Question 57.
Which cranial nerves originate from the midbrain?
Answer:
Cranial nerves (III) Occulomotor, (IV) Pathetic and (VI) Abducens originate from the midbrain.

Question 58.
What is the other name for the auditory cranial nerve?
Answer:
Vestibulocochlear.

Question 59.
What is the difference between unconditioned and conditioned reflexes?
Answer:
Unconditioned reflexes are inborn or hereditary and permanent while the conditioned reflexes are temporary, learnt or acquired during lifetime.

Question 60.
Give examples of unconditional reflexes.
Answer:
Blinking of eyes, withdrawing of hand upon pricking, suckling to breast by infant, swallowing, knee jerk, sneezing and coughing are some of the unconditional reflexes.

Question 61.
What do you mean by accommodation power of the lens?
Answer:
The ability of the lens by which the light ray from far and near objects is focused on the retina is called accommodation power of the lens. The lens makes fine adjustments to bring such sharp focus on retina.

Question 62.
Where is pituitary located?
Answer:
Pituitary is located inside a depression called sella turcica which is present in sphenoid bone of the skull.

Question 63.
What is the difference between Lorain dwarf and Frohlic dwarf?
Answer:
Lorain dwarf is mentally normal while Frohlic dwarf is mentally abnormal.

Question 64.
How is Simmond’s disease caused?
Answer:
Simmond’s disease is caused due to hyposecretion of GH during adulthood.

Question 65.
How is Addison’s disease caused?
Answer:
Addison’s disease is caused by the hyposecretion of ACTH that leads to adrenal failure.

Question 66.
How is Cushing’s disease caused?
Answer:
Hypersecretion of corticoids causes Cushing’s disease.

Question 67.
What is the main difference between diabetes mellitus and diabetes insipidus?
Answer:
Diabetes mellitus is caused due to deficiency of insulin while diabetes insipidus is caused due to deficiency of ADH.

Question 68.
Which cells secrete coherin? What is the function of coherin?
Answer:
Coherin is the hormone secreted by hypothalamic neurons that brings about prolonged, rhythmic integrated contractions of the jejunum.

Question 69.
What is the difference between Gull’s disease (Myxoedema) and Grave’s disease?
Answer:
Gull’s disease is caused due to hyposecretion of thyroxine while Grave’s disease is caused due to hypersecretion of thyroxine.

Question 70.
In which part thyroid gland stores its hormones?
Answer:
The lumen of thyroid follicles store the thyroid hormones in the form of thyroglobulins.

Question 71.
What are thymosins?
Answer:
Thymosins are hormones secreted by thymus gland which promote the production of antibodies.

Question 72.
Which hormone is secreted by the heart?
Answer:
Heart secretes ANF or Atrial Natriuretic Factor.

Name the following

Question 1.
Name the region consisting of nerve fibres that connects cerebrum and medulla oblongata.
Answer:
Pons Varolii.

Question 2.
Give the names of cranial nerve number VIth and VIIth.
Answer:
VTth cranial nerve is Abducens and Vllth cranial nerve is Facial.

Question 3.
Name the three sulci present on the cerebral hemispheres.
Answer:
Central sulcus, lateral sulcus and parieto¬occipital sulcus.

Question 4.
Name the band of nerve fibres that connect cerebrum, cerebellum and spinal cord.
Answer:
Crura cerebri.

Question 5.
Name the second largest part of the brain.
Answer:
Cerebellum.

Question 6.
Name the three branches of trigeminal nerve.
Answer:
Ophthalmic, Maxillary and Mandibular.

Question 7.
Name the nerve which arises from ventral side of medulla and supplies the tongue.
Answer:
Hypoglossal.

Question 8.
Name of emergency hormones secreted by sympathetic nervous system.
Answer:
Adrenaline and nor-adrenaline are the emergency hormones secreted by sympathetic nervous system.

Question 9.
Name the disorders caused by hyposecretion of thyroxine in children and adults.
Answer:

  1. Hyposecretion of thyroxine in children : Cretinism.
  2. Hyposecretion of thyroxine in adults : Myoxedema.

Question 10.
Name the dual exocrine as well as endocrine gland. Name the hormones secreted by it.
Answer:
Pancreas is the dual gland, exocrine as well as endocrine, it secretes hormones like insulin, glucagon and somatostatin.

Question 11.
Name the four peptide hormones secreted by endocrine cells of alimentary canal.
Answer:
Gastrin, secretin, cholecystokinin and GIPT or Gastric inhibitory peptide.

Question 12.
Name the disorder caused by the under secretion of thyroxine in children.
Answer:
Cretinism is the disorder seen in children due to under secretion of thyroxine.

Give functions of the following

Question 1.
Meninges and CSF.
Answer:
Functions of meninges:

  1. Meninges give protection to the brain and the spinal cord.
  2. They are also nutritive in function.
  3. Cerebrospinal fluid acts as a shock absorber. It protects the brain from mechanical injuries and from desiccation.
  4. It also maintains constant pressure inside and outside the CNS and regulates the temperature.

Functions of CSF:

  1. CSF helps in exchange of nutrients and wastes between the blood and the brain tissue.
  2. CSF supplies oxygen to the brain.

Question 2.
The functions of forebrain.
Answer:
(A) Functions of cerebrum:

  1. The cerebrum controls the voluntary activities.
  2. The cerebrum perceives various sensory stimuli received through vision, taste, smell, sound, touch, speech, etc.
  3. It is the centre of memory, will-power, intelligence, reasoning and learning.
  4. The cerebrum is the centre for emotions, thoughts and feelings, pain, pleasure, fear, fatigue, pressure, temperature, etc.
  5. It is also the centre for micturition, defecation, weeping, laughing, etc

(B) Function of olfactory lobes: Sensation of smell.

(C) Functions of diencephalon:

  1. Diencephalon acts as a relay centre for motor and sensory impulses between spinal cord, brainstem and various areas of cerebral cortex.
  2. Diencephalon consists of epithalamus, thalami and hypothalamus. Therefore it acts as a centre for homeostasis and higher centre of autonomous nervous system.
  3. Hypothalamic nuclei secrete neurohormones which influence the pituitary gland.
  4. Diencephalon regulates heartbeats, blood pressure and water balance.
  5. Anterior choroid plexus which is located in the diencephalon secretes cerebrospinal fluid.
  6. Hypothalmic regions control many involuntary functions such as hunger, thirst, thermo-regulation, fear, anger, sleep, sexual desire, etc.

Question 3.
Write various functions of hindbrain.
Answer:
Functions of hindbrain:
(i) Cerebellum:

  1. Cerebellum is a primary centre for the control of equilibrium, posture, balancing and orientation.
  2. Neuromuscular activities are regulated by the cerebellum.
  3. Coordination of walking, running, speaking, etc. is under the control of hindbrain.

(ii) Pons:

  1. Activities of two cerebellar hemispheres are coordinated by pons.
  2. Nerve fibres cross over in this area and thus the right side of the brain controls the left part of the body and vice versa.
  3. Pons controls the consciousness of the brain.
  4. Breathing centre is located in pons along with medulla.

(iii) Medulla oblongata:

  1. Medulla oblongata controls all the involuntary activities such as heartbeats, respiration, vasomotor activities.
  2. Peristalsis and reflex actions such as coughing, sneezing, swallowing, etc. are also under the control of medulla oblongata.
  3. Medulla oblongata is essential for all the vital functions of the body.

Question 4.
Spinal cord.
Answer:
Functions of spinal cord:

  1. Spinal cord is the main pathway for conduction of sensory and motor nerve impulses.
  2. The sensory impulses travel from the body
    to the brain and the motor impulses travel from the brain to the body.
  3. Spinal reflexes are controlled by spinal cord.
  4. The spinal cord reduces the load on the brain by taking appropriate actions in a reflex way.

Question 5.
Pituitary gland.
Answer:
Functions of pituitary:

  1. Pituitary secretes seven main hormones viz. ACTH, TSH. GH or STH, LTH or Prolactin, MSH and gonadotropins such as FSH, LH or ICSH.
  2. These hormones are secreted upon receiving proper releasing factor from hypothalamus.
  3. These hormones bring about many coordinating functions in the body. Almost all endocrine glands are under the control of these hormones.
  4. The neurohypophysis part stores two hormones, viz. vasopressin and oxytocin which are secreted by hypothalamus.
  5. Important functions such as growth and reproductive processes, pregnancy, childbirth, lactation, etc. are under the control of pituitary.
  6. Neurohypophysis acts as a neurohaemal organ and stores the hormones for some time.

Question 6.
Functions of hormones secreted by the thyroid gland.
Answer:

  1. Thyroxine is the main metabolic hormone in the body.
  2. Thyroxine maintains basal metabolic rate (BMR) by increasing glucose oxidation. It brings about calorigenic effect by energy production.
  3. It also controls normal protein synthesis.
  4. The physical growth, development of gonads and development of mental faculties is under the control of thyroxine.
  5. It controls tissue differentiation during metamorphosis particularly in amphibia.
  6. Body weight, respiration rate, heart rate, blood pressure, temperature, digestion, etc. is regulated by thyroxine.
  7. Another hormone of thyroid, i.e. calcitonin regulates calcium metabolism of the body.

Question 7.
Give significance of relaxin and inhibin.
Answer:
1. Relaxin : Relaxin relaxes the cervix of the pregnant female and ligaments of pelvic girdle during parturition.
2. Inhibin : Inhibin inhibits the FSH and GnRH production.

Question 8.
Enlist hormones secreted by GI tract and state their role.
Answer:
Gastrointestinal tract:
In the gastrointestinal mucosa, certain ells are endocrine in function. These cells produce hormones which play vital role in digestive processes and flow of digestive juices.

  1. Gastrin : This hormone stimulates gastric glands to produce gastric juice.
  2. Secretin : This hormone is responsible for secretion of pancreatic juice and bile from pancreas and liver.
  3. Cholecystokinin CCK/Pancreozymin PZ : This hormone stimulates gall bladder to release bile and stimulates the pancreas to release its enzymes.
  4. Entero-gastrone/Gastric inhibitory peptide (GIP) : It slows gastric contractions and inhibits the secretion of gastric juice.

Distinguish between the following

Question 1.
Electrical and chemical synapses:
Answer:

Electrical synapse Chemical synapse
1. The gap between the successive neurons in electrical synapse is very less [3.8 nm], 1. The gap between two successive neurons in chemical synapse is larger than electrical synapse [10-20 nm].
2. Transmission across the gap is faster in electrical synapse. 2. Transmission across the gap in chemical synapse is relatively slower than electrical synapse.
3. Electrical synapse is less common. 3. Chemical synapse is more common.
4. Electrical synapse is found in those places of the body requiring instant response. 4. Chemical synapse is found almost everywhere and connects neuron to neuron, muscles or glands.

Question 2.
Sympathetic and parasympathetic nervous system.
Answer:

Sympathetic nervous system Parasympathetic nervous system
1. Sympathetic nervous system is formed by 22 pairs of sympathetic ganglia, 2 sympathetic cords which run parallel to vertebral column. 1. Parasympathetic nervous system has nerve fibres which run along with cranial and spinal nerves.
2. Sympathetic nervous system works through neurotransmitter, adrenaline. 2. Parasympathetic nervous system works through release of acetylcholine.
3. Sympathetic nervous system enhances all the involuntary functions. 3. Parasympathetic nervous system retards all the involuntary functions.
4. It brings about fight, fright and flight responses. 4. It brings about relaxation, comfort, pleasure, etc.
5. The pre-ganglionic nerve fibres are short and the post-ganglionic nerve fibres are long in sympathetic nervous system. 5. The pre-ganglionic nerve fibres are long and the post-ganglionic nerve fibres are short in parasympathetic nervous system.

Question 3.
Unconditional reflexes and Conditional reflexes
Answer:

Unconditional reflexes Conditional reflexes
1. Unconditional reflexes are inborn. 1. Conditional reflexes are not inborn, they require training.
2. Unconditional reflexes are permanent. 2. Conditional reflexes are temporary.
3. They never disappear and need no previous experience. 3. They may disappear after sometime and need proper training for developing it.
4. Unconditional reflexes are heritable. 4. Conditional reflexes are non-heritable.
5. Sneezing, coughing, blinking of eye, etc. are unconditional reflexes. 5. Cycling, driving, playing games, etc. are due to conditional reflexes.

Question 4.
Epithalamus and hypothalamus.
Answer:

Epithalamus hypothalamus
1. Epithalamus is the roof of diencephalon. 1. Hypothalamus is the floor of diencephalon.
2. Epithalamus shows pineal stalk to which pineal gland is attached. 2. Hypothalamus shows infundibulum to which pituitary gland is attached.
3. Epithalamus is non-nervous in nature. 3. Hypothalamus is the higher centre of autonomous nervous system.
4. Epithalamus has anterior choroid plexus which secretes cerebrospinal fluid. 4. Hypothalamus has neurons which secrete two endocrine hormones.
5. Epithalamus controls biological rhythm. 5. Hypothalamus controls homeostasis of the body.

Question 5.
Dura mater and pia mater.
Answer:

Dura mater pia mater
1. Dura mater is the outermost meninx. 1. Pia mater is the innermost meninx.
2. Dura mater lies on the innermost side of skull or cranium. 2. Pia mater lies on outermost side of the brain.
3. Dura mater is tough, thick and fibrous. 3. Pia mater is thin and highly vascular.
4. Dura mater is mainly protective in function. 4. Pia mater is mainly nourishing in nature.
5. Below dura mater is subdural space. 5. Above pia mater is sub-arachnoidal space.

Question 6.
Cerebrum and cerebellum
Answer:

Cerebrum Cerebellum
1. The cerebrum is the larger part forming 85% of the brain. It has four lobes. 1. The cerebellum is the smaller part forming 11%. of the brain. It has three lobes.
2. The cerebrum coordinates the functions of the sensory and motor areas. 2. The cerebellum coordinates the equilibrium of muscular movements during walking and running.
3. The cerebrum plays an important role in receiving the sensory impulses such as touch, pain, heat, cold, etc. 3. The cerebellum plays an important role in maintaining the posture and balance of the body.
4. The cerebrum is concerned with higher mental faculties such as memory, will and intelligence. 4. The cerebellum is concerned with muscular mechanism.

Question 7.
Cranial nerves and Spinal nerves
Answer:

Cranial nerves Spinal nerves
1. Nerves arising from the brain are cranial nerves. 1. Nerves arising from the spinal cord are spinal nerves.
2. There are 12 pairs of cranial nerves. 2. There are 31 pairs of spinal nerves.
3. Cranial nerves are of three types, viz sensory, mixed and motor. 3. All spinal nerves are of mixed type.
4. Cranial nerves are responsible for cerebral reflexes. 4. Spinal nerves are responsible for spinal reflexes.

Question 8.
Extero and entero receptors.
Answer:

Exteroceptors Interoceptors
1. Receptors receiving stimuli from outer environment of the body are called exteroceptors. 1. Receptors receiving stimuli from inside the body are called interoceptors.
2. These are somatic receptors. 2. These are visceral receptors.
3. Exteroceptors keep the body informed about . changes in the environment like temperature, pressure, touch, etc. 3. Interoceptors keep the homeostasis in the body by receiving stimuli from inside the body.
4. Mechanoreceptors, thermoreceptors, chemical receptors, photoreceptors and statoacoustic receptors are the different types of exteroceptors. 4. Propioceptors, enteroceptors, baroceptors are the different types of interoceptors.

Question 9.
Adenohypophysis and neurohypophysis.
Answer:

Adenohypophysis Neurohypophysis
1. Adenohypophysis is the anterior lobe of pituitary. 1. Neurohypophysis is the posterior lobe of pituitary.
2. There is portal system between adenohypo-physis and hypothalamus which has blood sinusoids. 2. There is axonal knobs and blood vessels that connect neurohypophysis and hypothalamus.
3. Adenohypophysis forms 75% of pituitary. 3. Neurohypophysis forms 25% of pituitary.
4. Adenohypophysis has three parts, pars tuberalis, pars distalis and pars intermedia. 4. Neurohypophysis has three parts, median eminence, infundibulum and pars nervosa
5. Adenohypophysis has chromophil (acidophil and basophil) and chromophobe cells. 5. Neurohypophysis has axonic fibres and pituicytes.
6. Adenohypophysis secretes seven different hormones after receiving an appropriate message from hypothalamus through releasing factors. 6. Neurohypophysis does not produce hormones on its own. It is a neurohaemal organ as it receives and stores two hormones from hypothalamus.

Question 10.
FSH and LH
Answer:

FSH LH
1. FSH is follicle stimulating hormone essential for the development of ovary. 1. LH is luteinizing hormone responsible for ovulation in females.
2. FSH stimulates ovary (follicular cells) to produce estrogen. 2. LH stimulates ovary (corpus luteum) to produce progesterone.
3. FSH in males is responsible for the spermatogenesis. 3. LH in females is responsible for the development of corpus luteum.
4. Negative feedback mechanism exists between amounts of FSH and estrogen in females. 4. Negative feedback mechanism exists between amounts of LH and progesterone in females.
5. FSH is indirectly responsible for the development of secondary sexual characters in females. 5. LH is indirectly responsible for maintenance of pregnancy in females.

Question 11.
Glucocorticoids and mineralcorticoids
Answer:

Glucocorticoids Mineralocorticoids
1. Glucocorticoids control carbohydrate metabolism. 1. Mineralocorticoids regulate mineral concentration.
2. These are secreted by the cells of zona fasciculata. 2. These are secreted by the cells of zona glomerulosa.
3. These also regulate protein and fat metabolism. 3. These regulate salt-water balance.
4. Cortisol is the main glucocorticoid. 4. Aldosterone is the main mineralocorticoid.

Give scientific reasons

Question 1.
Number of gyri is related to the degree of intelligence.
Answer:

  1. Gyri are the ridges in the folds present on the cerebral cortex.
  2. The number of folds increase the surface area of the cerebral cortex.
  3. Cerebral cortex has sensory and motor areas such as Wernicke’s area, Broca’s area, etc. If the surface area is greater, the neurons in these areas are also more in number.
  4. Greater the number of neurons greater is the intelligence.
  5. The number of gyri therefore is said to be related to the degree of intelligence.

Question 2.
A drunken person cannot maintain balance of the body.
Answer:

  1. Cerebellum is the primary centre for controlling equilibrium and balance of the body.
  2. Alcohol has an adverse effect on the neurons of cerebellum.
  3. Consciousness of brain is also controlled by cerebellum.
  4. When a person is drunk, the alcohol in his or her blood affects the activities of cerebellum and hence the person cannot maintain the balance of the body.

Question 3.
We are able to understand the smell of the first showers of rain or the sudden changes in the climate.
Answer:

  1. We are able to understand any smell because of our olfactory mucosa and olfactory lobes of the brain.
  2. Volatile substances are received by the olfacto-receptors in the nose.
  3. Nerve impulse generated are carried by olfactory nerve and transmitted to brain where the impulse is interpreted.
  4. The characteristic earthy smell is due to a compound ‘geosmin’.
  5. Geosmin is produced by some species of Streptomyces [ gram positive soil bacterium],
  6. Similarly, sudden change in the climate is easily noticed in the form of temperature change in the surrounding.
  7. This change is detected by caloreceptors of the skin. From these receptors the signal is transmitted to CNS where the change is perceived.

Question 4.
We are able to hear the chirping of the birds and recognize the sound of the bird.
Answer:

  1. The phonoreceptors of the body receive the sound waves and transfer the nerve impulses to the auditory areas of the brain.
  2. The interpretation, of the sound is a combined effort of sensory and association areas [auditory areas] of temporal lobes of the brain.
  3. This is how we are able to hear the chirping of the birds and recognize the sound of the bird.

Question 5.
We can see and enjoy the beautiful colours of the nature after the sunrise.
Answer:

  1. The light receptor are present in the retina of eyes.
  2. These are photosensitive rod and cone cells. Cone cells are sensitive to bright light-and colours.
  3. On receiving the light rays, these cells convert them into nerve impulses.
  4. The cones are of three types, which contain their own characteristic photo-pigments that respond to red, green and blue lights.
  5. Various combinations of these cones and their photo pigments produce sensation of different colours.
  6. These impulses are carried to the visual cortex of the occipital lobe where the image is interpreted.
  7. In this manner, we can see and enjoy the beautiful colours of the nature after the sunrise.

Question 6.
Cerebellum is well developed in humans.
Answer:

  1. Our posture is upright and mode of locomotion is bipedal.
  2. While standing, walking and running, our body has to be in a state of balance.
  3. Cerebellum controls balancing, posture, body equilibrium and orientation.
  4. Thus to control static as well as dynamic equilibrium of the body, cerebellum is well developed.

Question 7.
Mr. Sharma suffered from a stroke and the right side of his body was paralysed. However his response was normal for knee jerk reflex with either leg. Explain how and why?
Answer:

  1. Stroke is damage to the brain due to interruption of its blood supply.
  2. Due to this brain functions and cerebral reflexes are severely affected.
  3. However, spinal reflexes remain largely unaffected.
  4. In the above case. Mr. Sharma suffered from a stroke and developed paralysis. But his response to the knee jerk was normal as it is controlled by spinal cord.

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 8.
The word hormone is a misnomer.
Answer:

  1. Hormone is adapted from the Greek word ‘hormein’ means to excite.
  2. But the hormones secreted by the endocrine glands and cells carry out two fold functions, viz. excitatory and inhibitory.
  3. The word hormone is therefore a misnomer.

Question 9.
Pituitary may be considered as the coordinator of endocrine orchestra but not master endocrine gland.
Answer:

  1. The pituitary gland was formerly considered as a master endocrine gland, because all other endocrine glands are under the control of pituitary hormones.
  2. But now it is known that the pituitary gland itself is under the control of hypothalamus through hypo thalamo – hypophysial axis.
  3. Through various releasing factors and release inhibiting factors, the secretions of pituitary are regulated by hypothalamus.
  4. Pituitary in turn controls growth, secretion and maintenance of glands such as adrenal cortex, thyroid and gonads.

Question 10.
Pituitary gland plays an important role in pregnancy and childbirth.
Answer:
Pituitary gland plays an important role in pregnancy and childbirth for the following reasons:

  1. Luteinizing hormone secreted by the pituitary gland stimulates ovulation, formation of corpus luteum and the synthesis of progesterone which are necessary for pregnancy.
  2. Lactogenic hormone secreted by the pituitary gland promotes breast development during pregnancy and stimulates the secretion of milk after childbirth.
  3. Oxytocin secreted by hypothalamus and sent by pituitary gland stimulates the contraction of the uterus during childbirth.

Question 11.
Fall and rise in blood calcium stimulates secretion of parathyroid.
Answer:

  1. Normal calcium level in the blood is called calcemia.
  2. Increase in the blood calcium is called hypercalcemia while decrease in the level is called hypocalcemia.
  3. Decrease in the blood calcium, stimulates the parathyroid glands to secrete PTH.
  4. PTH stimulates osteoclasts of bone to start bone resorption. This will help to cause increase in the blood calcium level.
  5. Increase in the blood calcium above normal will retard the secretion of PTH. Hence further increase in the blood calcium is stopped.

Question 12.
Pancreas is both exocrine as well as endocrine gland.
Answer:

  1. Pancreas is heterocrine gland i.e. both exocrine and endocrine gland.
  2. The exocrine part is pancreatic acini. The cells of acini secrete pancreatic juice containing digestive enzymes like trypsinogen, chymotrypsinogen, etc.
  3. Endocrine part of pancreas is made up of groups of cells called Islets of Langerhans. There are four kinds of cells in islets of Langerhans which secrete hormones.

Alpha (α) cells (20%) secrete glucagon.
Beta (β)) cells (70%) secrete insulin.
Delta (δ) cell (5%) secrete somatostatin. PP cells or F cells (5%) secrete pancreatic polypeptide (PP).
Hence, pancreas is said to be exocrine as well as endocrine gland.

Question 13.
Patient suffering from hypothyroidism shows increased level of TSH. Why?
Answer:

  1. Hypothyroidism means decrease in the secretion of T3 and T4
  2. Decrease in T4, i.e. thyroxine in the blood triggers negative feedback mechanism.
  3. The hormone receptors in hypothalamus detect this change and secrete TRE
  4. TRF stimulates the pituitary to secrete TSH
  5. Thus, Patient suffering from hypothyroidism shows increased level of TSH due to negative feedback control.

Question 14.
We are advised to use iodized salt.
OR
Why do we use iodized salt?
Answer:

  1. Iodine is needed for synthesis of thyroid hormone.
  2. If there is deficiency of iodine in the diet, it causes enlargement of thyroid gland leading to simple goitre.
  3. This disease is common in hilly areas hence it is also called endemic goitre.
  4. Addition of iodine to table salt prevents this disease.
  5. Therefore we must use iodised salt.

Write short notes on the following

Question 1.
Nervous system of Hydra.
Answer:

  1. Hydra, a cnidarian shows the diffused nervous system in the form of nerve net.
  2. It is the most primitive nervous system.
  3. There are two nerve nets in the mesoglea-one connected towards the epidermis and second towards the gastro-dermis.
  4. Hydra lacks sensory organs, but the sensory cells scattered in the body wall.
  5. The nerve impulse shows no polarity or direction. As all neurons are interconnected the response is seen throughout the body.

Question 2.
Nervous system of Planaria.
Answer:

  1. Planaria is a flatworm and belongs to the phylum Platyhelminthes.
  2. It is the most primitive animal with a Central Nervous System (CNS) located on the ventral side of body.
  3. Nervous system consists of a mass of cerebral or cephalic ganglion appearing like an inverted U-shaped brain.
  4. Ventrally from below the ganglia arise a pair of Ventral Nerve Cords (VNC) or long nerve cords. These are interconnected to each other by transfer nerve or commissure in a ladder like manner.
  5. The PNS include sensory cells arranged in lateral cords in the body.

Question 3.
Resting potential of a nerve fibre.
Answer:

  1. The neurons have a property of excitability.
  2. The transmission of the nerve impulse along the long nerve fibre is a result of electrical changes across the neuronal membrane during conduction of an excitation.
  3. The plasma membrane separates the outer [extra cellular fluid] and inner solutions [intra cellular fluid/cytoplasm] of different chemical compounds.
  4. The external tissue fluid has both Na+ and K+
  5. On the inside there is an excess of K+ along with large amount of negatively charged protein molecules and nucleic acid.
  6. This condition of a resting nerve is also called a polarised state and it is established by maintaining an excess of Na+ on the outer side.

Question 4.
Electrical synapse.
Answer:

  1. In this type of synapse gap between the neighbouring neurons is very narrow.
  2. This electrical link is formed between the pre-and post-synaptic neurons.
  3. At the gap junction, the two cells are within almost 3.8 nm distance of each other.
  4. Transmission across the gap is faster.
  5. Electrical synapses are found in those places of the body requiring fastest response as in the defence reflexes.

Question 5.
Velocity of nerve impulse.
Answer:

  1. The rate of transmission of impulse is higher in long and thick nerves.
  2. It is higher in warm blooded animals [homeotherms] than in cold blooded animal [poikilotherms].
  3. The velocity of transmission is higher in voluntary fibres (100- 120 m/second in man) as opposed to autonomic or involuntary nerves (10-20 m/second).
  4. It is faster in medullated nerve fibre [up to 150 m/s], as the impulse has to jump from one node of Ranvier to the next as compared with non-medullated nerve fibre [10-25 m/s]

Question 6.
Meninges of CNS.
Answer:

  1. Meninges are the connective tissue membranes that cover the brain and the spinal cord. There are three meninges, viz. dura mater, arachnoid mater and pia mater that cover the Central nervous system.
  2. The outermost tough, thick and fibrous meninx is dura mater. It is protective in function as it is attached to the inner side of the cranium.
  3. The middle, thin and vascular membrane formed of reticular connective tissue is called arachnoid mater. It carries out nutritive function and also gives protection to the brain.
  4. The innermost highly vascular and thin membrane is pia mater. It lies in contact with CNS. It is nutritive in function.
  5. There is subdural space between the dura mater and arachnoid mater. It is filled with serous fluid.
  6. Besides, there is a sub-arachnoidal space lying between arachnoid mater and pia mater. It is filled with cerebrospinal fluid.

Question 7.
Ventricles in human brain.
Answer:

  1. Ventricles are the cavities present in different parts of the brain.
  2. There are four ventricles in the human brain. All the ventricles are connected with each other.
  3. They are filled with cerebrospinal fluid.
  4. Paracoel or lateral ventricles-I and-II are present inside the cerebral hemispheres.
  5. The diencephalon has ventricle-III.
  6. Ventricle-III is in connection with lateral ventricles by foramen of Monro.

Question 8.
Sympathetic nervous system.
Answer:

  1. Sympathetic Nervous System is formed by 22 pairs of sympathetic ganglia. These ganglia are linearly arranged on two sympathetic cords. Sympathetic nerve cords run on either side of the vertebral column.
  2. Sympathetic nerve cords are connected to CNS by rami communicans of spinal nerve fibres.
  3. This system works during stress, pain, anger, fear or emergency. It is supposed to bring about fight, flight or fright reactions.
  4. Action of sympathetic nervous system is dependent on adrenaline or noradrenaline. This neurotransmitter is secreted by sympathetic nervous system as an emergency hormone.

Question 9.
Parasympathetic nervous system.
Answer:

  1. Parasympathetic nervous system consists of nerve fibres of some cranial nerves, sacral nerves and parasympathetic ganglia.
  2. These parasympathetic ganglia are present on the sides of visceral organs like heart, lungs, stomach, kidney, etc.
  3. Parasympathetic ganglia gives out parasympathetic fibres which innervates these involuntary organs.
  4. Parasympathetic nervous system works through release of acetylcholine which acts as neurotransmitter. It is an inhibiting neurotransmitter which affects visceral organs.
  5. This system works during rest and brings about relaxation, comfort, pleasure, etc.

Question 10.
Parkinson’s disease.
Answer:

  1. Degeneration of dopamine-producing neurons in the CNS causes Parkinson’s disease.
  2. Symptoms develop gradually over the years.
  3. Symptoms are tremors, stiffness, difficulty in walking, balance and coordination.
  4. Seen in old age and is incurable.

Question 11.
Alzheimer’s disease.
Answer:

  1. Alzheimer’s disease is the most common form of dementia.
  2. Its incidence increases with the age.
  3. Symptoms include the loss of cognitive functioning, thinking, remembering, reasoning and behavioural abilities. It interferes with the person’s daily life and activities.
  4. It occurs due to loss of cholinergic and other neurons in the CNS and accumulation of amyloid proteins.
  5. There is no cure for Alzheimer’s, but treatment slows down the progression of the disease and may improve the quality of life.

Question 12.
Types of reflex actions.
Answer:

  1. The reflex actions are of two types, viz. cerebral and spinal.
  2. Cerebral reflex actions are controlled by the brain.
  3. Spinal reflex actions are controlled by the spinal cord.
  4. In man, most of the reflex actions are controlled by the spinal cord.

Question 13.
Pavlov’s experiment about conditional reflex.
Answer:

  1. Conditional reflex was demonstrated by Pavlov while performing experiments with dogs.
  2. Pavlov offered some food to dog and noticed that the dog starts salivating after smelling and seeing the food.
  3. Simultaneously he rang the bell so that the dog associated the food with the sound of bell. This experiment was repeated many a times by him.
  4. Later he only rang the bell and did not give any food to the dog. But still the dog salivated.
  5. This shows that the dog was conditioned to the sound of bell. The dog learnt that there is a relation between food and sound of bell. This is called conditional response.

Question 14.
Mechanism of vision.
Answer:

  1. The light rays of visible wavelength pass through the cornea and the lens and are focused on the retina of the eye.
  2. The sight is possible due to conjugated proteins present in the rods and the cones.
  3. These are photo pigments which are composed of opsin (a protein) and retinal (Vitamin A derivative).
  4. The light induces dissociation of retinal from the opsin, which causes a change in the structure of the opsin.
  5. This causes the change in the permeability of the retinal cells.
  6. It generates action potential which is carried via bipolar cells and ganglion cells and further conducted by the optic nerves to the visual cortex (vision centre) of the brain.
  7. The neural impulses are analyzed and the image formed on the retina is thus recognized.

Question 15.
Mechanism of hearing.
Answer:

  1. The external ear receives the sound waves and sends to the tympanic membrane. The tympanum vibrates transmitting the vibrations to the chain of three ossicles and then to the oval window.
  2. The vibrations are further passed on to the fluid of cochlea.
  3. The waves in the perilymph and endolymph induces movements in the basilar membrane.
  4. The hair cells of organ of Corti bend and are pressed against the tectorial membrane.
  5. Due to this pressure, the nerve impulses are generated and are sent to the afferent nerve fibres.
  6. The impulses are carried by the auditory nerves to the auditory centre of the brain, where the impulses are analyzed and the sound is perceived.

Question 16.
Types of endocrine systems.
Answer:
There are 3 types of endocrine systems.

  1. Discrete endocrine system : The glands exclusively endocrine in function are called discrete endocrine glands.
  2. Mixed endocrine system : The glands endocrine as well as exocrine in function are called mixed endocrine glands.
  3. Diffused endocrine system : Some endocrine cells scattered in a particular region/gland form diffused endocrine system.

Question 17.
Thymus.
OR
Functions of Thymosin.
Answer:

  1. Thymus is located on the dorsal side of the heart and the aorta.
  2. It consists of many lobules.
  3. The thymus plays major role in the development of the immune system.
  4. Thymus secretes thymosin which plays an important role in the differentiation of T-lymphocytes. These cells built cell mediated immunity.
  5. The thymosin also promotes the production of antibodies providing humoral immunity.
  6. The degeneration of thymus gland occur in old individuals leading to decreased production of thymosin thereby weakening of immune response.

Question 18.
The role of heart and kidney in hormone secretion.
Answer:
(I) Kidney:

  1. Kidney produces renin, erythropoietin and calcitriol (calcitriol is the active form of vitamin cholecalciferol (D3).
  2. Renin along with angiotensin helps in maintaining the blood pressure in the renal artery by vasoconstriction.
  3. Erythropoietin stimulates erythropoiesis.
  4. Calcitriol helps in absorbing calcium from the stomach.

(II) Heart:

  1. Heart walls secrete Atrial natriuretic hormone /ANE
  2. ANF increases sodium excretion [natriuresis] along with water.
  3. It acts along with kidneys and reduces blood pressure by lowering blood volume.

Question 19.
Hormones secreted by adrenal gland.
Answer:

  1. The adrenal cortex secretes corticoids. Corticoids is a group of several hormones that control several vital body functions.
  2. Corticoids are of two types, viz. mineralocorticoids and glucocorticoids.
  3. Small amounts of androgenic steroids are also secreted by the adrenal cortex which have the role in the growth of axial and pubic hairs and facial hairs during puberty.
  4. The mineralocorticoids regulate the electrolyte balance while the glucocorticoids are involved in carbohydrate metabolism.
  5. Adrenal medulla secretes adrenaline or epinephrine and noradrenaline or norepinephrine.

Question 20.
Role of mineralocorticoids.
Answer:

  1. The mineralocorticoids regulate ionic and osmotic balance, by regulating the amounts of electrolyte and water.
  2. Aldosterone is the main mineralocorticoid that acts on the renal tubules.
  3. Aldosterone stimulates the re-absorption of Na+ and water and excretion of K+ and phosphate ions.
  4. The aldosterone helps in the maintenance of electrolytes, body fluid volume, osmotic pressure and blood pressure.

Question 21.
Secretions of adrenal medulla and their role.
Answer:

  1. The adrenal medulla secretes two catecholamine hormones, viz. adrenaline (epinephrine) and noradrenaline (nor-epinephrine).
  2. Adrenaline and noradrenaline increase alertness, dilation of pupils, piloerection, sweating, etc.
  3. Both the hormones increase the rate of heartbeat, strength of heart contraction and rate of respiration.
  4. These hormones also stimulate the breakdown of glycogen, lipids and proteins thereby increasing blood glucose level.
  5. All the above reactions are useful for survival during emergency situations and in stress condition. Therefore, they are called emergency hormones or 3 F hormones of fright, fight or flight.

Question 22.
Cortisols and their role.
Answer:
I. Cortisol : Cortisol is the main glucocorticoid hormone.

II. Role of cortisol:

  1. Cortisol stimulates many metabolic reactions such as gluconeogenesis, lipolysis and proteinolysis.
  2. It inhibits cellular uptake and utilization of amino acids.
  3. Cortisol also plays an important role in maintaining the cardiovascular system and kidney functions.
  4. It is also involved in anti-inflammatory reactions and suppresses the immune response.
  5. Cortisol stimulates the RBC production.

Question 23.
Disorders of adrenal cortical hormones.
Answer:

  1. Disorders of adrenal cortical secretions are of two types, viz. hyposecretion and hypersecretion.
  2. Hyposecretion of corticosteroids causes Addison’s disease.
  3. The symptoms of Addison’s disease are general weakness, weight loss, low body temperature, feeble heart action, low BR acidosis, excessive loss of Na+ and Cl in urine, impaired kidney functioning and kidney failure, etc.
  4. Hypersecretion of corticoids causes Cushing’s disease.
  5. The symptoms of Cushing’s disease are alkalosis, enhancement of total quantity of electrolytes in extracellular fluid, polydipsia, increased BR muscle paralysis, etc.

Question 24.
Hormones of adenohypophysis.
Answer:
I. Somatotropic Hormone (STH) or Growth Hormone (GH):

  1. The secretion of GH is under dual control of hypothalamus through GHRF (Growth hormone releasing factor) and GHIF (Growth hormone inhibiting factor).
  2. The GH brings about general growth of the body.
  3. The principal actions of GH Eire promotion of linear growth in the skeleton, increase in the size of the muscles and connective tissue.
  4. GH enhances the protein synthesis. The lipolysis in adipose tissue to release more fatty acids is also stimulated by GH.
  5. The growth of bones by absorption of calcium takes place due to GH.

II. Thyroid Stimulating Hormone (TSH) or Thyrotropin:

  1. TSH is regulated by TRF (Thyrotropin releasing factor) from hypothalamus’
  2. For inhibition there is a negative feedback between thyroxine level in the blood and secretion of TSH.
  3. TSH stimulates thyroid glands to increase uptake of iodine for synthesis of thyroxine. It brings breakdown of colloid to release thyroxine.

III. Adrenocorticotropic Hormone (ACTH) Corticotropin :

  1. ACTH stimulates growth of adrenal cortex Eind stimulates it to secrete glucocorticoids Eind mineralocorticoids.
  2. The regulation of ACTH secretion is under the control of hypothalamic CRF (Corticotropin releasing factor) and the negative feedback mechanism between plasma level of cortisol and ACTH.

IV. Prolactin (PRL) or Luteotropic hormone (LTH):
1. Secretion of prolactin is under duad control by hypothalamus by two factors such as PRF (Prolactin releasing factor) and PIF (Prolactin inhibiting factor) of hypothalamus.

2. Prolactin performs many functions therefore it has many terms as follows :

  • Development of mammary glands (Mammo tropin).
  • Milk secretion by mammary glands (Lactogenic hormone).
  • Maintenance of corpus luteum so that- it keeps on secreting progesterone during pregnancy (Luteotropin).

3. It may be inhibiting the chances of pregnancy during lactation period.

V. Gonadotropic Hormones (GTH) or Gonadotropins:
1. There are two types of gonadotropins, viz. FSH and LH or ICSH.

2. The secretions of gonadotropin are regulated by gonadotropin releasing factor (GHRF) of hypothalamus.

(3) They are regulated by negative feedback by sex hormones such as testosterone and estrogen.
(a) Follicle Stimulating Hormone (FSH):

  • FSH in female stimulates development of Graafian follicles. It helps in the formation of ovum by stimulating oogenesis.
  • It also stimulates ovarian follicular cells for secretion of female sex hormones, estrogen.
  • Under influence of estrogen, development of secondary sexual characters occurs in female.
  • In males, FSH stimulates germinal epithelium of seminiferous tubules for spermatogenesis and helps in the production and maturation of sperms.
  • Deficiency of FSH leads to infertility in both the sexes.

(b) Luteinizing hormone (LH) in females and Interstitial cell stimulating hormone (ICSH) in males:

  • LH brings about ovulation, i.e. rupture and release of ovum from the mature Graafian follicle. The empty Graafian follicle is transformed into corpus luteum.
  • Corpus luteum is a secondary endocrine source which secretes gestational hormone progesterone. Progesterone is a pregnancy stabilizing hormone.
  • In males, ICSH stimulates interstitial cells of Leydig which in turn secretes male sex hormone, the testosterone.
  • Testosterone develops secondary sexual characters in males.
  • High level of progesterone in female signals negative feedback, to pituitary to stop secretion of LH.
  • In males, high level of testosterone in blood gives negative feedback signal to Inhibit the secretion of FSH.

Short answers questions

Question 1.
Give one point of distinction between nervous coordination and hormonal coordination.
Answer:

  1. The activity of nervous coordination is quick, immediate and fast as it sends the electrical signals.
  2. Hormonal coordination is slow and long lasting as it takes place through the action of hormones.

Question 2.
Write about types of nerves.
Answer:
Nerve is a group of neurons enclosed in a connective tissue sheath epineurium. It is classified as:

  1. Sensory nerve : A nerve having all sensory neurons is called sensory nerve. It carries information from sense organs to CNS. It is also called afferent nerve.
  2. Motor nerve : A nerve having all motor neurons is called motor nerve. It carries information from CNS to effector organs. It is also called efferent nerve.
  3. Mixed nerve : A nerve having with both sensory and motor neurons is called a mixed nerve. Sensory neurons in it carry nerve impulses from sense organs to CNS while motor neurons carry nerve impulses from CNS to effector organs.

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 3.
What is the composition of neural tissue?
Answer:
Neural tissue is derived from embryonic ectoderm. It consists of two types of cells.

  1. Neurons or nerve fibres : These are structural and functional units of nervous tissue. They conduct nerve impulses and coordinate various body activities.
  2. Neuroglial cells : These are supportive cells which protect neurons throughout CNS and PNS. They perform other functions like secretion of myelin sheath, phagocytosis, production of CSF, etc. e.g Schwann cells, astrocytes, satellite cells, etc.

Question 4.
Explain the structure of cyton.
Answer:

  1. Cyton is the main body of a neuron or nerve fibre.
  2. The cyton has a distinct central nucleus with a nucleolus and neuroplasm.
  3. Cytoplasm surrounds the nucleus around which there are neurofibrils, Nissl’s granules and other cell organelles.
  4. Nissl’s granules are rich in ribosomes and proteins.
  5. Neurofibrils play an important role in transmission of nerve impulse.
  6. The cytons are generally found inside the brain, spinal cord (CNS) and in the ganglia.
  7. Cytons within CNS form ‘nuclei’ while those present outside CNS in nerves form ‘ganglia’.

Question 5.
Enlist the various connective tissue layers in a nerve along with their location.
Answer:
Connective tissue layers in a nerve are:

  1. Endoneurium : Covers each nerve fibre.
  2. Perineurium : Covers each nerve bundle having a number of neurons.
  3. Epineurium : Covers many nerve bundles to form a peripheral nerve.

Question 6.
What is a synapse?
Answer:

  1. Synapse is a microscopic functional gap between two successive neurons.
  2. In this telodendrites of pre-synaptic neuron are in close proximity with dendrites of post-synaptic neuron.
  3. This gap is also called synaptic cleft.
  4. During transmission of nerve impulse, the synapse get filled with neurotransmitters like acetyl choline.

Question 7.
What are the three divisions of nervous system? What are their chief functions?
Answer:

  1. The three divisions of nervous system are central nervous system, peripheral nervous system and autonomous nervous system.
  2. The central nervous system (CNS) consists of brain and spinal cord. The brain and spinal cord are the coordinators for all nervous functions.
  3. The peripheral nervous system (PNS) is constituted by several nerves given by the central nervous system to all the body parts. All these nerves carry impulses to the CNS and bring back the responses from them. They are divided into cranial nerves and spinal nerves.
  4. The autonomous nervous system controls all the internal organs and is not under voluntary control.

Question 8.
Does this CSF remain enclosed inside the ventricles? What can be the outcome of such a situation?
Answer:

  1. CSF is present within the CNS as well as around it.
  2. This fluid communicates with each other on the roof of medulla oblongata through 3 apertures, viz. Foramina of Luschka and foramen of Magendie.
  3. This communication ensures constant pressure of CSF within as well as outside the CNS.
  4. In the absence of this communication, there would be a pressure difference within as well as outside the CNS which will result in disturbances in the activities of CNS. Moreover, intercranial pressure would rise.

Question 9.
Enlist the different parts of the brain.
Answer:

  1. There are three divisions of the brain, viz. forebrain (prosencephalon), midbrain mesencephalon) and hindbrain (rhombencephalon).
  2. Forebrain is divided into cerebrum (telencephalon) and diencephalon (thalamencephalon). Underdeveloped of factory lobes (rhinencephalon) can also be seen in the anterior region.
  3. Midbrain consists of corpora quadrigemina and crura cerebri.
  4. Hindbrain has cerebellum (metencephalon) and brain stem. It is divided into pons varolii and medulla oblongata (myelencephalon).

Question 10.
Describe functional areas of cerebral cortex.
Answer:
Functional areas of cerebrum:

  1. There are three functional areas in cerebrum viz., sensory, association and motor area.
  2. In sensory area, sensory receptors bring the sensory inputs. These inputs are analysed in sensory area.
  3. The sensory speech area is located in parietal lobe. It is called Wernicke’s area.
  4. Association area forms the major portion of the cerebrum. It processes, analyses and stores the information given by the inputs. Power of reasoning, will, understanding, memory, etc. are the faculties present in the cerebral cortex.
  5. Motor area is present in the frontal lobe lying anterior to the premotor area. In the lower part of the motor area just above the lateral sulcus lies the Broca’s area or motor speech area. The Broca’s area controls the movements necessary for speech.

Question 11.
Explain in detail the regions associated with the diencephalon.
Answer:
Diencephalon is a part present between forebrain and midbrain. It has three regions epithalamus, thalami and hypothalamus.
(1) Epithalamus : Epithalamus is the roof of diencephalon. It is highly vascular and non- nervous. It forms anterior choroid plexus that secretes cerebrospinal fluid. Pineal body is attached to epithalamus with the help of pineal stalk. Pineal body secretes serotonin and melatonin.

(2) Thalami : The lateral parts of diencephalon which are interconnected with the habencular commissure are called thalami. From thalami all sensory impulses (except olfactory impulses) pass on to the cerebrum.

3. Hypothalamus : Hypothalamus is the floor of the brain. Pituitary gland is attached to this floor by an infundibular stalk. Hypothalamus has many hypothalamic nuclei which are scattered in the white matter.

Question 12.
What is EBG? What information can be obtained from the EEG?
Answer:

  1. EEG stands for electroencephalography.
  2. It refers to the recordings of the brain’s spontaneous electrical activities in certain period of time.
  3. These are recorded using multiple electrodes.
  4. EEG is non-invasive method and measures voltage fluctuations resulting from ionic current within the neurons.
  5. The basic concepts involved in this are similar to ECG.
  6. It is used to diagnose conditions like epilepsy, sleep disorders, encephalopathies, coma, etc.

Question 13.
Find out how different functional areas of the brain can be mapped?
Answer:
Functional areas and status of the brain can be mapped by several imaging techniques available such as-

  1. MRI : Magnetic Resonance Imaging
  2. CT : Computed Tomography
  3. PET : Positron Emission Tomography

Question 14.
Which are silent areas of the brain?
Answer:

  1. Silent areas of the brain refer to association areas of the brain.
  2. One such area is in the prefrontal cortex of brain.
  3. These are the areas of the brain in which pathogenic conditions may occur without producing symptoms.
  4. Injury to these areas is not accompanied by symptoms related to sensory and motor functions.

Question 15.
Is nervous tissue without lymphatic vessels?
Answer:

  1. CSF is the lymph of CNS.
  2. CSF is continuously generated by the ependymal cells lining the ventricles and central canal and simultaneously drained out of the brain into the blood stream.
  3. There are no lymphatic vessels in the nervous system.
  4. But the CSF is drained into peripheral blood circulation with the help of lymph vessels associated with meninges mainly the dura mater.

Question 16.
Explain the structure of spinal cord.
Answer:
Structure of spinal cord:

  1. Spinal cord is a 42 to 45 cm long, 2 cm thick and hollow tube, extending from medulla oblongata to lumbar region.
  2. It lies in the neural canal of vertebral column.
  3. At the other end, it tapers down and is called conus medullaris. The posterior most end is called filum terminale which appears as a thread-like structure.
  4. Beyond the second lumbar vertebra, it forms a horse tail-like structure called cauda equina. Cauda equina is a bunch of dorsal and ventral roots of last pair of spinal nerves.
  5. There are two swellings on the spinal cord. The upper is cervical swelling and lower is lumbar swelling. Accordingly there are two plexuses, the cervical plexus supplying nerves to hands and the lumbar plexus supplying nerves to legs.
  6. 31 pairs of spinal nerves arise from spinal cord.

Question 17.
What is the significance of reflex action?
Answer:
Significance of reflex action :

  1. Reflex action helps the animals to adjust quickly to the changing environment.
  2. Reflex action is for quick actions necessary for survival. The life may have been in danger in the absence of reflex action.
  3. Most of the reflexes are spinal reflexes, i.e. reflexes controlled by spinal cord. Thus the brain is not involved in these actions. This prevents overloading of the brain and brain fatigue.
  4. Some reflexes are inborn and hence training or learning is not required for these.

Question 18.
During extraction of a tooth, the dentist gives an injection of Anaesthesia to the patient before extraction. Is the action potential generated? How does the local anaesthesia work? What is the effect of pain killer on the nervous system?
Answer:

  1. Teeth are innervated by branches of trigeminal nerve [Vth cranial nerve]
  2. Extraction of tooth stimulates this nerve which then carries the impulse [action potential) to the pain centre of the brain where the pain is perceived.
  3. To avoid this, dentists give anaesthesia, to numb the nerve.
  4. Action potential is not generated due to anaesthesia.
  5. Hence the pain is not perceived.
  6. Similarly, some common pain killers act on the nerve endings and pain centres of the brain, preventing generation of action potential.

Question 19.
Give a list of psychological disorders.
Answer:

  1. Autism spectrum disorder.
  2. Bipolar disorder.
  3. Depression.
  4. Anxiety disorder.
  5. ADHD (Attention Deficit Hyperactivity Disorder).
  6. Stress related disorders.

Question 20.
What are endocrine glands?
Answer:

  1. Endocrine glands are ductless glands which are capable of secreting hormones.
  2. The hormones are poured directly into the bloodstream as the endocrine glands do not have duct.
  3. Hormones regulate the function of target tissue or organ.
  4. They either have excitatory effect or have an inhibitory effect.

Question 21.
What are the main endocrine glands in human body?
Answer:
The main endocrine glands in human body are as follows:

  1. Pituitary or hypophysis
  2. Hypothalamus
  3. Thyroid
  4. Parathyroid
  5. Adrenal or suprarenal
  6. Islets of Langerhans in pancreas
  7. Endocrine parts of gonads, i.e. testis and ovary.
  8. Pineal gland and thymus are also endocrine glands of less importance.

Question 22.
What are the common properties of hormones?
OR
State properties of hormones.
Answer:

  1. Hormones are specifically produced in response to a certain stimulus.
  2. Depending on nature and intensity of the stimulus, the rate of secretion of a hormone varies from low to very high.
  3. Hormones are produced in one organ and show their effect on distant ‘target’ organ. The source and the target region may be distantly located.
  4. Hormones are directly poured in blood circulation and always carried through blood.
  5. Hormones are always bound to specific carrier proteins while being transported through the blood.
  6. Hormones have a high degree of target specificity.
  7. Every hormone acts basically by modifying some aspect of cellular metabolism.
  8. The excessive secretions or deficiencies- of hormones may lead to serious disorders. Such disorders are called hyper – and hypo- disorders, respectively.

Question 23.
What are the disorders caused due to hyposecretion and hypersecretion of GH or STH?
Answer:
(1) Hypersecretion is excessive secretion. In children, the hypersecretion of GH causes gigantism. In adults, it causes Acromegaly.

(2) Hyposecretion, i.e. lesser secretion of GH in children cause dwarfism. The person is also referred to as midget. There are two types of dwarfs, viz. Frohlic dwarf who are mentally abnormal and Lorain dwarf who are mentally normal.

(3) Hyposecretion of GH in adults cause Simmond’s disease.

Question 24.
What are the disorders caused due to hyposecretion and hypersecretion of ACTH?
Answer:

  1. Hyposecretion of ACTH leads to Addison’s disease, i.e. adrenal failure. This results in affected carbohydrate metabolism leading to weakness and fatigue.
  2. The hypersecretion leads to excessive growth of adrenal cortex. This causes Cushing’s disease.

Question 25.
Write an account of hormones secreted by the thyroid gland.
Answer:

  1. Thyroid secretes triiodothyronine or T3, tetraiodothyronine or thyroxine or T4 and thyr ocalcitonin.
  2. The thyroid gland synthesize, store and discharge these hormones.
  3. T3 and T4 are iodinated derivatives of amino acid tyrosine which are secreted by thyroid follicular cells and stored in follicles. They have similar function. The secretion of T3 and T4 are regulated by Thyroid stimulating hormone (TSH) or thyrotropin of pituitary gland in negative feedback manner. T3 is more active and T4 is more potent hormone.
  4. Thyrocalcitonin is secreted by the parafollicular cells.
  5. Thyrocalcitonin regulates blood calcium level. It stimulates bones to take up Ca++ from the blood and deposit it in the form of calcium phosphates in the bones, thereby decreasing blood Ca++ level. Increased calcium level of blood stimulates ‘C’ cells to secrete thyrocalcitonin and vice versa.

Question 26.
Describe adrenal glands with respect to morphology, histology and secretions.
Answer:

  1. A pair of adrenal or suprarenal glands are located just on the upper border of kidneys.
  2. The adrenal gland shows two distinct regions, viz. thicker outer cortex and thinner inner medulla.
  3. The adrenal cortex consists of three distinct regions. The outer zona glomerulosa, the middle zona fasciculata and inner zona reticularis.
  4. Adrenal cortex produces corticoids. Corticoids is a collective term for many hormones, such as glucocorticoids, mineralocorticoids and steroid sex hormones.
  5. Adrenal medulla secretes adrenaline or epinephrine and noradrenaline or norepinephrine.

Question 27.
Why are reproductive organs called dual in function?
Answer:

  1. A pair of testes in males and a pair of ovaries in female both secrete hormones which are essential for sexual characters and function.
  2. Besides this, they also produce male and female gametes respectively. Therefore they are said to be dual in function.

Question 28.
What are male hormones? What is their source and functions?
OR
Write a short note on the functions of androgens.
Answer:

  1. Androgens are male hormones. The most significant androgen is the testosterone.
  2. Interstitial cells of Leydig present in the testis of mature man produce androgen. Androgens are steroid in chemical nature.
  3. Androgens regulate and stimulate the development, maturation and functions of the male reproductive organs like seminiferous tubules, epididymis, vas deferens, seminal vesicles, prostate glands and urethra.
  4. Androgens are made sex hormones. They produce secondary sexual characteristics. Low pitch of voice is produced due to changes in the vocal cords which take place due to testosterone, etc. They stimulate muscular growth and growth of facial and axillary hairs.
  5. The mental make up of a man like aggressiveness is due to testosterone.
  6. They stimulate seminiferous tubules for the process of spermatogenesis.

Question 29.
What are female sex hormones? What role do they play?
Answer:
(1) The ovaries secrete two steroid hormones viz., estrogen and progesterone.

(2) The estrogen is secreted by the developing ovarian follicles. It has many roles in stimulation of female reproductive functions and growth of ovaries, fallopian tubes, uterus and vagina.

(3) It also controls female secondary sexual characteristics like high pitch of voice, development of mammary glands, broadening of pelvis, growth of pubic hairs and deposition of subcutaneous fats to produce feminine stature.

(4) The estrogen also regulates female sexual behaviour.

(5) The empty Graafian follicle after ovulation is converted into a structure called corpus luteum which secretes a hormone known as progesterone. Progesterone is a gestational hormone which is essential for maintaining the pregnancy. It also acts on the mammary glands and stimulates them for lactation, milk synthesis and ejection.

Question 30.
Why is pancreas called a dual gland?
Answer:

  1. Pancreas is called a dual gland because it is exocrine as well as endocrine in nature.
  2. The exocrine pancreas secretes digestive enzymes through acini.
  3. The endocrine pancreas secretes hormones through its endocrine cells called Islets of Langerhans.

Question 31.
What are the hormones of pancreas? Describe the functions of pancreatic hormones.
OR
Pancreas plays an important role in controlling diabetes mellitus. Explain.
Answer:

  1. Islets of Langerhans consists of three types of cells known as a-cells, β-cells and δ-cells.
  2. α-cells secrete glucagon while β-cells secrete insulin. δ-cells secrete somatostatin.
  3. The glucagon is a hyperglycemic hormone. It is a peptide hormone which acts mainly on the liver cells. Here it stimulates hepatocytes for glycogenolysis (i.e. breakdown of glycogen) leading to increased level of blood glucose (i.e. hyperglycemia).
  4. It also stimulates gluconeogenesis (i.e. formation of glucose from non-carbohydrate sources). This in turn brings rise in blood glucose level or hyperglycemia.
  5. Glucagon reduces the cellular glucose uptake and utilisation.
  6. Insulin is also a peptide hormone, which plays a major role in maintenance of blood glucose level.
  7. Insulin stimulates hepatocytes and adipocytes for cellular glucose uptake and utilization.

Therefore glucose from the blood decreases causing hypoglycemia. This hormone helps in the conversion of glucose to glycogen (i.e. glycogenesis) that occurs in target cells.

Question 32.
How is blood glucose level maintained?
Answer:
The blood glucose level is maintained by the joint but antagonistic action of insulin and glucagon.
Insulin is hypoglycemic hormone while glucagon is hyper/glycemic hormone.

When there is excess sugar in the blood, more insulin is secreted by the pancreatic islets. This causes the conversion of blood glucose into glycogen. This process is known as glycogenesis. This causes decline in the level of glucose in the blood.

When there is less blood glucose level then the glucagon is secreted. It causes stored glycogen to be converted into glucose. This process is called glycogenolysis.

Question 33.
What happens when there is insufficiency or deficiency of insulin in the body?
Answer:

  1. Due to insufficiency, of insulin level there is prolonged hyperglycemia. This leads to diabetes mellitus.
  2. In this diabetic condition cells are unable to utilize glucose. Therefore, in a diabetic person blood glucose levels are high. The glucose is excreted in urine.
  3. The harmful compounds like ketone bodies are formed leading to ketosis.
  4. Diabetes can be treated by taking insulin injections or tablets (insulin therapy) or with hypoglycemic drugs.

Question 34.
Where are parathyroid glands located? What are their functions?
OR
Write a short note on the functions of Parathyroid hormone (PTH).
Answer:

  1. Parathyroid glands are located on the back side of the thyroid gland.
  2. There are two pairs of parathyroid glands. One pair of parathyroid is in each lobe of thyroid.
  3. Parathyroid glands secrete a peptide hormone known as parathromone or parathyroid hormone (PTH).
  4. The level of Ca++ in the blood regulates the secretion of PTH.
  5. PTH is hypercalcemic hormone, it increases blood calcium level. Thus the calcium balance is maintained by TCT and PTH.

Question 35.
What are the gastrointestinal hormones? Explain the function of each.
Answer:

  1. There are scattered endocrine cells in different parts of alimentary canal.
  2. These cells secrete four peptide hormones which are gastrin, secretin, cholecystokinin (CCK) and gastric inhibitory peptide (GIP).
  3. Gastrin stimulates gastric glands for the secretion of hydrochloric acid and pepsinogen.
  4. The secretin acts on exocrine pancreas and stimulates secretion of water and bicarbonate ions to form pancreatic juice.
  5. CCK acts on pancreas and gall bladder and stimulates the secretion of pancreatic enzymes and bile juice respectively.
  6. GIP inhibit gastric secretion and motility.

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 36.
Name the hormone secreted by the heart. What is its function?
Answer:

  1. The atrial wall of the heart secrete a peptide hormone known as atrial natriuretic factor (ANF).
  2. When the blood pressure increases, ANF hormone is secreted.
  3. It causes dilation of the blood vessels.
  4. Blood then can easily flow with lesser resistance and hence BP decreases.

Question 37.
What are the hormones of kidney? What function do they carry out ?
Answer:

  1. The juxtaglomerular cells of the kidney produce a peptide hormone known as erythropoietin.
  2. Erythropoiesis stimulates bone marrow for the production of RBCs. It thus stimulates the process of erythropoiesis.
  3. Hormone calcitriol from kidney helps in the formation of bones.

Question 38.
Give importance of hypothalamus.
Answer:

  1. Hypothalamus is the controlling centre for hypophysis.
  2. Hypothalamus secretes releasing factors and inhibiting factors and hence regulate the secretions of hypophysis. E.g. Adrenocorticotropin hormone releasing factor or CRF; Thyrotropin releasing factor or TSHRF; GHRF and GHRIE i.e. Growth hormone releasing and release inhibiting factor, etc.
  3. Hypothalamus forms the hypothalamo- hypophyseal axis through which transportation of neurohormones take place.
  4. Hormones like vasopressin and oxytocin are secreted by neurosecretory cells of hypothalamus.
  5. Hypothalamus can register the internal changes in the body as it is a part of diencephalon and thus it accordingly brings about coordination in the body through endocrine system.

Question 39.
Write a brief account of releasing factors secreted by hypothalamus.
Answer:
(1) In the hypothalamus, there are several groups of neurosecretory cells which form different nuclei.

(2) These hypothalamic nuclei are supraoptic, paraventricular, dorso-median and ventromedian nuclei. These neurosecretory cells produce releasing and inhibiting factors.

(3) The hypothalamic neurohormones regulating the release of pituitary hormones are called releasing factors. The following are some of J the important releasing factors:

  • CRF or corticotropin releasing factor or ACTH releasing factor releases secretion of Adrenocorticotropin hormone (ACTH).
  • TRF or TSHRF (Thyroid stimulating hormone releasing factor) stimulates release of TSH.
  • FSH RF (Follicle stimulating hormone ; releasing factor) stimulates release of FSH.
  • GHRF (Growth hormone releasing factor) GHRIF (Growth hormone release inhibiting factor) act on release and regulation of growth hormone.
  • PRF (Prolactin releasing factor) and PRIF ; (Prolactin release inhibiting factor) act on release and regulation of prolactin.
  • MSHRF (Melanocyte stimulating hormone releasing factor) and MSH RIF (Melanocyte stimulating hormone release inhibiting factor) act on release and regulation of MSH.

Question 40.
Hormones are called chemical messengers and regulators. Explain.
Answer:

  1. Hormones bring about coordination in the body with the help of nervous system.
  2. Endocrine system and nervous system together form neuro-endocrine system.
  3. This system works in tune with the external and internal environmental changes.
  4. The hormones are either excitatory or inhibitory. They bring about the actions accordingly to keep the body in homeostasis or equilibrium.
  5. Almost all endocrine glands are controlled by negative feedback inhibition. Some glands are auto-regulatory. Therefore, the concentration of hormones cannot be in excess or in deficiency.
  6. Almost all the functions such as metabolism, growth, reproduction, etc. are under the control of hormones. Therefore hormones are called regulators and messengers.

Chart based/Table based questions

Question 1.
Draw a flow chart of – steps in generation and conduction of a nerve impulse.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 1

Question 2.
Enlist the names of following cranial nerves: I, II, VII, XII
Answer:

Number NAME NATURE
I Olfactory Sensory
II Optic Sensory
VII Facial Mixed
XII hypoglossal Motor

Question 3.
Enlist the names of following cranial nerves : III, W VI, XI
Answer:

Number NAME NATURE
III Occulomotor Motor
IV Trochlear/Pathetic Motor
VI Abducens Motor
XI Spinal accessory Motor

Question 4.
Complete the table.

Number Type No. of Pairs Region
———— Cervical ————- —————
T1 – T12 ————- 12 pairs ————-
L1 – L5 ————- 5 pairs Lower back
————- Sacral ————- Pelvic
————– Coccygeal ————— Tall region

Answer:

Number Type No. of Pairs Region
C1 – C8 Cervical 8 pairs Neck
T1-T12 Thoracic 12 pairs Thorax / Upper back
L1 -L5 Lumber 5 pairs Lower back
S – S5 Sacral 5 pairs Pelvic
Co1 Coccygeal 1 pair Tall region

Question 5.
Write types of neuroglial cells of CNS and PNS in tabular form.
Answer:

CNS – glial cells PNS – glial cells Functions
Oligodendrocytes [cells with few branches] Schwann cells Secrete myelin sheath
Astrocytes [star-shaped and most abundant glial cells in CNS] Satellite cells Protect, cushion and supply nutrients to nearby neurons. Help in maintaining blood-brain barrier.
Microglia

[small cells with few branches]

Macrophages Phagocytosis
Ependymal cells lining the ventricles of brain [mostly columnar] Ependymal cells lining central canal of spinal cord Secrete cerebrospinal fluid

Question 6.
Enlist the various receptors found at various location in the body.
Answer:

Receptors Types locations
Mechanoreceptors Thermoreceptors Skin
Tango [touch and pressure] receptors Skin
Tactile [light touch] receptors Skin
Chemoreceptors Gustato receptors tongue
Olfacto receptors Olfactory mucosa
Photoreceptors Rod and cone cells Retina of eye
Phonoreceptors Organ of Corti Cochlea of internal ear
Stato receptors Cristae and maculae Semicircular canals, utricle, saccule of internal ear

Question 7.
Sketch the concept maps for mechanism of vision and mechanism of hearing.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 2
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 3

Question 8.
Complete the table given below by putting a tick (✓) in the boxes where applicable.

Action Reflex Voluntary
1. Touching a hot object ———- ———–
2. Releasing saliva on smelling food ———– ————
3. Applying a car’s brakes in an emergency ———— ————–
4. Blinking of eyes when a small insect touches the eye ———– ————

Answer:

Action Reflex Voluntary
1. Touching a hot object
2. Releasing saliva on smelling food
3. Applying a car’s brakes in an emergency can be a conditioned feclex too.
4. Blinking of eyes when a small insect touches the eye ————

Question 9.
Complete the following table

Action Reflex Voluntary
1. Optic nerve ———– ———–
2. Facial ———– ————
3. Hypoglossal ———— ————–
4. Trigeminal ———– ————
5. Auditory
6. Glosso-pharyngeal

Answer:

Action Reflex Voluntary
1. Optic nerve Sensory Sense of vision and light
2. Facial Mixed Facial expression, movement of neck, tongue, etc. and saliva secretion
3. Hypoglossal Motor Movement of tongue
4. Trigeminal Mixed Sensation of touch, taste and jaw movements
5. Auditory Sensory Hearing and equilibrium
6. Glosso-pharyngeal Mixed Taste, pharyngeal contractions ‘and saliva secretion

Diagram based questions

Question 1.
Sketch and label – nerve net of Hydra.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 4

Question 2.
Sketch and label – nervous system of Planaria
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 5

Question 3.
Sketch and label – depolarization and repolarization along nerve.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 6

Question 4.
Sketch and label ultrastructure of synapse.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 7

Question 5.
Sketch and label – lateral view of brain.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 8

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 6.
Sketch and label – functional areas of Brain?
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 9

Question 7.
Sketch and label – ventral view of human brain.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 10

Question 8.
Sketch and label – ventricles of brain.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 11

Question 9.
Sketch and label T.S. of spinal cord.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 12

Question 10.
Sketch and label – formation of spinal nerve.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 13

Question 11.
Sketch and label – mechanism of hormone action.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 14
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 15

Question 12.
Sketch and label – V.S. of pituitary.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 16

Question 13.
Sketch and label – morphology of thyroid
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 17

Question 14.
Sketch and label – histology of thyroid
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 18

Question 15.
Sketch and label – parathyroid glands
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 19

Question 16.
Sketch and label thymus.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 20

Question 17.
Sketch and label – adrenal gland.
Answer:
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 21

Long answer questions

Question 1.
Explain transmission of nerve impulse across a synapse.
OR
Explain how is impulse transmitted through a synapse?
Answer:

  1. The nerve impulse travels along the axon of the pre-synaptic neuron to the axon terminal.
  2. Pre-synaptic neurons or axons have several synaptic knobs at their ends or terminals.
  3. These knobs have membranous sacs, called synaptic vesicles having neurotransmitter molecules.
  4. When an impulse reaches a synaptic knob, voltage sensitive Ca++ channels open and calcium ions (Ca++) diffuse inward from the extracellular fluid.
  5. The increased calcium concentration inside the cells, initiates a series of events that help to fuse the synaptic vesicles with the cell membrane of pre-synaptic neuron, where they release their neurotransmitters by exocytosis.
  6. The neurotransmitters bind to the receptors of the post-synaptic cell,
  7. This action is either excitatory (stimulating) or inhibitory (slowing down/stopping).
  8. Once the impulse has been transferred across the synapse, the enzyme like acetyl cholinesterase destroys the
  9. neurotransmitter and the synapse is ready to receive a new impulse.

Question 2.
Explain transmission of nerve impulse along the axon.
OR
Describe the conduction of a nerve impulse in the neuron.
Answer:
1. Before conduction of nerve impulse, the cell membrane is in the polarized state.

2. When a stimulus is applied at a site on the polarised membrane, the membrane at that site becomes freely permeable to Na+.

3. This leads to a rapid influx of Na+ followed by the reversal of the polarity at that site, i.e., the outer surface of the membrane becomes negatively charged and the inner side becomes positively charged.

4. The polarity of the membrane at that site [site A] is thus reversed and hence depolarised. The electrical potential difference across the plasma membrane at the site of stimulation is called the action potential, which is in fact termed as a nerve impulse.

5. At sites immediately ahead [site B], the axon membrane has a positive charge on the outer surface and a negative charge on its inner surface. As a result, a current flows on the inner surface from site A to site B.
Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 22

6. On the outer surface current flows from site B to site A to complete the circuit of current flow. Hence, the polarity at the site is reversed, and an action potential is generated at site B. Thus, the impulse (action potential) generated at site A arrives at site B.

7. The sequence is repeated along the length of the axon and consequently the impulse is conducted.

8. The rise in the stimulus-induced permeability to Na+ is extremely short-lived. It is quickly followed by a rise in permeability to K+.

9. Within a fraction of a second, K+ diffuses outside the membrane and restores the resting potential of the membrane at the site of excitation and the fibre becomes once more responsive to further stimulation.

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 3.
Explain the structure of cerebrum. Structure of cerebrum
Answer:
Answer: Structure of cerebrum:

  1. Cerebrum is the largest part of the brain. It forms 80-85% volume of the brain.
  2. A median longitudinal fissure divides the cerebrum into two cerebral hemispheres. These hemispheres are interconnected by a thick band of transverse nerve fibres called corpus callosum.
  3. The outer part of cerebrum is called cerebral cortex while the inner part is called cerebral medulla.
  4. The roof of cerebrum is called pallium. Pallium is highly folded forming sulci and gyri. Sulci are depressions while gyrl are ridges. The gyri increase the surface area of cerebral cortex.
  5. The ventro-lateral walls of cerebrum are thickened and are called corpora striata.
  6. The cerebral cortex has three deep sulci, the central, lateral and parieto-occipital.
  7. These sulci divide the cerebral hemisphere into four lobes. These are frontal, parietal, occipital and temporal lobes. A fifth median lobe called insula or insular cortex is folded deep within the lateral sulcus.
  8. The central sulcus separates frontal and parietal lobes, the lateral sulcus separates parietal and temporal lobes and the parieto¬occipital sulcus separates parietal and occipital lobe.

Question 4.
Describe the structure and function of midbrain.
Answer:
1. Structure of midbrain:

  • Midbrain is the middle part of the brain situated between the forebrain and the hindbrain. It is present between the pons varolii and diencephalon.
  • It has two distinct regions : Corpora quadrigemina and crura cerebri.
  • Corpora quadrigemina consists of two pairs of lobes, viz., superior colliculi and inferior colliculi. These are located in the thick wall of midbrain.
  • Crura cerebri are thick bands of longitudinal nerve fibres, present on the floor of midbrain.

2. Functions of midbrain:

  • Inferior colliculi control and coordinate auditory reflexes.
  • Superior colliculi control head and eye movements.
  • Crura cerebri connect the cerebrum to cerebellum and spinal cord.

Question 5.
Give an account of structure of hindbrain.
Answer:
Structure of hindbrain:

  1. Hindbrain includes cerebellum, pons varolii and medulla oblongata.
  2. Cerebellum is 11% of the total brain and is the second largest part of the brain.
  3. It has three lobes, median vermis and lateral two cerebral hemispheres. It has outer grey and inner white matter.
  4. Cerebral cortex shows sulci and gyri. The inner white matter of cerebellar medulla shows arbor vitae or branching tree-like processes.
  5. Pons is the part that connects the two cerebral hemispheres. It has outer white and inner grey matter. Pons is made up of nerve fibres which form bridges between cerebrum and medulla oblongata.
  6. Medulla oblongata is the last part of the hindbrain which continues further as a spinal cord. It has outer white and inner grey matter.
  7. Its roof shows has posterior choroid plexus.
  8. Eight pairs of cranial nerves arise from medulla oblongata.

Question 6.
Describe T.S. of spinal cord.
Answer:

  1. Externally there are three meninges covering spinal cord Duramater, arachnoid membrane and pia mater.
  2. Dorsoventrally there are two fissures, the shallow dorsal or posterior fissure and the deeper ventral or anterior fissure.
  3. From dorsal fissure a dorsal septum extends inside.
  4. Neurocoel or central canal is situated in the centre of spinal cord.
  5. The central canal is filled with cerebro¬spinal fluid and is lined by cuboidal epithelial cells called layer of ependyma.
  6. There is inner grey and outer white matter in the spinal cord. This grey matter is in the shape of ‘H’ with two dorsolateral horns and two ventro-lateral horns.
  7. Dorsal horns form dorsal roots and ventral horns form ventral roots.
  8. White matter is divided into three columns, viz., the dorsal funiculi, ventral funiculi and lateral funiculi on either side.
  9. Ascending and descending tracts of nerve fibres arise from dorsal and ventral roots of the spinal cord. Ascending tracts are sensory while descending tracts are motor in nature.

Question 7.
What are the different types of reflexes?
Answer:
1. Based on the location of their action : Thereflexes are divided into somatic reflexes and visceral reflexes.

  • When effector is located in body structures such as skeletal muscles, it is called a somatic reflex.
  • When the effector is located in the visceral organs such as glands or smooth muscles then it is called a visceral reflex.

2. Based on the basis of number of neurons : Reflexes are of two types, viz. monosynaptic reflexes and polysynaptic reflexes.

  • Simple or monosynaptic reflexes are those in which one sensory and one motor neuron are involved in the reflex action.
  • Polysynaptic or complex reflexes are those when more than two neurons are involved in the reflex action.

3. Based on inheritance and experience of learning : The reflexes are subdivided into unconditional or inborn and conditional or acquired.

  • Unconditional or inborn reflexes are inborn or hereditary. They are permanent, never disappear and need no previous experience, e.g. blinking of eyes, suckling, swallowing, knee jerk, sneezing, coughing, etc.
  • Conditional or acquired reflexes are acquired during life by experience or learning. They are based on individual learning or experience. These are not heritable, temporary and may disappear or reappear, e.g. driving, cycling, etc.

Question 8.
Explain the mechanism of reflex action.
Answer:

  1. Mechanism of reflex action: There are series of sequential events in which reflex action is completed:
  2. Stimulus is picked up by any receptors, e.g. pricking of a needle in the hand, causes skin to be a receptor.
  3. Sensory impulse is formed in grey matter of spinal cord. It receives sensory impulse, interprets it and generates motor impulse.
  4. The cyton of motor neuron present in the ventral horn of grey matter and axon conducts motor impulse from spinal cord to effector organ. This is further carried by dendrites innervating the skin.
  5. Impulse is carried to the association neuron by axon of sensory neuron, when impulse reaches the end of the axon there is a synapse.
  6. Transmission takes place by releasing acetylcholine from the synaptic buttons at the end of the axon.
  7. It fills the synaptic gap and helps in chemical transmission of the impulse from axon of one neuron to dendron of the other neuron. Once the impulse reaches the dendrites of association neuron; axonic button releases an enzyme, acetylcholine esterase which neutralizes the acetylcholine and again a synaptic gap is formed. This mechanism helps to receive new impulse or avoid the mixing of different impulses.
  8. The association neuron receives sensory impulse, interprets it, analyses it and generates motor impulse. Motor impulse again travels through synapse between association neuron and motor neuron.
  9. Impulse travels through motor neuron and reaches the effector organ like skeletal muscles or the gland. The effector organ gives a proper response like contraction of the muscles or secretion by the gland.

Question 9.
Define receptors. Enlist different types of receptors.
Answer:
1. Receptors : Receptors are specialized cells, tissues or organs present in the body which receive different stimuli.

2. Types of receptors:

  • Receptors are of two types, viz. exteroceptors and interoceptors.-
  • Exteroceptors receive stimuli directly from the external environment. They are somatic in nature.
  • Interoceptors are located inside the body and are visceral in nature. They respond to internal changes in the body.
  • The various types of exteroceptors and interoceptors, their location and functions have been summarized in the table given below:
    Types of Exteroceptors Location Function
    1. Mechanoreceptors Touch corpuscles in skin Tangoreceptors Pressure Tactile receptors- Touch
    2. Thermoreceptors Skin Frigido receptors (cold) Heat receptors (warmth)
    3. Chemoreceptors Tongue, nasal mucosa Gustatoreceptors – Taste Olfactoreceptors- Smell
    4. Statoacoustic receptors Internal ear Cochlea – Hearing Semicircular canals-Balance and equilibrium
    5. Photoreceptors Retina of the eye Rods and cones interpret images Rods-black and white image. Sensitive to dim light. Cones – Coloured image. Sensitive to bright light.

Question 10.
Describe the different parts of human eye.
OR
Describe briefly the structure of eye.
Answer:

  1. Human eyes are a pair of organs located in sockets of the skull called orbits.
  2. Eyeball is spherical and has three layers.
  3. Sclera is the outer layer of dense connective tissue with anterior transparent cornea.
  4. Choroid is the middle layer. It is bluish in colour containing many blood vessels. The anterior region is thick and forms the ciliary body. Posterior 2/3rd region is thinner.
  5. Iris is the forward segment of the ciliary body which is pigmented and opaque. This part is the visible coloured portion of the eye.
  6. Lens is present anteriorly inside the iris and is held in position by the ligaments of ciliary body.
  7. The aperture surrounded by the iris in front of the lens is known as pupil. The movement of the pupil is regulated by the muscle fibres of iris.
  8. The innermost layer of the eye is the retina having three sub-layers formed by ganglion cells, bipolar cells and photoreceptor cells, which are sensitive to light.
  9. There are two types of photoreceptor cells, viz. rods and cones containing light sensitive proteins. They are termed as photo pigments, rhodopsin which is a derivative of vitamin A (in rods) and iodopsin (in cones).
  10. The cones are responsible for daylight or photopic vision and colour vision. The rods function in dim light giving scotopic vision.
  11. The cones are of three types, each containing its own characteristic photopigments that respond to red, green and blue lights.
  12. The optic nerve leaves the eye at a point slightly away from the median posterior pole of the eyeball. In this region, the rods and cones are absent therefore this region is known as blind spot. Macula lutea, a yellowish pigmented spot is present lateral to the blind spot.
  13. Fovea is a central pit present beside it. Fovea is a thinned out portion of the retina where only the cones are densely packed and therefore have greatest visual acuity (resolution).
  14. A space between the cornea and the lens is called aqueous chamber. It contains a thin watery fluid known as aqueous humor.
    Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 24

Question 11.
Describe the internal structure of human ear.
OR
Ear is one of the important sense organs known for its role in hearing and balancing. Describe those structures present in the internal ear which helps in these functions.
Answer:

  1. The ears are the auditory sensory organs, also involved in maintaining equilibrium of the body.
  2. The ear is composed of three divisions namely the outer ear, middle ear and internal ear.
  3. The external ear consists of the pinna and external auditory meatus (canal). The pinna is for the collection of sound waves coming from the environment. The external auditory canal is the circular tube leading inside up to the eardrum or tympanic membrane.
  4. The tympanic membrane or eardrum is formed of connective tissues having outer skin cover and inner mucus membrane.
  5. The middle ear consists of chain of three ossicles called malleus, incus and stapes, The malleus is attached to the tympanic membrane and the stapes is connected to the oval window of the internal ear. They help in the transmission of sound waves from external auditory canal to internal ear.
  6. Connecting middle ear with the pharynx is eustachian tube which helps in equalizing the air pressure on either side of the tympanic membrane.
  7. The internal ear is fluid filled structure called labyrinth. It has two parts, bony and the membranous labyrinth.
  8. The outer bony labyrinth is formed by the series of channels in which the membranous abyrinth containing endolymph fluid is present.
  9. The membranes consist of coiled cochlea, the reissner’s membrane and basilar membranes. These membranes divide the surrounding perilymph filled bony labyrinth into an upper scala vestibule and a lower scala tympani.
  10. The space within cochlea which is known as scala media is filled with endolymph. The scala vestibule ends at the oval window at the base of cochlea.
  11. The scala tympani terminates at the round window which opens to the middle ear. The organ of corti is located on the basilar membrane. It contains the hair cells which act as auditory receptors.
  12. The hair cells are columnar cells present in rows. The basal ends of the hair cells are in close contact with the afferent nerve fibres while their apical end contains numerous cilia. A thin elastic membrane projects above the rows of the hair cells called tectorial membrane.
  13. Above the cochlea, the internal ear also contains vestibular apparatus. It consists of three semicircular canals and the otolith organ formed of the sacculus and utriculus. The semicircular canals lie in different plane at right angles to each other and are suspended in the perilymph.
  14. The bases of canals are swollen and are called ampullae, which contain a projecting ridge known as crista ampullaris which contain hair cells.
  15. The sacculus and utriculus also have projecting ridge called macula. The crista and macula are the specific receptors of vestibular apparatus. They are responsible for maintenance of body posture and the balance.
    Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination 25

Question 12.
Write an account of position and structure of pituitary gland.
Answer:
Pituitary gland (Hypophysis):
I. Position : Pituitary or Hypophysis is located on the ventral side of brain below the hypothalamus. Infundibulum or hypophyseal stalk attaches pituitary to hypothalamus just behind the optic chiasma. It is well protected in sella turcica which is a depression of the sphenoid bone of the skull.

II. Morphological structure of pituitary- gland: The pituitary gland shows two distinct regions : Anterior lobe or adenohypophysis and posteriorlobe or neuro-hypophysis.
(1) Adenohypophysis or Anterior lobe : It is the largest lobe of the gland and forms about 75% of pituitary gland. It develops as an outgrowth called Rathke’s pouch from the roof of embryonic buccal cavity. It has three divisions, viz. pars tuberalis, pars distalis and pars intermedia.

(i) Pars tuberalis : Tubular region present below the hypothalamus is known as pars tuberalis. It is like a collar around the infundibulum. It is non-secretory in nature.
(ii) Pars distalis : The largest anterior region which is secretory in nature is called pars distalis. It is made up of loose cords of epitheloid secretory cells which are separated by reticular connective tissue containing blood sinusoids. It is connected to the hypothalamus by portal system formed by blood sinusoids.
(iii) Pars intermedia : The narrow cleft between the pars distalis and pars nervosa of neuro – hypophysis is called the intermediate part or pars intermedia. It is reduced, less developed and non-functional in human being.

(2) Neuro-hypophysis or Posterior lobe : The posterior lobe of the pituitary which is attached to hypothalamus by infundibular stalk is called neuro-hypophysis. It is smaller and constitute 25% of pituitary. It has the following three parts:

  1. Median eminence : The swollen median part of the hypothalamus where infundibulum gets attached is called median eminence.
  2. Infundibulum : Infundibulum is the hypophyseal stalk that helps in attachment of pituitary gland to the hypothalamus. It contains mainly the axonic fibres of neurosecretory cells present in hypothalamus. It forms the major connection of hypothalamo-hypophysis axis.
  3. Pars nervosa : The lowermost, larger region of neuro-hypophysis that contains axons is called pars nervosa. It acts as a neurohaerhal organ and contains specialized cells called pituicytes.

Maharashtra Board Class 12 Biology Important Questions Chapter 9 Control and Co-ordination

Question 13.
In a person, Pars distalis part of the Pituitary gland is not producing hormones in sufficient quantity. Explain the effects it will produce with respect to the different hormones.
OR
Give names and functions of hormones secreted by adenohypophysis.
Answer:
Pars distalis of the pituitary gland produces following hormones:
GH, ACTH, TSH, FSH, LH/ICSH, LTH and MSH. If these hormones are produced in deficient quantities, following disorders are seen.
1. GH:
(a) Hyposecretion of GH in childhood leads to dwarfism. Frohlich dwarf or Lorain dwarf may be produced based on mental capacity. Hyposecretion in adulthood causes Simmonds’s disease.
(b) Hypersecretion of GH in childhood causes gigantism and in adulthood it causes acromegaly.

2. TSH :
(a) Hyposecretion of TSH leads to thyroid atrophy.
(b) Hypersecretion of TSH causes excessive functioning of thyroid gland.

3. ACTH :
(a) Hyposecretion of ACTH causes Addisons’ disease, in which adrenal gland shows failure of functions.
(b) Hypersecretion of ACTH causes Cushing’s disease, in which the adrenal cortex undergoes excessive growth.

4. FSH : Hyposecretion of FSH leads to infertility in both the sexes. Hypersecretion of FSH in females cause disturbances in menstrual cycle.

5. LH/ICSH : Hyposecretion of LH in females will cause lack of ovulation. Hyposecretion of ICSH in males cause reduction in masculinity. Sperm production may be affected. Hypersecretion of LH/ICSH can cause disturbances in reproductive cycles.

6. LTH : Corpus luteum is not maintained due to lesser amount of LTH. Lactogenesis will also hamper if there is hyposecretion of LTH.

Question 14.
Describe the hormones of neuro¬hypophysis.
Answer:
Hormones of neuro-hypophysis : Neuro-hypophysis does not secrete any hormone itself but stores the hormones which are secreted by hypothalamic neurons. It stores and releases the following hormones, viz. ADH, Oxytocin and coherin.
1. Anti Diuretic Hormone (ADH) or Vasopressin:

  • ADH brings about anti-diuretic action and also increases blood pressure.
  • It is a regulatory hormone which plays a major role in osmoregulation.
  • It increases the permeability of distal convoluted tubule or collecting tubules of uriniferous tubules of kidney.
  • Higher ADH levels decrease the urine output and helps for water conservation. It helps in the absorption of water from the ultrafiltrate thus regulates the water balance of body fluids.
  • ADH also controls constriction of arterioles and increases blood pressure in kidney which facilitates ultra filtration. Therefore it is also called vasopressin.
  • ADH is regulated by increase or decrease of osmotic pressure of blood in a feedback manner.
  • The osmotic pressure is detected by osmoreceptors in the hypothalamus.

2. Oxytocin (Birth hormone):

  • Oxytocin helps in parturition.
  • It is a powerful stimulant of contraction of uterine myometrium at the end of gestation due to which the labour is initiated.
  • It also stimulates myoepithelial cells of mammary glands for milk ejection during lactation.
  • It also helps in fertilization by powerful contractions of the uterine musculature to drive the sperms upward towards fallopian tubes.
  • Oxytocin also excites musculature of gallbladder, ureters, urinary bladder, intestine, etc. for proper functioning of these organs.

3. Coherin : Coherin induces prolonged, rhythmic integrated contractions of the jejunum.

Question 15.
Describe the morphology of thyroid gland.
Or
With the help of a suitable diagram describe the structure of thyroid gland.
Answer:
Morphology of thyroid gland:

  1. Thyroid is the largest endocrine gland in the body.
  2. It weighs about 25 to 30 g and measures about 5 cm in length and 3 cm in width.
  3. It is located in the neck region anteriorly just below the larynx and situated ventrolaterally to the trachea.
  4. The thyroid is derived from the endoderm of the embryo.
  5. The thyroid can vary in size as per age, sex and diet.
  6. It is reddish brown, bilobed and highly vascular
  7. The two lobes are joined by connective tissue called isthmus which is located at 2nd to 4th tracheal cartilage.
  8. Therefore, the right and left lobe of thyroid are seen on both sides of the trachea.
  9. The gland is H-shaped having butterfly-like appearance.
  10. The structural and functional units of thyroid gland are the thyroid follicles.
  11. From the outer surface there lies a connective tissue capsule. A number of septa arise from the connective tissue which are called trabeculae. They divide the gland into lobules. Each lobule has follicles which store hormone. The number of follicles are about three million.

Question 16.
Describe neurohormonal regulation of pituitary and thyroid gland.
Answer:
Pituitary gland is directly under the influence of neurohormones of hypothalamus while thyroid is indirectly influenced.
I. Neurohormonal regulation of pituitary:

  1. Hypothalamus secretes releasing factors and inhibiting factors and hence regulate the secretions of pituitary (hypophysis).
  2. Hypothalamus forms the hypothalamohypophysial axis through which transportation of neuro-hormones take place.
  3. Pituitary secretes a variety of hormones which influence other endocrine glands of the body. E.g. GH, PRL, TSH, ACTH, Gonadotropins

II. Neurohormonal regulation of thyroid :

  1. Hypothalamus secretes TRF [Thyrotropin releasing factor] which influences the anterior pituitary to release TSH.
  2. TSH in turn stimulates thyroid follicles to produce and release two thyroid hormones – T3 and T4. (Thyroxin)
  3. Increase in T3 and T4 triggers negative feedback mechanism that stops the secretion of TRF.

(4) As the pituitary does not get the signal in the form of TRF TSH secretion is stopped.

Question 17.
Name the hormones secreted by the adrenal cortex and state their role.
Answer:
Adrenal cortex secretes 3 types of corticoids – mineralocorticoids, glucocorticoids and sex corticoids.
I. Mineralocorticoids:

  1. The mineralocorticoids regulate ionic and osmotic balance, by regulating the amounts of electrolyte and water.
  2. Aldosterone is the main mineralocorticoid that acts on the renal tubules.
  3. Aldosterone stimulates the re-absorption of Na+ and water and excretion of K+ and phosphate ions.
  4. The aldosterone helps in the maintenance of electrolytes, body fluid volume, osmotic pressure and blood pressure.

II. Glucocorticoids:

  1. Cortisol is the main glucocorticoid. Cortisol stimulates many metabolic reactions such as gluconeogenesis, lipolysis and proteinolysis.
  2. It inhibits cellular uptake and utilization of amino acids.
  3. Cortisol also plays an important role in maintaining the cardiovascular system and kidney functions.
  4. It is also involved in anti-inflammatory reactions and suppresses the immune response.
  5. Cortisol stimulates the RBC production.

III. Sex corticoids (Gonadocorticoids).

  1. Sex corticoids, Androgens and estradiols are produced by the adrenal cortex.
  2. In males, they have a role in development and maintenance of external sex characters.
  3. Excess sex corticoids in female causes adrenal virilism and hirsutism (excess hair on face)
  4. Excess sex corticoids in males causes gynaecomastia i.e. enlarged breast.

Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation

Balbharti Maharashtra State Board 11th Physics Important Questions Chapter 5 Gravitation Important Questions and Answers.

Maharashtra State Board 11th Physics Important Questions Chapter 5 Gravitation

Question 1.
Mention some main characteristics of gravitational force.
Answer:
Characteristics of gravitational force:

  1. Every massive object in the universe experiences gravitational force.
  2. It is the force of mutual attraction between any two objects by virtue of their masses.
  3. It is always an attractive force with infinite range.
  4. It does not depend upon the intervening medium.
  5. It is much weaker than other fundamental forces. Gravitational force is 10 times weaker than strong nuclear force.

Question 2.
State and explain Kepler’s law of orbits.
Answer:
Statement:
All planets move in elliptical orbits around the Sun with the Sun at one of the foci of the ellipse.
Explanation:

  1. The figure M shows the orbit of a around the planet P Sun.
    Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 1
  2. Here, S and S’ are the foci of the ellipse and the Sun is situated at S.
  3. P is the closest point along the orbit from S and is called perihelion.
  4. A is the farthest point from S and is called aphelion.
  5. PA is the major axis whose length is 2a. PO and AO are the semimajor axes with lengths ‘a’ each.
    MN is the minor axis whose length is 2b. MO and ON are the semiminor axes with lengths ‘b’ each.

Maharashtra Board Solutions

Question 3.
State and prove Kepler’s law of equal areas.
Answer:
Statement:
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 2
The line that joins a planet and the Sun sweeps equal areas in equal intervals of time.
Explanation:
i)Kepler observed that planets move faster when they are nearer to the Sun while they move slower when they are farther from the Sun.

ii) Suppose the Sun is at the origin. The position of planet is denoted by \vec{r} and its momentum is denoted by \vec{p} (component ⊥ \vec{r}).
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 35
vi) For central force the angular momentum is conserved. Hence, from equations (4) and (5),
\frac{\overrightarrow{\Delta \mathrm{A}}}{\Delta \mathrm{t}}=\frac{\overrightarrow{\mathrm{L}}}{2 \mathrm{~m}} = constant
This proves the law of areas.

Question 4.
What is a central force?
Answer:
A central force on an object is a force which is always directed along the line joining the position of object and a fired point usually taken to the origin of the coordinate system.

Question 5.
State and explain Kepler’s law of periods.
Answer:
Statement:
The square of the time period of revolution of a planet around the Sun is proportional to the cube of the semimajor axis of the ellipse traced by the planet.
Explanation:
If r is length of semi major axis then, this law states that.
T2 × r3 or \frac{\mathrm{T}^{2}}{\mathrm{r}^{3}} = constant

Maharashtra Board Solutions

Solved Examples

Question 6.
What would be the average duration of year if the distance between the Sun and the Earth becomes
i) thrice the present distance.
ii) twice the present distance.
Solution:
i) Consider r1 be the present distance between the Earth and Sun
We know, T1 = 365 days.
When the distance is made thrice, r2 = 3r1
According to Kepler’s law of period,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 3
i) The duration of the year would be 1897 days when distance is made thrice.
ii) The duration of the year would be 1032 days when distance is made twice.

Question 7.
What would have been the duration of the year if the distance between the Earth and the Sun were half the present distance?
Solution:
Given: r2 = \frac{\mathrm{r}_{1}}{2}
\frac{r_{2}}{r_{1}}=\frac{1}{2}
To find. Time period (T2)
Formula: \left(\frac{T_{2}}{T_{1}}\right)^{2}=\left(\frac{r_{2}}{r_{1}}\right)^{3}
Calculation: We know. T1 = 365 days
From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 36
= 365 × 0.3536
= 129.1
T2 = 129.1 days
The duration of the year would be 129.1 days.

Question 8.
Calculate the period of revolution of Jupiter around the Sun. The ratio of the radius of Jupiter’s orbit to that of the Earth’s orbit is 5.
(Period of revolution of the Earth is 1 year.)
Solution:
Given: \frac{\mathrm{r}_{\mathrm{J}}}{\mathrm{r}_{\mathrm{E}}}=\frac{5}{\mathrm{l}}, TE = 1 year
To find: Period of revolution of Jupiter (TJ)
Formula: T2 ∝ r3
Calculation: From formula,
\left(\frac{T_{J}}{T_{E}}\right)^{2}=\left(\frac{r_{J}}{r_{E}}\right)^{3}
∴ TJ = 53/2
= 5 x \sqrt {5}
= 11.18 years.
Period of revolution of Jupiter around the Sun is 11.18 years.

Question 9.
A Saturn sear is 29.5 times the Earth’s year. How far is the Saturn from the Sun if the Earth is 1.50 × 108 km away from the Sun?
Solution:
Given: TS = 29.5 TE,
rE = 1.50 × 108 km
To find: Distance of Saturn form the Sun (rS)
Formula: T2 ∝ r3
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 37
∴ rS = 14.32 × 108 km
Saturn is 14.32 × 108 km away from the Sun.

Maharashtra Board Solutions

Question 10.
The distances of two planets from the Sun are 1013 m and 1012 m respectively. Find the ratio of time periods of the two planets.
Solution:
Given: r1 = 1013 m, r2 = 1012 m
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 4

Question 11.
Heavy and light objects are released from same height near the Earth’s surface. What can we conclude about their acceleration?
Answer:
Heavy and light objects, when released from the same height, fall towards the Earth at the same speed., i.e., they have the same acceleration.

Question 12.
Explain how Newton concluded that gravitational force F ∝ = \frac{\mathrm{Mm}}{\mathrm{r}^{2}}
Answer:
Before generalising and stating universal law of gravitation, Newton first studied the motion of moon around the Earth.

  1. The known facts about the moon were,
    • the time period of revolution of moon around the Earth (T) = 27.3 days.
    • distance between the Earth and the moon (r) = 3.85 × 105 km.
    • the moon revolves around the Earth in almost circular orbit with constant angular velocity ω.
  2. Thus, the centripetal force experienced by moon (directed towards the centre of the Earth) is given by,
    F = mrω2 …………… (1)
    Where, m = mass of the moon
  3. From Newton’s laws of motion,
    F = ma
    ∴ a = rω2 ……………… (2)
  4. Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 5
  5. This is the acceleration of the moon directed towards the centre of the Earth.
  6. This acceleration is much smaller than the acceleration felt by bodies near the surface of the Earth (while falling on Earth).
  7. The value of acceleration due to Earth’s gravity at the surface is 9.8 m/s2.
    Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 6
  8. Newton therefore concluded that the acceleration of an object towards the Earth is inversely proportional to the square of distance of object from the centre of the Earth.
    ∴ a ∝ \frac{1}{r^{2}}
    x. As, F = ma
    Therefore, the force exerted by the Earth on an object of mass m at a distance r from it is
    F ∝ \frac{\mathrm{m}}{\mathrm{r}^{2}}
    Similarly, an object also exerts a force on the Earth which is
    FE\frac{\mathrm{M}}{\mathrm{r}^{2}}
    Where M is the mass of the Earth. .
  9. According to Newton’s third law of motion, F = FE. Thus, F is also proportional to the mass of the Earth. From these observations, Newton concluded that the gravitational force between the Earth and an object of mass m is F ∝ \frac{\mathrm{Mm}}{\mathrm{r}^{2}}

Question 13.
Discuss the vector form of gravitational force between two masses with the help of diagram.
Answer:

  1. Consider two point masses m1 and m2 having position vectors \overrightarrow{\mathrm{r}_{1}} and \overrightarrow{\mathrm{r}_{2}} from origin O respectively as shown in figure.
    Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 7
  2. The position vector of mass m2 with respect to m1 is given by, \vec{r}_{2}-\vec{r}_{1}=\vec{r}_{21}
  3. Similarly, position vector of mass m1 with respect to m2 is, \overrightarrow{\mathrm{r}}_{1}-\overrightarrow{\mathrm{r}_{2}}=\overrightarrow{\mathrm{r}_{12}}
  4. Let \left|\overrightarrow{\mathrm{r}_{12}}\right|=\left|\overrightarrow{\mathrm{r}_{21}}\right| Then, the force acting on mass m2 due to mass m1 will be given as,
    \overrightarrow{\mathrm{F}_{21}}=\mathrm{G} \frac{\mathrm{m}_{1} \mathrm{~m}_{2}}{\mathrm{r}^{2}}\left(-\hat{\mathrm{r}}_{21}\right)
    where, \hat{\mathbf{r}}_{21} is the unit vector from m1 to m2.
    The force \overrightarrow{\mathrm{F}_{21}} is directed from m2 to m1.
  5. Similarly, force experienced by m1 due to m2 is given as, \overrightarrow{\mathrm{F}}_{12}=\mathrm{G} \frac{\mathrm{m}_{1} \mathrm{~m}_{2}}{\mathrm{r}^{2}}\left(-\hat{\mathrm{r}}_{12}\right)
    \overrightarrow{\mathrm{F}}_{12}=-\overrightarrow{\mathrm{F}}_{21}
    [Note: As \hat{\mathbf{r}}_{21} is defined as unit vector from m1 to m2, conceptually force \overrightarrow{\mathrm{F}}_{21} is directed from m2 lo m1.]

Maharashtra Board Solutions

Question 14.
Why Is the law of gravitation known as universal law of gravitation?
Answer:
The law of gravitation is applicable to all material objects in the universe. Hence it is known as the universal law of gravitation.

Question 15.
Give formula for the gravitational force due to a collection of masses and represent it diagrammatically.
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 8
For a collection of point masses, the force on any one of them is the vector sum of the gravitational forces exerted by all the other point masses.
For n particles, force on ith mass \overrightarrow{\mathrm{F}}_{\mathrm{i}}=\sum_{\mathrm{j}=1 \atop \mathrm{j} \neq \mathrm{i}}^{n} \overrightarrow{\mathrm{F}}_{\mathrm{ij}}
where, \vec{F}_{\mathrm{ij}} is the force on ith particle due to jth particle.

Question 16.
Discuss qualitative idea for the gravitational force of attraction due to a hollow, thin spherical shell of uniform density on a point mass situated inside it.
Answer:

  1. Let us consider the case when the point mass A, is at the centre of the hollow thin shell.
  2. In this case as every point on the shell is equidistant from A, all points exert force of equal magnitude on A but the directions of these forces are different.
  3. Consider the forces on A due to two diametrically opposite points on the shell.
  4. The forces on A due to them will be of equal magnitude but will be in opposite directions and will cancel each other.
  5. Thus, forces due to all pairs of points diametrically opposite to each other will cancel and there will be no net force on A due to the shell.
  6. When the point object is situated elsewhere inside the shell, the situation is not symmetric. However, gravitational force varies directly with mass and inversely with square of the distance.
  7. When the point object is situated elsewhere inside the shell, the situation is not symmetric. However, gravitational force varies directly with mass and inversely with square of the distance.
  8. Thus, some part of the shell may be closer to point A, but its mass is less. Remaining part will then have larger mass but its centre of mass is away from A.
  9. In this way, mathematically it can be shown that the net gravitational force on A is still zero, so long as it is inside the shell.
  10. Hence, the gravitational force at any point inside any hollow closed object of any shape is zero.

Question 17.
Discuss qualitative idea for the gravitational force of attraction between a hollow spherical shell or solid sphere of uniform density and a point mass situated outside the shell / sphere.
Answer:

  • Gravitational force caused by different regions of shell can be resolved into components along the line joining the point mass to the centre and along a direction perpendicular to this line.
  • The components perpendicular to this line cancel each other and the resultant force remains along the line joining the point to the centre.
  • Mathematical calculations show that, this resultant force on this point equals the force that would get exerted by the shell whose entire mass is situated at its centre.

Solved Problems

Question 18.
The gravitational force between two bodies is 1 N. If distance between them is doubled, what will be the gravitational force between them?
Solution:
Let m1 and m2 be masses of the given two bodies. If they are r distance apart initially, then the force between them will be,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 9
The force between two bodies reduces to 0.25 N.

Question 19.
Calculate the force of attraction between two metal spheres each of mass 90 kg, if the distance between their centres is 40 cm. (G = 6.67 × 10-11 N m2/kg2)
Solution:
Given: m1 = 90 kg, m2 = 90 kg,
r = 40 cm = 40 × 10-2 m.
G = 6.67 × 10-11 N m2/kg2
To find: Force of attraction (F)
Formula: F = \frac{\mathrm{Gm}_{1} \mathrm{~m}_{2}}{\mathrm{r}^{2}}
Calculation.
From formula,
F = \frac{6.67 \times 10^{-11} \times 90 \times 90}{\left(40 \times 10^{-2}\right)^{2}}
= \frac{6.67 \times 8100}{1600} \times 10^{-7}
∴ F = 3.377 × 10-6 N
The force of attraction between the two metal spheres is 3.377 × 10-6 N.

Maharashtra Board Solutions

Question 20.
Three particles A, B, and C each having mass m are kept along a straight line with AB = BC = 1. A fourth particle D is kept on the perpendicular bisector of AC at a distance ¡ from B. Determine the gravitational force on D.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 10
From figure,
distance of particle D, from particles A and C is.
ADCD = \sqrt{\mathrm{AB}^{2}+\mathrm{BD}^{2}}
= \sqrt{(l)^{2}+(l)^{2}}=l \sqrt{2}
Gravitational force on particle D is the vector sum of forces due to particles A, B, and C. Gravitational force due to A,
FA = \frac{\mathrm{Gmm}}{(l \sqrt{2})^{2}}=\frac{\mathrm{Gm}^{2}}{2 l^{2}} = along \overrightarrow{\mathrm{DA}}
This force can he resolved into horizontal and vertical components using rectangular unit vectors as shown in figure.
From figure,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 11
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 12
Negative sign indicates net force is acting along DB.
The net force acting on particle D is \frac{\mathbf{G m}^{2}}{l^{2}}\left(\frac{1}{\sqrt{2}}+1\right) directed along \overrightarrow{\mathbf{D B}}.

[Note: When force, in given case is resolved into its components, its horizontal component contains cos argument while vertical component contains sine argument.]

Question 21.
Three balls of masses 5 kg each are kept at points P(1, 2, 0) Q(2, 3, 0) and R(2, 2, 0). Find the gravitational force exerted on the ball at point R.
Solution:
The net force acting on ball placed at R will be vector sum of forces acting due to balls at P and Q.
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 13
= 2.358 × 10-9 N
The net force acting on the ball at point R will be 2.358 × 10-9 N.

Question 22.
For what purpose Cavendish balance is used?
Answer:
Cavendish balance is used to find the magnitude of the gravitational constant G.

Question 23.
Describe the construction of Cavendish balance with the help of neat labelled diagram.
Answer:

  1. The Cavendish balance consists of a light rigid rod. It is supported at the centre by a fine vertical metallic fibre about 100 cm long.
  2. Two small spheres, s1 and s2 of lead having equal mass m and diameter about 5 cm are mounted at the ends of the rod and a small mirror M is fastened to the metallic fibre as shown in figure.
    Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 14
  3. The mirror can be used to reflect a beam of light onto a scale and thereby measure the angel through which the wire will be twisted.
  4. Two large lead spheres L1 and L2 of equal mass M and diameter of about 20 cm are kept close to the small spheres on opposite side as shown in figure.

Question 24.
Describe the working of the experiment performed to measure the value of gravitational constant.
Answer:

  1. In the experiment performed to find the magnitude of gravitational constant (G), Cavendish balance is used.
  2. The large spheres in the balance attract the nearby smaller spheres by equal and opposite force \overrightarrow{\mathrm{F}}. Hence, a torque is generated without exerting any net force on the bar.
  3. Due to the torque the bar turns and the suspension wire gets twisted till the restoring torque due to the elastic property of the wire becomes equal to the gravitational torque.
  4. If r is the initial distance of separation between the centres of the large and the neighbouring small sphere, then the magnitude of the force between them is, F = G\frac{\mathrm{mM}}{\mathrm{r}^{2}}
  5. If length of the rod is L, then the magnitude of the torque arising out of these forces is
    τ = FL = G\frac{\mathrm{mM}}{\mathrm{r}^{2}}L
  6. At equilibrium, it is equal and opposite to the restoring torque.
    ∴ G\frac{\mathrm{mM}}{\mathrm{r}^{2}}L = Kθ
    Where, K is the restoring torque per unit angle and θ is the angle of twist.
  7. By knowing the values of torque τ1 it and corresponding angle of twist a, the restoring torque per unit twist can be determined as K = τ1/α.
  8. Thus, in actual experiment measuring θ and knowing values of τ, m, M and r, the value of G can be calculated from equation (2).

Maharashtra Board Solutions

Question 25.
Derive the expression for the acceleration due to gravity on the surface of the Earth.
Answer:

  1. The Earth is an extended object and can be assumed to be a uniform sphere.
  2. If the mass of the Earth is M and that of any point object is m, the distance of the point object from the centre of the Earth is r then the force of attraction between them is given by,
    F = \text { G } \frac{M m}{r^{2}} …. (1)
  3. If the point object is not acted upon by any other force, it will be accelerated towards the centre of the Earth under the action of this force. Its acceleration can be calculated by using Newton’s second law,
    F = ma … (2)
  4. From equations (1) and (2),
    ma = \frac{\mathrm{GMm}}{\mathrm{r}^{2}}
    ∴ Acceleration due to the gravity of the Earth
    =\frac{\mathrm{GMm}}{\mathrm{r}^{2}} \times \frac{1}{\mathrm{~m}}=\frac{\mathrm{GM}}{\mathrm{r}^{2}}
    This is denoted by g.
  5. If the object is close to the surface of the Earth, r ≈ R, then,
    gEarth’s surface = \frac{\mathrm{GM}}{\mathrm{R}^{2}}

Question 26.
Explain why the Earth doesn’t appear to move even though the object of mass m (m << M) kept on the Earth exerts equal and opposite gravitational force on it.
Answer:

  1. An object of mass m (much smaller than the mass of the Earth) is attracted towards the Earth and falls on it.
  2. At the same time, the Earth is also attracted by the equal and opposite force towards the mass m.
  3. However, its acceleration towards m will be,
    Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 38
  4. As m << M, aEarth << g and is nearly zero. As, a result, practically only the mass m moves towards the Earth and the Earth doesn’t appear to move.

Solved Examples

Question 27.
Calculate mass of the Earth from given data, Acceleration due to gravity g = 9.81 m/s2, Radius of the Earth RE = 6.37 × 106 m, G = 6.67 × 10-11 N m2/kg2
Solution:
Given: g = 9.81 m/s2, RE = 6.37 × 106 m,
G = 6.67 × 10-11 N m2/kg2
To find: Mass of the Earth (ME)
Formula: g = \frac{\mathrm{GM}_{\mathrm{E}}}{\mathrm{R}_{\mathrm{E}}^{2}}
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 39
= antilog {0.9912 + 0.8041 + 0.8041 – 0.8241) × 1023
= antilog {1.7753} × 1023
= 59.61 × 1023
= 5.961 × 1024 kg
Mass of the Earth is 5.961 × 1024 kg.

Maharashtra Board Solutions

Question 28.
Calculate the acceleration due to gravity at the surface of the Earth from the given data. (Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6.4 × 106 m, G = 6.67 × 10-11 N m2/kg2)
Solution:
Given. M = 6 × 1024 kg, R = 6.4 × 106 m, G = 6.67 × 10-11 N m2/kg2
Tofind. Acceleration due to gravity (g)
Formula: g = \frac{\mathrm{GM}}{\mathrm{R}^{2}}
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 40
The acceleration due to gravity at the surface of the Earth is 9.77 m/s2.

Question 29.
Calculate the acceleration due to gravity on the surface of moon if mass of the moon is 1/80 times that of the Earth and diameter of the moon is 1/4 times that of the Earth (g = 9.8 m/s2)
Solution:
Given: Mm = \frac{\mathrm{M}_{\mathrm{E}}}{80}, Rm = \frac{\mathrm{R}_{\mathrm{E}}}{4}, g = 9.8 m/s2
To find: Acceleration due to gravity on the surface of moon (gm)
Formula: g = \frac{\mathrm{GM}}{\mathrm{R}^{2}}
Calculation: For moon, from formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 41
Acceleration due to gravity on surface of the planet is 0.245 m/s2.

Question 30.
Find the acceleration due to gravity on a planet that is 10 times as massive as the Earth and with radius 20 times of the radius of the Earth (g = 9.8 m/s2).
Solution:
Given: MP = 10 × Mass of the Earth = 10 ME,
RP = 20 × radius of the Earth = 20 RE, g = 9.8 m/s2
To find: Acceleration due to gravity on surface of the planet (gP)
Formula: g = \frac{\mathrm{GM}}{\mathrm{R}^{2}}
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 42
Acceleration due to gravity on surface of the planet is 0.245 m/s2.

Maharashtra Board Solutions

Question 31.
Acceleration due to gravity on the Earth is g. A planet has mass and radius half that of the Earth. How much will be percentage change in the acceleration due to gravity on the planet?
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 43
The percentage change in acceleration due to gravity between the planet and the Earth will be 100%.

Question 32.
Explain the graph showing variation of acceleration due to gravity with altitude and depth.
Answer:
The value of acceleration due to gravity is calculated to be maximum at the surface of the Earth. The value goes on decreasing with
i) increase in depth below the Earth’s surface. [varies linearly with (R – d) = r]

ii) increase in height above the Earth’s surface. [varies inversely with (R + h)2 = r2].
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 44
Graph of g, as a function of r, the distance from the centre of the Earth, is plotted as shown in figure.
For r< R,
gd = g\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)
if r = R – d,
g(r) = g\left(\frac{r}{R}\right) \Rightarrow g(r) \propto r
Hence, the graph shows a straight line passing through origin and having slope \frac{\mathrm{g}}{\mathrm{R}}.
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 45
which is represented in the graph.

Question 33.
Why does the weight of a body of a finite mass m is zero at the centre of the Earth?
Answer:
Acceleration at depth d due to gravity is given
by,
gd = g\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)
As, at centre of the Earth d = R ⇒ gd = 0.
Hence, the weight of a body of a finite mass m is zero at the centre of the Earth.

Question 34.
Discuss the variation of acceleration due to gravity at poles and equator due to latitude of the Earth.
Answer:

  1. Effective acceleration due to gravity at P is given as,
    g’ = g – Rω2cos2θ.
  2. As the value of θ increases, cos θ decreases. Therefore g’ will increase as we move away from equator towards any pole due to the rotation of the Earth.
  3. At equator θ = 0°
    ∴ cos θ = 1
    ∴ g’e = g – Rω2
    The effective acceleration due to gravity (g’e) is minimum at equator, as here it is reduced by Rω2
  4. At poles θ = 90° cos θ = 0
    ∴ g’p = g – Rω2 cos θ
    = g – 0
    = g
    There is no reduction in acceleration due to gravity at poles, due to the rotation of the Earth as the poles are lying on the axis of rotation and do not revolve.

Question 35.
If g = 9.8 m/s2 on the surface of the Earth, find its value at h = \frac{\mathbf{R}}{\mathbf{2}} from the surface of the Earth.
Solution:
Given: g = 9.8 m/s2, h = \frac{\mathrm{R}}{2}
To find: Acceleration due to gravity (gh)
Formula: \frac{\mathrm{g}_{\mathrm{h}}}{\mathrm{g}} = \frac{\mathrm{R}^{2}}{(\mathrm{R}+\mathrm{h})^{2}}
Calculation:
From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 46
At h = \frac{\mathrm{R}}{2} from the surface of the Earth, the value of g is 4.35 m/s2.

Maharashtra Board Solutions

Question 36.
At what distance above the surface of Earth the acceleration due to gravity decreases by 10% of its value at the surface? (Radius of Earth = 6400 km)
Solution:
Given: gh = 90% of g i.e., \frac{g_{h}}{g} = 0.9,
R = 6400 km = 6.4 × 106 m
To find: Distance above the surface of the Earth (h)
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 47

Question 37.
Find the altitude at which the acceleration due to gravity is 25% of that at the surface of the Earth.
(Radius of the Earth = 6400 km)
Solution:
Given: gh = 25% of g = \frac{25}{100} \times \mathrm{g}=\frac{\mathrm{g}}{4}, R = 6400 km = 6.4 × 106 m
To find: Height (h)
Formula: gh = g\left(\frac{R}{R+h}\right)^{2}
Calculation: From formula,
\frac{\mathrm{g}}{4} = g\left(\frac{R}{R+h}\right)^{2}
(R + h)2 = 4R2
R + h = 2R
∴ h = 2R – R
∴ h = R
∴ h = 6400 km

Question 38.
A hole is drilled half way to the centre of the Earth. A body is dropped into the hole. How much will it weigh at the bottom of the hole if the weight of the body on the Earth’s surface is 350 N?
Solution:
Given: W = mg = 350 N, d = \frac{\mathrm{R}}{2}
To find: Weight at certain depth (Wd)
Formula: gd = \mathrm{g}\left[1-\frac{\mathrm{d}}{\mathrm{R}}\right]
Calculation: Since Wd = mgd,
from formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 48

Question 39.
Assuming the Earth to be a homogeneous sphere, determine the density of the Earth from following data. (g = 9.8 m/s2, G = 6.673 × 10-11 N m2/kg2, R = 6400 km)
Solution:
Given g = 9.8 m/s2,
G = 6.673 × 10-11 N m2/kg2, R = 6400 km = 6.4 × 106 m
To find: Density (ρ)
Formula: g = \frac{4}{3} \pi \mathrm{R} \rho \mathrm{G}
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 49

Question 40.
If the Earth were a perfect sphere of radius 6.4 × 106 m rotating about its axis with the period of one day (8.64 × 104 s), what is the difference in acceleration due to gravity from poles to equator?
Solution:
Given: R = 6.4 × 106 m, T = 8.64 × 104 s
To find: Difference in acceleration due to gravity (gP – gE)
Formula: g’ = g – Rω2 cos2θ
Calculation: Since ω = \frac{2 \pi}{\mathrm{T}}
∴ ω = \frac{2 \times 3.14}{8.64 \times 10^{4}} = \frac{6.28}{8.64 \times 10^{4}}
= 0.7268 × 10-4
ω = 7.268 × 10-5 rad/s
At poles, θ = 90°
From formula,
gP = g – Rω2cos2 (90°)
= g – 0 ….(∵ cos 90° = 0)
∴ gP = g …. (i)
At equator, θ = 0°,
∴ gE = g – Rω2cos2
gE = g – Rω2 …. (ii)
Subtracting equation (ii) from equation (i), we have,
gP – gE = g – (g – Rω2)
∴ gP – gE = Rω2
= 6.4 × 106 × (7.268 × 10-5)2
= 6.4 × 106 × 52.82 × 10-10
= 338 × 10-4
∴ gP – gE = 3.38 × 10-2 m/s2

Maharashtra Board Solutions

Question 41.
The Earth is rotating with angular velocity ω about its own axis. R is the radius of the Earth. If Rω2 = 0.03386 m/s2, calculate the weight of a body of mass 100 gram at latitude 25°. (g = 9.8 m/s2)
Solution:
Given: Rω2 = 0.03386 m/s2, θ = 25°,
m = 0.1 kg, g = 9.8 m/s2
To find: Weight (W)

Formulae:
i) g’ = g – Rω2 cos2 θ
ii) W = mg

Calculation:
From formula (i),
g’ = 9.8 – [0.03386 – cos2 (25°)]
∴ g’ = 9.8 – [0.03386 × (0.9063)2]
∴ g’ = 9.8 – 0.02781
∴ g’ = 9.772 m/s2
From formula (ii),
W = 0.1 × 9.772
∴ W = 0.9772 N

Question 42.
If the angular speed of the Earth is 7.26 × 10-5 rad/s and radius of the Earth is 6,400 km, calculate the change in weight of 1 kg of mass taken from equator to pole.
Solution:
Given: R = 6.4 × 106 m, ω = 7.26 × 10-5 rad/s
To find: Change in weight (∆W)
Formulae:
i) ∆g = gp – geq = Rω2
ii) ∆W = m∆g

Calculation: From formula (i) and (ii),
∆W = m(Rω2)
= 1 × 6.4 × 106 × (7.26 × 10-5)2
= 3373 × 10-5 N

Question 43.
Define potential energy.
Answer:
Potential energy is the work done against conservative force (or forces) in achieving a certain position or configuration of a given system.

Question 44.
Explain with examples the universal law which states that “Every system always configures itself in order to have minimum potential energy or every system tries to minimize its potential energy”.
Answer:
Example 1:

  1. A spring in its natural state, possesses minimum potential energy. Whenever we stretch it or compress it, we perform work against the conservative force.
  2. Due to this work, the relative distances between the particles of the system change i.e., configuration changes and potential energy of the spring increases.
  3. The spring finally regains its original configuration of minimum potential energy on removal of the applied force.
    This explains that the spring always try to rearrange itself in order to attain minimum potential energy.

Example 2:

  1. When an object is lying on the surface of the Earth, the system of that object and the Earth has minimum potential energy.
  2. This is the gravitational potential energy of the system as these two are bound by the gravitational force. While lifting the object to some height, we do work against the conservative gravitational force.
  3. In its new position, the object is at rest due to balanced forces. However, now, the object has a capacity to acquire kinetic energy, when allowed to fall.
  4. This increase in the capacity is the potential energy gained by the system. The object falls on the Earth to achieve the configuration of minimum potential energy on dropping it from the new position.

Maharashtra Board Solutions

Question 45.
Obtain an expression for change in gravitational potential energy of any object displaced from one point to another.
Answer:
i) Work done against gravitational force in displacing an object through a small displacement, stored in the system in the form of increased potential energy of the system.
∴ dU = –\overrightarrow{\mathrm{F}}_{\mathrm{g}} \cdot \overrightarrow{\mathrm{dr}}
Negative sign appears because dU is the work done against the gravitational force \overrightarrow{\mathrm{F}_{\mathrm{g}}}.

ii) For displacement of the object from an initial position \overrightarrow{\mathrm{r}_{\mathrm{i}}} to the final position \overrightarrow{\mathrm{r}_{\mathrm{f}}}, the change in potential energy ∆U, can be obtained by integrating dU.
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 50

 

iii) Gravitational force of the Earth, \overrightarrow{\mathrm{F}}_{\mathrm{g}} = –\frac{\mathrm{GMm}}{\mathrm{r}^{2}} \hat{\mathrm{r}} where \hat{r} is the unit vector in the direction of \overrightarrow{\mathrm{r}}.
Negative sign appears here because \overrightarrow{\mathrm{F}_{\mathrm{g}}} is directed towards centre of the Earth and opposite to \overrightarrow{\mathrm{r}}.

iv) For Earth and mass system,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 51
Hence, change in potential energy corresponds to the work done against conservative forces.

Question 46.
Using expression for change in potential energy, show that gravitational potential energy of the system of object of mass m and the Earth with separation of r is, –\frac{\text { GMm }}{\text { r }}
Answer:

  1. Change in P.E. for a system of Earth and mass is given by,
    ∆U = GMm\left(\frac{1}{r_{i}}-\frac{1}{r_{f}}\right)
  2. For gravitational force, point of zero potential energy is taken to be at r = ∞.
  3. Hence, U(ri) = 0 at ri = ∞
    Final point rf is the point where the potential energy of the system is to be determined.
  4. At rf = r
    Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 52
    This is gravitational potential energy of the system of object of mass m and Earth of mass M having separation r (between their centres of mass).

Question 47.
Derive the formula for increase in gravitational potential energy of a Earth – mass system when the mass is lifted to a height h provided h << R.
Answer:

  1. If the object is on the surface of Earth, r = R
    U1 = –\frac{\mathrm{GMm}}{\mathrm{R}}
    If the object is lifted to height h above the surface of Earth, the potential energy becomes _ GMm 12 ~~ R+h
    U2 = –\frac{G M m}{R+h}
  2. Increase in the potential energy is given by
    Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 53
  3. If g is acceleration due to gravity on the surface of Earth. GM = gR2
    ∴ ∆U = mgh\left(\frac{R}{R+h}\right) … (1)
  4. Equation (1) gives the work to be done to raise an object of mass rn to a height h, above the surface of the Earth.
  5. If h << R, we can use R + h ≈ R.
    ∴ ∆U = mgh
    Thus, mgh is increase in the gravitational potential energy of the Earth – mass system if an object of mass m is lifted to a height h, provided h << R.

Maharashtra Board Solutions

Question 48.
Write a short note on gravitational potential.
Answer:
The gravitational potential energy of the system of Earth and any mass m at a distance r from the centre of the Earth is given by,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 54
The factor –\frac{\mathrm{GM}}{\mathrm{r}} = (VE)r is defined as the
gravitational potential of Earth at distance r from its centre.

As the potential depends only upon mass of the Earth and location of the object, it is same for any mass m bound to the Earth.

Question 49.
Explain the relation between the gravitational potential energy and the gravitational potential.
Answer:

  1. In terms of potential, we can write the potential energy of the Earth-mass system as, Gravitational potential energy (U) = Gravitational potential (Vr) × mass (m)
  2. Thus, gravitational potential is gravitational potential energy per unit mass.
    ∴ Vr = \frac{\mathrm{U}}{\mathrm{m}}
  3. For any conservative force field, the concept of potential can be defined on similar lines.
  4. Gravitational potential difference between any two points in gravitational field can be written as,
    V2 – V1 = \frac{U_{2}-U_{1}}{m}
    = \frac{\mathrm{dW}}{\mathrm{m}}
    This is the work done (or change in potential energy) per unit mass.
  5. Therefore, in general, for a system of any two masses m1 and m2, separated by distance r, we can write,
    U = –\frac{\mathrm{G} \mathrm{m}_{1} \mathrm{~m}_{2}}{\mathrm{r}}
    = (V1)m2
    = (V2)m1
    Here V1 and V2 are gravitational potentials at r due to m1 and m2 respectively.

Solved Exmaples

Question 50.
What will be the change in potential energy of a body of mass m when it is raised from height RE above the Earth’s surface to 5/2 RE above the Earth’s surface? RE and ME are the radius and mass of the Earth respectively.
Solution:
Change in potential energy (P.E.) of a body of mass m is given by,
∆U = GMEm\left(\frac{1}{r_{i}}-\frac{1}{r_{f}}\right)
Here, ri = RE + RE = 2 RE
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 55
[Note: Answer calculated above is in accordance with textual methods of calculation.]

Question 51.
What will be the change in potential energy of a body of mass m when it is placed on the surface of the Earth from height R above the Earth’s surface?
Solution:
Change in potential energy (P.E.) of a body of mass m is given by,
∆U = GMEm\frac{1}{r_{i}}-\frac{1}{r_{r}}
Here, ri = R + R = 2R
Similarly, rf = R
∴ ∆U = GMEm \left[\frac{1}{2 R}-\frac{1}{R}\right] = GMEm\left(-\frac{1}{2 R}\right)
∴ ∆U = –\frac{\mathbf{G} \mathbf{M} \mathbf{m}}{\mathbf{2 R}}
Negative sign indicates that potential energy is decreasing.

Question 52.
Determine the gravitational potential of a body of mass 80 kg whose gravitational potential energy is 5 × 109 J on the surface of the Earth.
Solution:
Given: m = 80 kg, U = 5 × 109 J
To find: Gravitational potential (V)
Formula: V = \frac{\mathrm{U}}{\mathrm{m}}
Calculation: From formula,
V = \frac{5 \times 10^{9}}{80}=\frac{25}{4} × 107
= 6.25 × 107 J kg-1
Potential of the body at the surface of the Earth is 6.25 × 107 J kg-1.

Maharashtra Board Solutions

Question 53.
Calculate the escape velocity of a body from the surface of the Earth.
(Average density of Earth = 5.5 × 103 kg/m3, G = 6.67 × 10-11 N m2/kg2, radius of Earth R = 6.4 × 106 m)
Solution:
Given: ρ = 5.5 × 103 kg/m3, R = 6.4 × 106 m,
G = 6.67 × 10-11 N m2/kg2
To find: Escape velocity (ve)
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 27
= 2 × 6.4 × 106 × 8.759 × 10-4
∴ ve = 11.21 × 103 m/s = 11.21 km/s
The escape velocity of a body is 11.21 km/s.

Question 54.
What is a satellite?
Answer:
An object which revolves in an orbit around a planet is called as satellite.
Example:

  • Moon is a natural satellite of the Earth.
  • INSAT is an artificial satellite of the Earth.

Question 55.
Write a short note on Polar satellites.
Answer:

  1. Polar Satellites are placed in lower polar orbits.
  2. They are at low altitude 500 km to 800 km.
  3. Period of revolution of polar satellite is nearly 85 minutes, so it can orbit the Earth 16 time per day.
  4. They go around the poles of the Earth in a north-south direction while the Earth rotates in an east-west direction about its own axis.
  5. The polar satellites have cameras fixed on them. The camera can view small stipes of the Earth in one orbit. In entire day the whole Earth can be viewed strip by strip.
  6. Polar region and equatorial regions close to it can be viewed by these satellites.
  7. Polar satellites are used for weather forecasting and meteorological purpose. They are also used for astronomical observations and study of Solar radiations.

Maharashtra Board Solutions

Question 56.
Derive the expression for the critical velocity of a satellite revolving close to the surface of the Earth in terms of acceleration due to gravity.
Answer:

  1. When the satellite is revolving close to the surface of the Earth, the height is very small as compared to the radius of the Earth.
  2. Hence the height can be neglected and radius of the orbit is nearly equal to R, i.e., R + h ≈ R
  3. The critical speed of the satellite then becomes,
    vc = \sqrt{\frac{G M}{R}}
  4. G is related to acceleration due to gravity by the relation,
    g = \frac{G M}{R^{2}}
    ∴ GM = gR2
  5. Thus, critical speed in terms of acceleration due to gravity, neglecting the air resistance, can be obtained as,
    vc = \sqrt{\frac{\mathrm{gR}^{2}}{\mathrm{R}}}=\sqrt{\mathrm{gR}}

Question 57.
From an inertial frame of reference, explain the apparent weight for a person standing in a lift having zero acceleration.
Answer:

  1. A passenger inside a lift experiences only two forces:
    • Gravitational force mg directed vertically downwards and
    • normal reaction force N directed vertically upwards, exerted by the floor of the lift.
  2. As these forces are oppositely directed, the net force in the downward direction will be F = ma – N.
  3. Though the weight of a passenger is the gravitational force acting upon it, the person experiences his weight only due to the normal reaction force N exerted by the floor.
  4. A lift has zero acceleration when the lift is at rest or is moving upwards or downwards with constant velocity.
  5. Thus, a net force acting on the passenger inside the lift will be,
    F = 0 = mg – N
    ∴ mg = N
    Hence, in this case the passenger feels his normal weight mg.

Question 58.
What happens to the apparent weight of the person inside the lift moving with net upward acceleration?
Answer:

  1. The lift is said to be moving with net upward acceleration in two possible conditions:
    • when the lift just starts moving upwards or
    • is about to stop at a lower floor during its downward motion.
  2. As the net acceleration is upwards, the upward force must be greater.
    ∴ F = ma = N – mg
    ∴ N = mg + ma
    ∴ N > mg
  3. Thus, for a passenger inside this lift, his apparent weight is more than his actual weight when the lift was not accelerated.

Question 59.
Why does a passenger feel lighter when the lift is about to stop at a higher floor during its upward motion?
Answer:

  1. When the lift is about to stop at a higher floor during its upward motion it has a net downward acceleration.
  2. As the net acceleration is downwards, the downward force must be greater.
    ∴ F = ma = mg – N
    ∴ N = mg – ma
    i.e., N < mg
    Hence, a passenger feels lighter when the lift is about to stop at a higher floor during its upward motion.

Question 60.
When does a weighing machine will record zero for a passenger in a lift?
Answer:
If the cables of the lift are cut, the downward acceleration of the lift, ad = g. In this case, we get,
N = mg – mad = 0
Thus, there will not be any feeling of weight and the weighing machine will record zero.

Maharashtra Board Solutions

Question 61.
Define time period of a satellite.
Obtain an expression for the period of a satellite in a circular orbit round the Earth. Show that the square of the period of revolution of a satellite is directly proportional to the cube of the orbital radius.
Answer:
Definition:
The time taken by a satellite to complete one revolution around the Earth is called its time period.
Expression for time period:
i) Consider, m = mass of satellite, h = altitude of satellite. Thus, r = R + h = radius of orbit of the satellite.
ii) In one revolution, distance traced by satellite is equal to circumference of its circular orbit.
iii) If T is the time period of satellite, then
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 28
Since π2, G and M are constant,
∴ T2 ∝ r3
Hence, square of the period of revolution of a satellite is directly proportional to the cube of the radius of its orbit.

vi) Taking square roots on both the sides of equation (4), we get,
T = 2π\sqrt{\frac{\mathrm{r}^{3}}{\mathrm{GM}}}
T = 2π\sqrt{\frac{(R+h)^{3}}{G M}}
This is the required expression for period of satellite orbiting around the Earth in circular path.

Question 62.
For an orbiting satellite very close to surface of the Earth, show that T = 2π \sqrt{\frac{\mathrm{R}}{\mathrm{g}}}.
Answer:

  1. Time period of an orbiting satellite at certain height is given by, T = 2π \sqrt{\frac{(R+h)^{3}}{G M}}
  2. If satellite is orbiting very close to the Earth’s surface, then h ≈ 0
    Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 29

Solved Examples

Question 63.
Show that the critical velocity of a body revolving in a circular orbit very close to the surface of a planet of radius R and
mean density ρ is 2R\sqrt{\frac{G \pi \rho}{3}}.
Solution:
Since the body is revolving very close to the surface of a planet,
∴ h << R
R = radius of planet
ρ = mean density of planet
Critical velocity of a body very close to Earth is given by,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 30

Question 64.
Find the orbital speed of the satellite w hen satellite is revolving round the Earth in circular orbit at a distance 9 × 106 m from its centre. (Given: Mass of Earth = 6 × 1024 kg, G = 6.67 × 10-11 N m2/kg2)
Solution:
Given: r = 9 × 106 m, M = 6 × 1024kg,
G = 6.67 × 10-11 N m2/kg2
To find: Orbital speed (vc)
Formula: vc = \sqrt{\frac{\mathrm{GM}}{\mathrm{r}}}
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 31
∴ vc = 6.668 × 103 m/s
The orbital speed of the satellite is 6.668 × 103 m/s.

Question 65.
Taking radius of the Earth as 6400 km and g at the Earth’s surface as 9.8 m/s2, calculate the speed of revolution of a satellite orbiting close to the Earth’s surface.
Solution:
Given: R = 6400 km = 6.4 × 106 m, g = 9.8 m/s2
To find: Critical velocity (vc)
Formula: vc = \sqrt{\mathrm{gR}}
Calculation: From formula,
vc = \sqrt{9.8 \times 6.4 \times 10^{6}}
= \sqrt{98 \times 64 \times 10^{4}}
= 7\sqrt{2} × 8 ×102
= 7.92 × 103 m/s
The speed of revolution of the satellite orbiting close to the Earth’s surface is 7.92 × 103 m/s.

Maharashtra Board Solutions

Question 66.
The critical velocity of a satellite revolving around the Earth is 10 km/s at a height where gh = 8 m/s 2. Calculate the height of the satellite from the surface of the Earth. (R = 6.4 × 106 m)
Solution:
Given: vc = 10 km/s = 10 × 103 m/s,
gh = 8 m/s3, R = 6.4 × 106 m
To find: Height of the satellite (h)
Formula: vc = \sqrt{g_{\mathrm{h}}(R+h)}
Calculation: From formula,
10 × 103 = \sqrt{8 \times(\mathrm{R}+\mathrm{h})}
Squaring both the sides, we get,
100 × 106 = 8(R + h)
∴ 8(R + h) = 100 × 106
∴ R + h = \frac{100}{8} × 106
∴ h = 12.5 × 106 – R
= 12.5 × 106 – 6.4 × 106
= 6.1 × 106m
∴ h = 6100 km
The height of the satellite from the surface of the Earth is 6100 km.

Question 67.
An artificial satellite revolves around a planet in circular orbit close to its surface. Obtain the formula for period of the satellite in terms of density p and radius R of planet.
Solution:
Time period of a satellite revolving around the planet at certain height is given by,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 15

Question 68.
Calculate the period of revolution of a polar satellite orbiting close to the surface of the Earth. Given R = 6400 km, g = 9.8 m/s2.
Solution:
Given: For satellite close to Earth surface,
R + h ≈ R
R = 6400 km = 6.4 × 106 m, g = 9.8 m/s2
To find: Time period of satellite (T)
Formula: T = 2π \sqrt{\frac{R}{g}}
Calculation: From Formula,
T = 2 × 3.14 × \sqrt{\frac{6.4 \times 10^{6}}{9.8}}
= 6.28 × 8.081 × 102
= 5.075 × 103 sec
≈ 85 min
The time period of satellite very close to the Earth’s surface is nearly 85 minute.

Question 69.
A satellite orbits around the Earth at a height equal to R of the Earth. Find its period. (R = 6.4 × 106 m, g = 9.8 m/s2)
Solution:
Given: h = R = 6.4 × 106m, g = 9.8 m/s2
To find: Time period (T)
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 33
The time period of the satellite is 1.435 × 104 s.

Maharashtra Board Solutions

Question 70.
Calculate the height of the communication satellite. (Given: G = 6.67 × 10-11 N m2/kg2, M = 6 × 1024 kg, R = 6400 km)
Solution:
For communication satellite, T = 24 × 60 × 60 s,
Given: M = 6 × 1024 kg,
G = 6.67 × 10-11 N m2/kg2,
R = 6400 km = 6.4 × 106m
To find: Height (h)
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation 34
The height of the communication satellite is 35910 km.

Question 71.
How will you ‘weigh the Sun’, that is estimate its mass? The mean orbital radius of the Earth around the Sun is 1.5 × 108 km.
Solution:
Given: r = 1.5 × 108 × 103m,
T = 365 days = 365 × 24 × 60 × 60 s
To find: Mass (M)
Formula: T = 2π \sqrt{\frac{r^{3}}{G M}}
Calculation:
From formula,
M = \frac{4 \pi^{2} r^{3}}{G T^{2}}
= \frac{4 \times(3.14)^{2}\left(1.5 \times 10^{11}\right)^{3}}{\left(6.67 \times 10^{-11}\right)(365 \times 24 \times 60 \times 60)^{2}}
∴ M = 2.01 × 1030kg
The mass of the Sun is 2.01 × 1030 kg.
[Trick: To ‘weigh the Sun’, i.e., estimate its mass, one needs to know the period of one of its planets and the radius of the planetary orbit.]

Question 72.
Calculate the B.E. of a satellite of mass 2000 kg moving in an orbit very close to the surface of the Earth. (G = 6.67 × 10-11 N m2/kg2)
Solution:
Given: m = 2 × 103 kg, R = 6.4 × 106 m,
R = 6.4 × 106 m, M = 6 × 1024kg,
G = 6.67 × 10-11 N m2/kg2,
M = 6 × 1024 kg
To find: Binding Energy (B.E.)
Formula: For satellite very close to Earth,
B.E. = \frac{1}{2} \times \frac{\mathrm{GMm}}{\mathrm{R}}
Calculation: From formula,
B.E. = \frac{1}{2} \times \frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 2 \times 10^{3}}{6.4 \times 10^{6}}
∴ B.E. = 6.25 × 1010 joule
The binding energy of the satellite is 6.25 × 1010 joule.

Question 73.
Find the binding energy of a body of mass 50 kg at rest on the surface of the Earth. (Given: G = 6.67 × 10-11 N m2/kg2, R = 6400 km, M = 6 × 1024 kg)
Solution:
Given: G = 6.67 × 10-11 N m2/kg2,
R = 6400 km = 6.4 × 106m,
M = 6 × 1024 kg, m = 50 kg
To find: Binding energy (B.E.)
Formula: B.E. = \frac{\text { GMm }}{\mathrm{R}}
Calculation: From formula,
B.E. = \frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 50}{6.4 \times 10^{6}}
= \frac{2001}{6.4} × 107
∴ B.E. = 3.127 × 109 J
The binding energy of the body 3.127 × 109 J.

Maharashtra Board Solutions

Question 74.
Find the total energy and binding energy of an artificial satellite of mass 1000 kg orbiting at height of 1600 km above the Earth’s surface.
(Given: G = 6.67 × 10-11 N m2/kg2, R = 6400 km, M = 6 × 1024 kg)
Solution:
Given: h = 1600 km = 1.6 × 106 m,
G = 6.67 × 10-11 N m2/kg2,
R = 6400 km = 6.4 × 106m,
m = 1000 kg, M = 6 × 1024kg
To find:
i) Total Energy (T.E.)
ii) Binding Energy (B.E.)
Formulae: i. T.E. = –\frac{\mathrm{GMm}}{2(\mathrm{R}+\mathrm{h})}
ii. B.E. = -T.E.

Calculation: From formula (i),
T.E = – \frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 1000}{2(6.4+1.6) \times 10^{6}}
= –\frac{40020 \times 10^{7}}{2 \times 8}
∴ T.E. = -2.501 × 1010J
From formula (ii),
B.E. = 2.501 × 1010 J
i) The total energy of the artificial satellite is -2.501 × 1010 J.
ii) The binding energy of the artificial satellite is 2.501 × 1010 J.

Question 75.
Determine the binding energy of satellite of mass 1000 kg revolving in a circular orbit around the Earth when it is close to the surface of Earth. Hence find kinetic energy and potential energy of the satellite. (Mass of Earth = 6 × 1024 kg, radius of Earth = 6400 km; gravitational constant G = 6.67 × 10-11 N m2/kg2)
Solution:
Given: m = 1000 kg, M = 6 × 1024 kg,
R = 6400 km, G = 6.67 × 10-11 N m2/kg2
To find:
i) Binding Energy (B.E.)
ii)Kinetic Energy (K.E.)
iii) Potential Energy (P.E.)

Formulae: For satellite very close to Earth,
i) B.E. = \frac{1}{2} \times \frac{\mathrm{GMm}}{\mathrm{R}}
ii) K.E.= B.E.
iii) P.E. = -2 K.E.

Calculation: From formula (i),
B.E. = \frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 1000}{2 \times 6.4 \times 10^{6}}
∴ B.E. = 3.1265 × 1010 J
From formula (ii),
K.E. = 3.1265 × 1010
∴ K.E. = 3.1265 × 1010 J
From formula (iii),
P.E. = -2(3.1265 × 1010)
∴ P.E. = -6.2530 × l010J
i) The binding energy of the satellite is 3.1265 × 1010 J.
ii) The kinetic energy of the satellite is 3.1265 × 1010 J.
iii) The potential energy of the satellite is -6.2530 × 1010J.

Apply Your Knowledge

Question 76.
How are Kepler’s law of periods and Newton’s law of gravitation related?
Answer:
Consider a planet of mass m revolving around the Sun of mass M in a circular orbit.
Let,
r = radius of the circular orbit of the planet.
T = Time period of revolution of planet around the Sun.
ω = angular velocity of planet.
F = Centripetal force exerted by the Sun on the planet.
Centripetal force is given by,
F = mrω2;
But ω = \frac{2 \pi}{T}
∴ F = mr (\frac{2 \pi}{\mathrm{T}})2
∴ F = \frac{4 \pi^{2} \mathrm{mr}}{\mathrm{T}^{2}} …(i)
According to Kepler’s third law,
T2 ∝ r3
T2 = Kr3 ……….. (where, K = constant) (ii)
Substituting equation (ii) in equation (i),
F = \frac{4 \pi^{2} \mathrm{mr}}{\mathrm{Kr}^{3}}
∴ F = \frac{4 \pi^{2}}{\mathrm{~K}} \frac{\mathrm{m}}{\mathrm{r}^{2}}
∴ F ∝ \frac{\mathrm{m}}{\mathrm{r}^{2}} ….(∵ \frac{4 \pi^{2}}{\mathrm{~K}} is a constant quantity)
Since, the gravitational attraction between the Sun and the planet is mutual, force exerted by the planet on the Sun will be proportional to the mass M of the Sun.
∴ F ∝ \frac{\mathrm{Mm}}{\mathrm{r}^{2}}
∴ F = \frac{\mathrm{GMm}}{\mathrm{r}^{2}}
The above equation represents Newton’s law of gravitation. In this manner, Newton’s law of gravitation is derived from Kepler’s law of periods.

Maharashtra Board Solutions

Question 77.
Represent graphically the variation of total energy, kinetic energy and potential energy of a satellite with its distance from the centre of the Earth.
Answer:
For a satellite,
Potential energy (U) =
Kinetic energy (K) = and
Total energy (E) = , where, r = R + h
Also, U and E remain negative whereas K remains positive.
Hence, the graph will be:
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 1.1

Multiple Choice Questions

Question 1.
Kepler’s law of equal areas is an outcome of
(A) conservation of energy
(B) conservation of linear momentum
(C) conservation of angular momentum
(D) conservation of mass
Answer:
(C) conservation of angular momentum

Question 2.
Amongst given statements, choose the correct statement.
(I) Kepler derived the laws of planetary motion.
(II) Newton provided the reason behind the laws of planetary motion.
(A) (I) is correct.
(B) (II) is correct.
(C) Both (I) and (II) are correct.
(D) Neither (I) nor (II) is correct.
Answer:
(B) (II) is correct.

Question 3.
The figure shows the motion of a planet satellite in terms of mean density of Earth. around the Sun in an elliptical orbit with Sun at the focus. The shaded areas A and B are also shown in the figure which can be assumed to be equal. If t1 and t2 represent the time for the planet to move from a to b and d to c respectively, then
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 16
(A) t1 < t2
(B) t1 >t2
(C) t1 = t2
(D) t1 ≤ t2
Answer:
(C) t1 = t2

Question 4.
A planet is revolving around a star in a circular orbit of radius R with a period T. If the gravitational force between the planet and the star is proportional to R-3/2, then
(A) T2 ∝ R5/2
(B) T2 ∝ R-7/2
(C) T2 ∝ R3/2
(D) T2 ∝ R4
Answer:
(A) T2 ∝ R5/2

Question 5.
Time period of revolution of a satellite around a planet of radius R is T. Period of revolution around another planet whose radius is 3R is
(A) T
(B) 9T
(C) 3T
(D) 3\sqrt{3} T
Answer:
(D) 3\sqrt{3} T

Question 6.
Newton’s law of gravitation is called universal law because
(A) force is always attractive.
(B) it is applicable to lighter and heavier bodies.
(C) it is applicable at all times,
(D) it is applicable at all places of universe for all distances between all particles.
Answer:
(D) it is applicable at all places of universe for all distances between all particles.

Question 7.
If the mass of a body is M on the surface of the Earth, the mass of the same body on the surface of the moon is
M
(A) 6M
(B) \frac{M}{6}
(C) M
(D) Zero
Answer:
(C) M

Maharashtra Board Solutions

Question 8.
Which of the following statements about the gravitational constant is true?
(A) It has no units.
(B) It has same value in all systems of units.
(C) It is a force.
(D) It does not depend upon the nature of medium in which the bodies lie.
Answer:
(D) It does not depend upon the nature of medium in which the bodies lie.

Question 9.
The gravitational force between two bodies is ______
(A) attractive at large distance only
(B) attractive at small distance only
(C) repulsive at small distance only
(D) attractive at all distances large or small
Answer:
(D) attractive at all distances large or small

Question 10.
Mass of a particle at the centre of the Earth is
(A) infinite.
(B) zero.
(C) same as at other places.
(D) greater than at the poles.
Answer:
(C) same as at other places.

Question 11.
Which of the following is not a property of gravitational force?
(A) It is an attractive force.
(B) It acts along the line joining the two bodies.
(C) The forces exerted by two bodies on each other form an action-reaction pair.
(D) It has a very finite range of action.
Answer:
(D) It has a very finite range of action.

Question 12.
If the distance between Sun and Earth is made two third times of the present value, then gravitational force between them will become
(A) \frac{4}{9}times
(B) \frac{2}{3}times
(C) \frac{1}{3}times
(D) \frac{9}{4} times
Answer:
(D) \frac{9}{4} times

Question 13.
The gravitational constant G is equal to 6.67 × 10-11 N m2/kg2 in vacuum. Its value in a dense matter of density 1010 g/cm3 will be
(A) 6.67 × 10-1 N m2/kg2
(B) 6.67 × 10-11 N m2/kg2
(C) 6.67 × 10-10 N m2/kg2
(D) 6.67 × 10-21 N m2/kg2
Answer:
(B) 6.67 × 10-11 N m2/kg2

Question 14.
Acceleration due to gravity above the Earth’s surface at a height equal to the radius of the Earth is ______
(A) 2.5 m/s2
(B) 5 m/s2
(C) 9.8 m/s2
(D) 10 m/s2
Answer:
(A) 2.5 m/s2

Question 15.
If R is the radius of the Earth and g is the acceleration due to gravity on the Earth’s surface, the mean density of the Earth is
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 2
Answer:
(D) \frac{3 \mathrm{~g}}{4 \pi \mathrm{RG}}

Maharashtra Board Solutions

Question 16.
Variation of acceleration due to gravity (g) with distance x from the centre of the Earth is best represented by (R → Radius of the Earth)
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 3
Answer:
(D)

Question 17.
Which of the following statements is not correct for the decrease in the value of acceleration due to gravity?
(A) As we go down from the surtce of the Earth towards its centre.
(B) As we go up from the surface of the Earth.
(C) As we go from equator to the poles on the surface on the Earth.
(D) As the rotational velocity of the Earth is increased.
Answer:
(C) As we go from equator to the poles on the surface on the Earth.

Question 18.
Calculate angular velocity of Earth so that acceleration due to gravity at 60° latitude becomes zero. (Radius of Earth = 6400 km, gravitational acceleration at poles = 10 m/s2, cos60° = 0.5)
(A) 7.8 × 10-2 rad/s
(B) 0.5 × 10-3 radis
(C) 1 × 10-3 radis
(D) 2.5 × 10-3 rad/s
Answer:
(D) 2.5 × 10-3 rad/s

Question 19.
The gravitational potential energy per unit mass at a point gives ________ at that point.
(A) gravitational field
(B) gravitational potential
(C) gravitational potential energy
(D) gravitational force
Answer:
(B) gravitational potential

Question 20.
A satellite is orbiting around a planet at a constant height in a circular orbit. If the mass of the planet is reduced to half, the satellite would
(A) fall on the planet.
(B) go to an orbit of smaller radius.
(C) go to an orbit of higher radius,
(D) escape from the planet.
Answer:
(D) escape from the planet.

Question 21.
How does the escape velocity of a particle depend on its mass?
(A) m2
(B) m
(C) m0
(D) m-1
Answer:
(C) m0

Question 22.
Escape velocity on a planet is ve. If radius of the planet remains same and mass becomes 4 times, the escape velocity becomes
(A) 4ve
(B) 2ve
(C) ve
(D) 0.5 ve
Answer:
(B) 2ve

Question 23.
If the escape velocity of a body on Earth is 11.2 km/s, the escape velocity of the body thrown at an angle 45° with the horizontal will be
(A) 11.2 km/s
(B) 22.4 km/s
(C) \frac{11.2}{\sqrt{2}}km/s
(D) 11.2 \sqrt{2} km/s
Answer:
(A) 11.2 km/s

Question 24.
Potential energy of a body in the gravitational field of planet is zero. The body must be
(A) at centre of planet.
(B) on the surface of planet.
(C) at infinity.
(D) at distance equal to radius of Earth.
Answer:
(C) at infinity.

Maharashtra Board Solutions

Question 25.
If gravitational force of Earth disappears, what will happen to the satellite revolving round the Earth?
(A) Satellite will come back to Earth.
(B) Satellite will continue to revolve.
(C) Satellite will escape in tangential path.
(D) Satellite will start falling towards centre.
Answer:
(C) Satellite will escape in tangential path.

Question 26.
If ve and vo represent the escape velocity and orbital velocity of a satellite corresponding to a circular orbit of radius R respectively, then
(A) ve = vo
(B) \sqrt{2}vo = ve
(C) ve = \frac{1}{\sqrt{2}}vo
(D) ve and vo are not related
Answer:
(B) \sqrt{2}vo = ve

Question 27.
If the kinetic energy of a satellite is 2 × 104 J, then its potential energy will be
(A) – 2 × 104 J
(B) 4 × 104 J
(C) -4 × 104 J
(D) -104J
Answer:
(C) -4 × 104 J

Competitive Corner

Question 1.
A body weighs 200 N on the surface of the Earth. How much will it weigh half way down to the centre of the Earth?
(A) 250 N
(B) 100 N
(C) 150 N
(D) 200 N
Answer:
(B) 100 N
Hint:
Acceleration due to gravity at depth d,
gd = g (1 – \frac{\mathrm{d}}{\mathrm{R}})
= g(1 – \frac{1}{2}) …(∵ d = \frac{1}{2})
∴ gd = \frac{\mathrm{g}}{2}
Weight of the body at depth d = R/2,
Wd = mgd = m × g/2 = \frac{1}{2} × 200
∴ Wd = 100 N

Maharashtra Board Solutions

Question 2.
The work done to raise a mass m from the surface of the Earth to a height h, which is equal to the radius of the Earth, is:
(A) \frac{1}{2} mgR
(B) \frac{3}{2} mgR
(C) mgR
(D) 2mgR
Answer:
(A) \frac{1}{2} mgR
Hint:
Initial potential energy on Earth’s surface,
Ui = \frac{-\mathrm{GMm}}{\mathrm{R}}
Final potential energy at height h = R
Uf = \frac{-\mathrm{GMm}}{2 \mathrm{R}}
Work done, W = Uf – Ui
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 4
∴ W = \frac{1}{2} mgR

Question 3.
The time period of a geostationary satellite is 24 h, at a height 6RE (RE is radius of Earth) from surface of Earth. The time period of another satellite whose height is 2.5 RE from surface will be,
(A) \frac{12}{2.5}h
(B) 6\sqrt{2} h
(C) 12\sqrt{2} h
(D) \frac{24}{2.5}h
Answer:
(B) 6\sqrt{2} h
Hint:
By Kepler’s third law,
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 5
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 6

Question 4.
Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final – initial) of an object of mass m, when taken to a height h from the surface of Earth (of radius R), is given by,
(A) \frac{\text { GMm }}{R+h}
(B) – \frac{\text { GMm }}{R+h}
(C) \frac{\text { GMmh }}{R(R+h)}
(D) mgh
Answer:
(C) \frac{\text { GMmh }}{R(R+h)}
Hint:
Potential energy of object of mass m on the surface of Earth,
P.E = \frac{-\mathrm{GMm}}{\mathrm{R}}
Potential energy of object of mass m at a height h from the surface of the Earth,
P.E.’ = \frac{-\mathrm{GMm}}{\mathrm{R}+\mathrm{h}}
∴ Change in potential energy
= P.E.’ – P.E.
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 7

Question 5.
A body mass ‘m’ is dropped from height , from Earth’s surface, where ‘R’ is the radius of Earth. Its speed when it will hit the Earth’s surface is (ve = escape velocity from Earth’s surface)
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 8
Answer:
(B) \frac{\mathbf{v}_{\mathrm{e}}}{\sqrt{3}}
Hint:
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 9
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 10

Question 6.
According to Kepler’s Law, the areal velocity of the radius vector drawn from the Sun to any planet always
(A) decreases.
(B) first increases and then decreases.
(C) remains constant.
(D) increases.
Answer:
(C) remains constant.

Maharashtra Board Solutions

Question 7.
A body is thrown from the surface of the Earth with velocity ‘u’ m/s. The maximum height in m above the surface of the Earth upto which it will reach is (R = radius of Earth, g = acceleration due to gravity)
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 11
Answer:
(A) \frac{u^{2} R}{2 g R-u^{2}}
Hint:
(T.E.) on surface = (T.E.) at height ‘h’
∴ (K.E.)1 + (P.E.)1 = (K.E.)2 + (P.E.)2
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 12
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 13

Question 8.
A satellite is revolving in a circular orbit at a height ‘h’ above the surface of the Earth of radius ‘R’. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the Earth. The relation between ‘h’ and ‘R’ is
(A) h = 2R
(B) h = 3R
(C) h = 5R
(D) h = 7R
Answer:
(D) h = 7R
Hint:
Maharashtra Board Class 11 Physics Important Questions Chapter 5 Gravitation q 14

Question 9.
Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:
(A) keep floating at the same distance between them.
(B) move towards each other.
(C) move away from each other.
(D) will become stationary.
Answer:
(B) move towards each other.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Balbharti Maharashtra State Board 11th Physics Important Questions Chapter 4 Laws of Motion Important Questions and Answers.

Maharashtra State Board 11th Physics Important Questions Chapter 4 Laws of Motion

Question 1.
‘Rest and motion are relative concepts.’ Explain the statement with an example.
Answer:

  1. A body can be described to be at rest or in motion with respect to a system of co¬ordinate axes known as the frame of reference.
  2. A body is in motion if it changes its position with respect to a fixed reference point in a frame of reference. On the other hand, a body is at rest if it does not change its position with respect to a fixed reference point in a frame of reference.
  3. An object can be said to be at rest with respect to a frame of reference while the same object can be said to be in motion with respect to a different frame of reference.
    Example: In a running train, all the travellers in the train are in a state of rest if the train is taken as the frame of reference. On the other hand, all the travellers in the train are in a state of motion if ground (or platform) is taken as the frame of reference.
  4. Thus, motion and rest always need a frame of reference to be described. Hence, rest and motion are relative concepts.

Question 2.
Explain how acceleration and initial velocity decides trajectory of a motion.
Answer:

  1. The resultant motion is linear if:
    • initial velocity \overrightarrow{\mathrm{u}} = 0 (starting from rest) and acceleration \overrightarrow{\mathrm{a}} is in any direction.
    • initial velocity \overrightarrow{\mathrm{u}} ≠ 0 and acceleration a is in line with the initial velocity (same or opposite direction).
  2. The resultant motion is circular if initial velocity \overrightarrow{\mathrm{u}} ≠ 0 and acceleration \overrightarrow{\mathrm{a}} is perpendicular to the velocity throughout.
  3. The resultant motion is parabolic if the initial velocity \overrightarrow{\mathrm{u}} is not in line with the acceleration \overrightarrow{\mathrm{a}} and \overrightarrow{\mathrm{a}} = constant.
    e.g., trajectory of a projectile motion.
  4. Similarly, various other combinations of initial velocity and acceleration will result into more complicated motions.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 3.
State Newton’s first law of motion.
Answer:
Statement: Every inanimate object continues to be in a state of rest or of uniform unaccelerated motion along a straight line, unless it is acted upon by an external, unbalanced force.

Question 4.
An astronaut accidentally gets separated out of his small spaceship accelerating in inter stellar space at a constant rate of 100 m s-2. What is the acceleration of the astronaut the instant after he is outside the spaceship? (Assume that there are no nearby stars to exert gravitational force on him.) (NCERT)
Answer:

  1. Assuming absence of stars in the vicinity, the only gravitational force exerted on astronaut is by the spaceship.
  2. But this force is negligible.
  3. Hence, once astronaut is out of the spaceship net external force acting on him can be taken as zero.
  4. From the first law of motion, the acceleration of astronaut is zero.

Question 5.
Give the magnitude and direction of the net force acting on:

  1. a drop of rain falling down with a constant speed.
  2. a cork of mass 10 g floating on water.
  3. a kite skilfully held stationary in the sky.
  4. a car moving with a constant velocity of 30 kmh-1 on a rough road.
  5. a high speed electron in space far from all gravitating objects, and free of electric and magnetic fields. (NCERT)

Answer:

  1. The drop of rain falls down with a constant speed, hence according to the first law of motion, the net force on the drop of rain is zero.
  2. Since the 10 g cork is floating on water, its weight is balanced by the up thrust due to water. Therefore, net force on the cork is zero.
  3. As the kite is skilfully held stationary in the sky, in accordance with first law of motion, the net force on the kite is zero.
  4. As the car is moving with a constant velocity of 30 km/h on a road, the net force on the car is zero.
  5. As the high-speed electron in space is far from all material objects, and free of electric and magnetic fields, it doesn’t accelerate and moves with constant velocity. Hence, net force acting on the electron is zero.

Question 6.
State Newton’s second law of motion and its importance.
Answer:
Statement: The rate of change of linear momentum of a rigid body is directly proportional to the applied (external unbalanced) force and takes place in the direction of force.
\overrightarrow{\mathrm{F}}=\frac{\mathrm{d} \overrightarrow{\mathrm{p}}}{\mathrm{dt}}
Where, \overrightarrow{\mathrm{F}} = Force applied
p = m\overrightarrow{\mathrm{v}} = linear momentum

Importance of Newton’s second law:

  1. It gives mathematical formulation for quantitative measure of force as rate of change of linear momentum.
  2. It defines momentum instead of velocity as the fundamental quantity related to motion.
  3. It takes into consideration the resultant unbalanced force on a body which is used to overcome Aristotle’s fallacy.

Question 7.
Explain why a cricketer moves his hands backwards while holding a catch. (NCERT)
Answer:

  1. In the act of catching the ball, by drawing hands backward, cricketer allows longer time for his hands to stop the ball.
  2. By Newton’s second law of motion, force applied depends on the rate of change of momentum.
  3. Taking longer time to stop the ball ensures smaller rate of change of momentum.
  4. Due to this the cricketer can stop the ball by applying smaller amount of force and thereby not hurting his hands.

Question 8.
Large force always produces large change in momentum on a body than a small force. Is this correct?
Answer:
No. From Newton’s second law, we have.
\frac{\mathrm{dP}}{\mathrm{dt}}=\mathrm{F} …. (i)
dP = Fdt …. (ii)
From equation (ii), we can infer that a small force acting for a longer time can produce same change in momentum of a body as a large force acting in the same direction for a short time. Hence, the given statement is incorrect.

Question 9.
Newton’s first law is contained in the second law. Prove it.
Answer:

  1. From Newton’s second law of motion, we have, \overrightarrow{\mathrm{F}}=\frac{\mathrm{d} \overrightarrow{\mathrm{p}}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}(\mathrm{m} \overrightarrow{\mathrm{v}})
  2. For a given body, mass m is constant.
    \overrightarrow{\mathrm{F}}=\mathrm{m} \frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}=\mathrm{m} \overrightarrow{\mathrm{a}}
  3. If \overrightarrow{\mathrm{F}} = zero, \overrightarrow{\mathrm{v}} is constant. Hence if there is no force, velocity will not change. This is nothing but Newton’s first law of motion.

Question 10.
State Newton’s third law of motion
Answer:
Statement: To every action (force) there is always an equal and opposite reaction force).

Question 11.
State the importance of Newton’s third law of motion.
Answer:

  1. Newton’s third law of motion defines action and reaction as a pair of equal and opposite forces acting along the same line.
  2. Action and reaction forces always act on different objects.

Question 12.
State the consequences of Newton’s third law of motion.
Answer:

  1. Two interacting bodies exert forces which are always equal in magnitude, have the same line of action and are opposite in direction, upon each other. Thus, forces always occur in pairs.
  2. If a body A exerts an action force \overrightarrow{\mathrm{F}}_{\mathrm{BA}} on body B, then body B also exerts an equal and opposite reaction force \overrightarrow{\mathrm{F}}_{\mathrm{AB}} on body A, simultaneously.
  3. Body A experiences the force \overrightarrow{\mathrm{F}}_{\mathrm{AB}} only and
    body B experiences the force \overrightarrow{\mathrm{F}}_{\mathrm{BA}} only.
  4. Both the forces, action and reaction act at the same instant.
  5. Both the forces always act on different bodies. Hence, they never cancel each other.
  6. Both the forces do not necessarily arise due to contact i.e., they can be non-contact forces. Example: Repulsive forces between two magnets.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 13.
If a constant force of 800 N produces an acceleration of 5 m/s2 in a body, what is its mass? If the body starts from rest, how much distance will it travel in 10 s?
Solution:
Given: F = 800 N, a = 5 m/s2, u = 0, t = 10 s
To find: mass (m), distance travelled (s)
Formulae:

i. F = ma
ii. s = ut + \frac{1}{2} \mathrm{at}^{2}

Calculation:
From formula (i),
∴ m = \frac{\mathrm{F}}{\mathrm{a}}=\frac{800}{5} = 160 kg
From formula (ii),
s = \frac{1}{2} × 5 × (10)2 [∵ u = 0]
∴ s = 250 m
Answer:
Mass of the body is 160 kg and the distance travelled by the body is 250 m.

Question 14.
A constant force acting on a body of mass 3 kg changes its speed from 2 m s-1 to 3.5 m/s in 25 s. The direction of motion of the body remains unchanged. What is the magnitude and direction of the force? (NCERT)
Solution:
Given: u = 2 ms-1, m = 3 kg,
v = 3.5 m s-1, t = 25s
To find: Force (F)
Formula: F = ma
Calculation: Since, v = u + at
∴ 3.5 = 2 + a × 25
a = \frac{3.5-2}{25} = 0.06 m s-2
From formula,
F = 3 × 0.06 = 0.18 N
Since, the applied force increases the speed of the body, it acts in the direction of the motion.
Answer:
The applied force is 0.18 N along the direction of motion.

Question 15.
A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 ms-1. How long does the body take to stop? (NCERT)
Solution:
Given: m = 20 kg, u = 15ms-1, v = 0,
F = – 50 N (retarding force)
To find: Time (t)
Formula: v = u + at
Calculation: Since, F = ma
∴ a = \frac{\mathrm{F}}{\mathrm{m}}=\frac{-50}{20} = -2.5 m s-2
From formula,
0 = 15 + (-2.5) × t
∴ t = 6s
Answer:
Time taken to stop the body is 6 s.

Question 16.
A hose pipe used for gardening is ejecting water horizontally at the rate of 0.5 m/s. Area of the bore of the pipe is 10 cm2. Calculate the force to be applied by the gardener to hold the pipe horizontally stationary.
Solution:
Let ejecting water horizontally be considered as the action force on the water, then the water exerts a backward force (called recoil force) on the pipe as the reaction force.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 1
Where, V = volume of water ejected
A = area of cross section of bore = 10 cm2
ρ = density of water = 1 g/cc
l = length of the water ejected in time t
\frac{\mathrm{d} l}{\mathrm{dt}} = v = velocity of water ejected
= 0.5 m/s = 50 cm/s
F = \frac{\mathrm{dm}}{\mathrm{dt}} \mathrm{v}
= (Aρv) v
= Aρv2
= 10 × 1 × 502
∴ F = 25000 dyne = 0.25 N
Answer:
The gardener must apply an equal and opposite force of 0.25 N.

Question 17.
What does the term frame of reference mean?
Answer:
A system of co-ordinate axes with reference to which the position or motion of an object is described is called a frame of reference.

Question 18.
Explain the terms inertial and non-inertial frame of reference.
Answer:

  1. Inertial frame of reference:
    • A frame of reference in which Newton ‘s first law of motion is applicable is called inertia/frame of reference.
    • A body moves with a constant velocity (which can be zero) in the absence of a net force. The body does not accelerate.
    • Example: A rocket in inter-galactic space (gravity free space between galaxies) with all its engine shut.
  2. Non-inertial frame of reference:
    • A frame of reference in which an object suffers acceleration in absence of net force is called non-inertial frame of reference.
    • The body undergoes acceleration.
    • Example: If a car just start its motion from rest, then during the time of acceleration the car will be in a non-inertial frame of reference.

Question 19.
State the limitations of Newton’s laws of motion.
Answer:

  1. Newton’s laws of motion are not applicable in a non-inertial (accelerated) frame of reference.
  2. Newton’s laws are only applicable to point objects.
  3. Newton’s laws are only applicable to rigid bodies.
  4. Results obtained by applying Newton’s laws of motion for objects moving with speeds comparable to that of light do not match with the experimental results and Einstein special theory of relativity has to be used.
  5. Newton’s laws of motion fail to explain the behaviour and interaction of objects having atomic or molecular sizes, and quantum mechanics has to be used.

Question 20.
Name the different types of fundamental forces in nature.
Answer:
Fundamental forces in nature are classified into four types:

  1. Gravitational force
  2. Electromagnetic force
  3. Strong nuclear force
  4. Weak nuclear force

Question 21.
Define gravitational force. Give its examples.
Answer:
Force of attraction between two (point) masses separated by a distance is called as gravitational force.
F = \mathrm{G} \frac{\mathrm{m}_{1} \mathrm{~m}_{2}}{\mathrm{r}^{2}}
where ‘G’ is constant called the universal gravitational constant = 6.67 × 10-11 Nm2/kg2

Examples:

  1. The motion of moon, artificial satellites around the earth and motion of planets around the sun is due to gravitational force of attraction.
  2. The concept of weight of a body in the earth’s gravitational field is due to gravitational force exerted by the earth on a body.

Question 22.
Write down the main characteristics of gravitational force.
Answer:
Characteristics of gravitational force:

  1. It is always attractive.
  2. It is the weakest of the four basic forces in nature.
  3. Its range is infinite.
  4. Structure of the universe is governed by this force.

Question 23.
Write a note on electromagnetic (EM) force.
Answer:
Electromagnetic force:

  1. The attractive and repulsive force between electrically charged particles is called electromagnetic force.
  2. It can be attractive or repulsive.
  3. It is stronger than the gravitational force.
  4. Example: force of friction, normal reaction, tension in strings, collision forces, elastic forces, fluid friction etc. are electromagnetic in nature.
  5. Reaction forces are a result of the action of electromagnetic forces.
  6. Since majority of forces are electromagnetic in nature, our life is practically governed by these forces.

Question 24.
Write a note on strong and weak nuclear force.
Answer:

  1. Strong nuclear force: The strong force which binds protons and neutrons (nucleons) together in the nucleus of an atom is called strong nuclear force.
    Characteristics of strong nuclear force:

    • It is a very strong attractive force.
    • It is a short range force of the order of 10-14 m.
    • it is charge independent.
  2. Weak nuclear force: The force of interaction between subatomic particles which results in the radioactive decay of atoms is called weak nuclear force.

Characteristics of weak nuclear force:

  • It acts between any two elementary particles (pair of subatomic particles).
  • It is a stronger force than gravitational force.
  • It is much weaker than electromagnetic force or strong nuclear force.
  • It is a short range force of the order of 10-16m.

Question 25.
Three identical point masses are fixed symmetrically on the periphery of a circle. Obtain the resultant gravitational force on any point mass M at the centre of the circle. Extend this idea to more than three identical masses symmetrically located on the periphery. How far can you extend this concept?
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 2
i. Consider three identical points A, B and C of mass m on the periphery of a circle of radius r. Mass M is at the centre of the circle.
Gravitational forces on M due to these masses are attractive and are given as,
In magnitude, \mathrm{F}_{\mathrm{MA}}=\mathrm{F}_{\mathrm{MB}}=\mathrm{F}_{\mathrm{MC}}=\frac{\mathrm{GMm}}{\mathrm{r}^{2}}

ii. Forces \overrightarrow{\mathrm{F}}_{\mathrm{MB}} and \overrightarrow{\mathrm{F}}_{\mathrm{MC}} are resolved along \overrightarrow{\mathrm{F}}_{\mathrm{MA}} and perpendicular to \overrightarrow{\mathrm{F}}_{\mathrm{MA}}. Components perpendicular to \overrightarrow{\mathrm{F}}_{\mathrm{MA}} cancel each other. Components along \overrightarrow{\mathrm{F}}_{\mathrm{MA}} are,
FMB cos 60° = FMC cos 60° = \frac{1}{2} F_{M A} each.

Magnitude of their resultant is FMA and its direction is opposite to that of FMA. Thus, the
resultant force on mass M is zero. For any even number of equal masses, the force due to any mass m is balanced (cancelled) by diametrically opposite mass. For any odd number of masses, the components perpendicular to one of them cancel each other while the components parallel to one of these add up in such a way that the resultant is zero for any number of identical masses m located symmetrically on the periphery.

As the number of masses tends to infinity, their collective shape approaches circumference of the circle, which is nothing but a ring. Thus, the gravitational force exerted by a ring mass on any other mass at its centre is zero.

iii. This concept can be further extended to three-dimensions by imagining a uniform hollow sphere to be made up of infinite number of such rings with a common diameter. Thus, the gravitational force for any mass kept at the centre of a hollow sphere is zero.

Question 26.
A car of mass 1.5 ton is running at 72 kmph on a straight horizontal road. On turning the engine off, it stops in 20 seconds. While running at the same speed, on the same road, the driver observes an accident 50 m in front of him. He immediately applies the brakes and just manages to stop the car at the accident spot. Calculate the braking force.
Solution:
Given: m = 1.5 ton = 1500 kg,
u = 72 kmph = 72 × \frac{5}{18} \mathrm{~m} / \mathrm{s}m/s = 20 m
s-1 (on turning engine off),
v = 0, t = 20 s, s = 50 m
To find: Braking force (F)

Formula:

i. v = u + at
ii. v2 – u2 = 2as
iii. F = ma

Calculation:
On turning the engine off,
From formula (i),
a = \frac{0-20}{20} = -1 m s-2
This is frictional retardation (negative acceleration).
After seeing the accident,
From formula (ii),
a1 = \frac{0^{2}-20^{2}}{2(50)} = -4 m s-2
This retardation is the combined effect of braking and friction
∴ braking retardation =4 – 1 = 3 m s-2
From formula (iii), the braking force, F = 1500 × 3 = 4500 N
Answer:
The braking force is 4500 N.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 27.
A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by \overrightarrow{\mathbf{F}}=(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) N where \hat{\mathbf{i}}, \hat{\mathbf{j}}, \hat{\mathbf{k}} are unit vectors along the x, y and z axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis? (NCERT)
Solution:
Given: \overrightarrow{\mathbf{F}}=(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) N, \overrightarrow{\mathrm{s}}=4 \hat{\mathrm{k}}
To find: work done (W)

Formula: W = \overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{s}}
Calculation: From formula,
W = (-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}) \cdot(4 \hat{\mathrm{k}})
= 12 \hat{\mathrm{k}} \cdot \hat{\mathrm{k}} = 12 J
Answer:
The work done by the force is in moving the body 12 J.

Question 28.
Over a given region, a force (in newton) varies as F = 3x2 – 2x + 1. In this region, an object is displaced from x1 = 20 cm to x2 = 40 cm by the given force. Calculate the amount of work done.
Solution:
Given: F = 3x2 – 2x + 1, x1 = 20 cm = 0.2 m,
x2 = 40 cm = 0.4 m.
To find: Work done (W)
Formula: W = \int_{A}^{B} \vec{F} \cdot \overrightarrow{d s}
Calculation:
From formula,
W = \int_{x_{1}}^{x_{2}} F \cdot d x=\int_{0.2}^{0.4}\left(3 x^{2}-2 x+1\right) d x
= [x3 – x2 + x]0.4
= [0.43 – 0.42 + 0.4] – [0.23 – 0.22 + 0.2]
= 0.304 – 0.168 = 0.136 J
The work done is 0.136 J.

Question 29.
A position dependent force f = 7 – 2x + 3x2 newton acts on a small body of mass 2 kg and displaces from x = 0 m to x = 5 m, calculate the work done.
Solution:
Given: F = 7 – 2x + 3x2, x = 0 at A and x = 5 at B.
To find: Work done (W)
Formula: W = \int_{A}^{B} \vec{F} \cdot \overrightarrow{d s}
Calculation: From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 3
∴ W = 135 J
Answer:
The work done is 135 J.

Question 30.
State the principle of work-energy theorem in case of a conservative force and explain.
OR
Show that work done on a body by a conservative force is equal to the change in its kinetic energy
Answer:
Principle: Decrease in the potential energy due to work done by a conservative force is entirely converted into kinetic energy. Vice versa, for an object moving against a conservative force, its kinetic energy decreases by an amount equal to the work done against the force.

Work-energy theorem in case of a conservative force:

  1. Consider an object of mass m moving with velocity u experiencing a constant opposing force F which slows it down to v during displacement s.
  2. The equation of motion can be written as, v2 – u2 = -2as (negative acceleration for
    opposing force.)
    Multiplying throughout by \frac{\mathrm{m}}{2}, we get,
    \frac{\mathrm{1}}{2}mu2\frac{\mathrm{1}}{2}mv2 = (ma)s …. (1)
  3. According to Newton’s second law of motion,
    F = ma … (2)
  4. From equations (1) and (2), we get,
    \frac{\mathrm{1}}{2}mu2\frac{\mathrm{1}}{2}mv2 = F.s
  5. But, \frac{\mathrm{1}}{2}mv2= Kf = final K.E of the body,
    \frac{\mathrm{1}}{2}mu2 = Ki = initial K.E of the body. and, work done by the force = F.s
    ∴ work done by the force = kf – ki
    = decrease in K.E of the body.
  6. Thus, work done on a body by a conservative force is equal to the change in its kinetic energy.

Question 31.
Explain the work-energy theorem in case of an accelerating conservative force along with a retarding non-conservative force.
Answer:

  1. Consider an object dropped from some point at height h.
  2. While coming down its potential energy decreases.
    ∴ Work done = decrease in P.E of the body.
  3. But, in this case, some part of the energy is used in overcoming the air resistance. This part of energy appears in some other forms such as heat, sound, etc. Thus, the work is not entirely converted into kinetic energy. In this case, the work-energy theorem can mathematically be written as,
    ∴ ∆ PE = ∆ K.E. + Wair resistance
    ∴ Decrease in the gravitational P.E. = Increase in the kinetic energy + work done against non-conservative forces.

Question 32.
A liquid drop of 1.00 g falls from height of cliff 1.00 km. It hits the ground with a speed of 50 m s-1. What is the work done by the unknown force? (Take g = 9.8 m/s2)
Solution:
Given: m = 1.0 g = 1.0 × 10-3 kg,
h = 1 km = 103 m, v = 50 ms-1
To find: Work done (Wf)
Formula: Wf = ∆ K.E – Wg

Calculation:

i. The change in kinetic energy of the drop
∆ K.E = (K.E.)final (K.E.)initial
∴ ∆ K.E. = \frac{1}{2} \mathrm{mv}^{2}-0
= \frac{1}{2} \times 1.0 \times 10^{-3} \times(50)^{2}
∴ ∆ K.E.= 1.25 J

ii. Work done by the gravitational force is,
Wg = mgh = 1.0 × 10-3 × 9.8 × 103 = 9.8 J
∴ Wg = 9.8J
From formula,
Wf = ∆K.E. – Wg = 1.25 – 9.8
Wf = -8.55 J
Answer:
Work done by the unknown force is – 8.55 J.

Question 33.
A body of mass 0.5 kg travels in a straight line with velocity y = ax3/2, where a = 5 m1/2s-1. What is the work done by the net force during its displacement from x = 0 to x = 2m? (NCERT)
Solution:
Given: M = 0.5 kg, y = ax3/2,
where a = 5 m-1/2s-1
Let v1 and v2 be the velocities of the body, when x = 0 and x = 2 m respectively. Then,
v1 = 5 × 03/2 = 0, v2 = 5 × 23/2 = 10 \sqrt{2} m
To find: Work done (W)
Formula: Work done = Increase in kinetic energy
W = \frac{1}{2} \mathrm{M}\left(\mathrm{v}_{2}^{2}-\mathrm{v}_{1}^{2}\right)
Calculation: From formula,
W = \frac{1}{2} × 0.5 × [latex](10 \sqrt{2})^{2}-0^{2}[/latex]
∴ W = 50J
Answer:
Work done by the net force on the body is 50 J.

Question 34.
A particle of mass 12 kg is acted upon by a force f = (100 – 2x2) where f is in newton and ‘x’ is in metre. Calculate the work done by this force in moving the particle x = 0 to x = -10 m. What will be the speed at x = 10 m if it starts from rest?
Solution:
Given: F = 100 – 2x2
at A, x = 0 and at B, x = -10 m
To find: Work done (W), speed (v)

Formulae:

i. W = \int_{A}^{B} \vec{F} \cdot d s
ii. W = K.E. = \frac{1}{2} \mathrm{mv}^{2}

Calculation:
From formula (i),
W = \int_{A}^{B} \vec{F} \cdot \overline{d s}=\int_{x=0}^{x=-10} F d x
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 4
Answer:

  1. Work done by the force on the particle is 333.3 J.
  2. The speed of the particle at x = 10 will be 7.45 m/s.

Question 35.
Define free body diagram. In the figure given below, draw the free body diagrams for mass of 2 kg, 4 kg and 5 kg and hence state their force equations.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 5
Answer:
i. The diagram showing the forces acting on only one body at a time along-with its acceleration is called a free body diagram.

ii. The free body diagram for the mass of 2 kg is
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 6
Free body diagram for 2 kg mass
The force equation is given as,
2a = T3 – 2g

iii. The free body diagram for the mass of 4 kg is,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 7
The force equation is given as, 4a = T1 + 4g – T2

iv. The free body diagram for the mass of 5kg is,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 8

The force equation for the mass of 5 kg is given as,
N + F sin 60° = 5g, along the vertical direction.
T1 + 10 = F cos 60°, along the horizontal direction (Considering the mass is in equilibrium).

Question 36.
Figure shows a fixed pulley. A massless inextensible string with masses m1 and m2 > m1 attached to its two ends is passing over the pulley. Such an arrangement is called an Atwood machine. Calculate accelerations of the masses and force due to the tension along the string assuming axle of the pulley to be frictionless.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 9
Solution:
Method I: As m2 > m1, mass m2 is moving downwards and mass m1 is moving upwards.
Net downward force = F = (m2) g – (m1) g
= (m2 – m1)g
the string being inextensible, both the masses travel the same distance in the same time. Thus, their accelerations are equal in magnitude (one upward, other downward). Let it be a.
Total mass in motion, M = m2 + m1
∴ a = \frac{F}{M}=\left(\frac{m_{2}-m_{1}}{m_{2}+m_{1}}\right) g …. (i)

For mass m1, the upward force is the force due to tension T and downward force is mg. It has upward acceleration a. Thus, T – m1g = m1a
∴ T = m1(g + a)
Using equation (i), we get,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 10
From the free body equation for the first body,
T – m1g = m1a .. (i)

From the free body equation for the second body,
m2g – T = m2a … (ii)
Adding (i) and (ii), we get,
a = \left(\frac{\mathrm{m}_{2}-\mathbf{m}_{1}}{\mathrm{~m}_{2}+\mathrm{m}_{1}}\right) \mathbf{g} ….(iii)
Solving equations. (ii) and (iii) for T, we get,
T = m2(g – a) = \left(\frac{2 m_{1} m_{2}}{m_{1}+m_{2}}\right) g

Question 37.
Write a note on elastic collision.
Answer:

  1. Collision between two bodies in which kinetic energy of the entire system is conserved along with the linear momentum is called as elastic collision.
  2. In an elastic collision,
    \mathrm{m}_{1} \overrightarrow{\mathrm{u}_{1}}+\mathrm{m}_{2} \overrightarrow{\mathrm{u}_{2}}=\mathrm{m}_{1} \overrightarrow{\mathrm{v}_{1}}+\mathrm{m}_{2} \overrightarrow{\mathrm{v}}_{2}
  3. In an elastic collision,
    \sum \mathrm{K} \cdot \mathrm{E}_{\text {‘initial }}=\sum \mathrm{K} \cdot \mathrm{E}_{\text {. final }}
  4. An elastic collision is impossible in daily life.
  5. However, in many situations, the interatomic and intermolecular collisions are considered to be elastic.

Question 38.
Write a note on inelastic collision.
Answer:

  1. A collision is said to be inelastic if there is a loss in the kinetic energy during collision, but linear momentum is conserved.
  2. In an inelastic collision, m1u1 + m2u2 = m1v1 + m2v2.
  3. In an inelastic collision,
    \sum \mathrm{K} \cdot \mathrm{E}_{\text {.initial }} \neq \sum \mathrm{K} \cdot \mathrm{E}_{\text {.final }}
  4. The loss in kinetic energy is either due to internal friction or vibrational motion of atoms causing heating effect.

Question 39.
Define perfectly inelastic collision. Give an example of it.
Answer:

  1. Collision in which the colliding bodies stick together after collision and move with a common velocity is called perfectly inelastic collision.
  2. The loss in kinetic energy is maximum in perfectly elastic collision.
  3. Example: Lump of mud thrown on a wall sticks to the wall due to the loss of kinetic energy.

Question 40.
In case of an elastic head on collision between two bodies, derive an expression for the final velocities of the bodies in terms of their masses and velocities before collision.
Answer:
Head on elastic collision of two spheres:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 11

i. Consider two rotating smooth bodies A and B of masses m1 and m2 respectively moving
along the same straight line.

ii. Let \overrightarrow{\mathrm{u}}_{1} = initial velocity of the sphere A before collision.
\overrightarrow{\mathrm{u}}_{2} = initial velocity of the sphere B before collision.
\overrightarrow{\mathrm{v}}_{1} = velocity of the sphere A after collision.
\overrightarrow{\mathrm{v}}_{2} = velocity of the sphere B after collision.

iii. After the elastic collision, the spheres separate and move along the same straight line without rotation.

iv. According to the law of conservation of momentum,
m1\overrightarrow{\mathrm{u}}_{1} + m2\overrightarrow{\mathrm{u}}_{2} = m1\overrightarrow{\mathrm{v}}_{1} + m2\overrightarrow{\mathrm{v}}_{2} ….(i)
According to the law of conservation of energy (as kinetic energy is conserved during elastic collision),
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 12

v. Since kinetic energy is a scalar quantity, the terms involved in the above equations are scalars.

vi. The equation (1) can be written in scalar form as,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 13

vii. Also the equation (2) can be written as,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 14

viii. Now dividing equation (4) by (3) we get,
(u1 + v1) = (u2 + v2)
∴ u1 + v1 = u2 + v2
∴ v2 = u1 – u2 + v1 … (5)

ix. Comparing equation (3) and (5),
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 15
Equations, (6) and (7), represent the final velocities of two spheres after collision.

Question 41.
Are you aware of elasticity of materials? Is there any connection between elasticity of materials and elastic collisions?
Answer:
(Students should answer the question as per their understanding).

Question 42.
Two bodies undergo one-dimensional, inelastic, head-on collision. State an expression for their final velocities in terms
of their masses, initial velocities and coefficient of restitution.
Answer:
If e is the coefficient of restitution, the final velocities after an inelastic, head on collision are given as,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 16

Question 43.
Two bodies undergo one-dimensional, inelastic, head-on collision. State an expression for the loss in the kinetic energy.
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 17
ii. As e < 1, (1 – e2) is always positive. Thus, there is always a loss of kinetic energy in an inelastic collision.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 44.
Two bodies undergo one-dimensional, inelastic, head-on collision. Obtain an expression for the magnitude of impulse.
Answer:
i. When two bodies undergo collision, the linear momentum delivered by the first body to the second body must be equal to the change in momentum or impulse of the second body and vice versa.
∴ Impulse,
|J| = |∆p1| = |∆p2|
= |m1v1 – m1u1| = |m2v2 – m2u2| ….(1)

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 18
In equation (1) and solving, we get,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 19

Question 45.
Two bodies undergo one-dimensional, perfectly inelastic, head-on collision. Derive an expression for the loss in the kinetic energy.
Answer:
i. Let two bodies A and B of masses m1 and m2 move with initial velocity \overrightarrow{\mathrm{u}}_{1} and \overrightarrow{\mathrm{u}}_{2}, respectively such that particle A collides head on with particle B i.e., u1 > u2.

ii. If the collision is perfectly inelastic, the particles stick together and move with a common velocity \overrightarrow{\mathrm{v}} after the collision along the same straight line.
loss in kinetic energy = total initial kinetic energy – total final kinetic energy.

iii. By the law of conservation of momentum,
m1u1 + m2u2 = (m1 + m2)v
∴ v = \frac{\mathrm{m}_{1} \mathrm{u}_{1}+\mathrm{m}_{2} \mathrm{u}_{2}}{\mathrm{~m}_{1}+\mathrm{m}_{2}}

iv. Loss of Kinetic energy,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 20

iv. Both the masses and the term (u1 – u2)2 are positive. Hence, there is always a loss in a perfectly inelastic collision. For a perfectly inelastic collision, as e = 0, the loss is maximum.

Question 46.
Distinguish between elastic and inelastic collision.
Answer:

No. Elastic Collision Inelastic Collision
i. In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not conserved.
ii. The total kinetic energy after collision is equal to the total kinetic energy before collision. The total kinetic energy after the collision is not equal to the total kinetic energy before collision.
iii. Coefficient of restitution (e) is equal to one. Coefficient of restitution (e) is less than one. For a perfectly inelastic collision coefficient of restitution is equal to zero.
iv. Bodies do not stick together in elastic collision. Bodies stick together in a perfectly inelastic collision.
v. Sound, heat and light are not produced. Sound or light or heat or all of these may be produced.

Question 47.
Explain elastic collision in two dimensions.
Answer:
i. Suppose a particle of mass mi moving with initial velocity \overrightarrow{\mathrm{u}_{1}}, undergoes a non head-on collide with another particle of mass m2 and initial velocity \overrightarrow{\mathrm{u}_{2}}.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 21

ii. Let us consider two mutually perpendicular directions; Common tangent at the point of impact, along which there is no force (or no change of momentum).
Line of impact which is perpendicular to the common tangent through the point of impact, in the two-dimensional plane of initial and final velocities.

iii. Applying the law of conservation of linear momentum along the line of impact, we have, m1u1 cos α1 + m2u2 cos α2 = m1v1 cos β1 + m2v2 cos β2
As there is no force along the common tangent,
m1u1 sin α1 = m1u1 sin β1 and m2u2 sin α2 = m2v2 sin β2
iv. Coefficient of restitution (e) along the line of impact is given as
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 22

Question 48.
Two bodies undergo a two-dimensional collision. State an expression for the magnitude of impulse along the line of impact and the loss in kinetic energy.
Answer:
i. For two bodies undergoing a two-dimensional collision, the magnitude of impulse along the line of impact is given as, Magnitude of the impulse, along the line of impact,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 23

ii. The loss in the kinetic energy is given as Loss in the kinetic energy = ∆ (K.E.)
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 24

Question 49.
0ne marble collides head-on with another identical marble at rest. If the collision is partially inelastic, determine the ratio of their final velocities in terms of coefficient of restitution e.
Solution:
According to conservation of momentum,
m1u1 + m2u2 = m1v1 + m2v2
As m1 = m2, we get, u1 + u2 = v1 + v2
∴ If u2 = 0, we get, v1 + v2 = u1 ….. (i)
Coefficient of restitution,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 25

Question 50.
A 10 kg mass moving at 5 m/s collides head- on with a 4 kg mass moving at 2 m/s in the same direction. If e = \frac{1}{2}, find their velocity after impact.
Solution:
Given: m1 = 10 kg, m2 = 4 kg
u1 = 5 m/s, u2 = 2 m/s, e = \frac{1}{2}
To find: Velocity after impact (v1 and v2)

Formulae:

i. m1u1 + m2u2 = m1v1 + m2v2
ii. e = \left(\frac{v_{2}-v_{1}}{u_{1}-u_{2}}\right)

Calculation:

From formula (i),
10 × 5 + 4 × 2 = 10v1 + 4v2
∴ 5v1 + 2v2 = 29 … (1)

From formula (ii),
v2 – v1 = e(u1 – u2) = \frac{1}{2} (5 – 2) = \frac{3}{2}
∴ 2v2 – 2v1 = 3 … (2)
Solving (1) and (2), we have
∴ v1 = \frac{26}{7} m/s and v2 = \frac{73}{14} m/s
Answer:
The respective velocities of the two masses are \frac{26}{7} m/s and \frac{73}{14} m/s.

Question 51.
A metal ball falls from a height 1 m on a steel plate and jumps upto a height of 0.81 m. Find the coefficient of restitution.
Solution:
As the ball falls to the steel plate P.E changes to kinetic energy.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 26
As ground is stationary, both its initial and final velocities are zero.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 27

Question 52.
Two bodies of masses 5 kg and 3 kg moving in the same direction along the same straight line with velocities 5 m s-1 and 3 m s-1 respectively suffer one-dimensional elastic collision. Find their velocities after the collision.
Solution:
Given: m1 = 5kg, u1 = 5ms-1, m2 = 3kg, u2 = 3 m s-1
To find: velocities after collision (v1 and v2)
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 281
Answer:
The velocities of the two bodies after collision are 3.5 m/s and 5.5 m/s.

Question 53.
A 20 g bullet leaves a machine gun with a velocity of 200 m/s. If the mass of the gun is 20 kg, find its recoil velocity. If the gun fires 20 bullets per second, what force is to be applied to the gun to prevent recoil?
Solution:
Given: m1 = 20g = 0.02 kg, m2 = 20 kg, v1 = 200 m/s, t = \frac{1}{20} s,
To find: Recoil velocity (v2), applied force (F)

Formulae:

i. v2 = -\frac{\mathrm{m}_{1} \mathrm{v}_{1}}{\mathrm{~m}_{2}}
ii. F = ma

Calculation: From formula (i),
∴ v2 = -\frac{0.02}{20} \times 200
= -0.2 m/s

Negative sign shows that the machine gun moves in a direction opposite to that of the bullet.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 29
From formula (ii),
∴ F = m2 × a = 20 × 4 = 80N
Answer:
The recoil velocity of gun is 0.2 m/s and the required force to prevent recoil is 80 N.

Question 54.
A shell of mass 3 kg is dropped from some height. After falling freely for 2 seconds, it explodes into two fragments of masses 2 kg and 1 kg. Kinetic energy provided by the explosion is 300 J. Using g = 10 m/s2, calculate velocities of the fragments. Justify your answer if you have more than one options.
Solution:
Total mass = m1 + m2 = 3 kg
Initially, when the shell falls freely for 2 seconds, v = u+ at = 0 + 10(2) = 20 ms-1 = u1 = u2
According to conservation of linear momentum,
m1u1 + m2u2 = m1v1 + m2v2
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 30
There are two possible answers since the positions of two fragments can be different as explained below.
Case 1: v1 = 30 m s-1 and v2 = 0 with the lighter fragment 2 above.
Case 2: v1 = 10 m s-1 and v2 = 40 m s-1 with the lighter fragment 2 below, both moving downwards.

Question 55.
Bullets of mass 40 g each, are fired from a machine gun at a rate of 5 per second towards a firmly fixed hard surface of area 10 cm2. Each bullet hits normal to the surface at 400 m/s and rebounds in such a way that the coefficient of restitution for the collision between bullet and the surface is 0.75. Calculate average force and average pressure experienced by the surface due to this firing.
Solution:
For the collision,
u1 = 400 m s-1, e = 0.75
For the firmly fixed hard surface, u2 = v2 = 0
e = 0.75 = \frac{v_{1}-v_{2}}{u_{2}-u_{1}}=\frac{v_{1}-0}{0-400}
∴ v1 = -300 m/s.
Negative sign indicates that the bullet rebounds in exactly opposite direction.
Change in momentum of each bullet = m(v1 – u1)
The same momentum is transferred to the surface per collision in opposite direction.
∴ Momentum transferred to the surface, per collision,
p = m (u1 – v1) = 0.04(400 – [-300]) = 28 Ns
The rate of collision is same as rate of firing.
∴ Momentum received by the surface per second, \frac{\mathrm{dp}}{\mathrm{dt}} = average force experienced by the surface = 28 × 5 = 140 N

This is the average force experienced by the surface of area A = 10 cm2 = 10-3 m2
∴ Average pressure experienced,
P = \frac{\mathrm{F}}{\mathrm{A}}=\frac{140}{10^{-3}} = 1.4 × 105 N m-2
∴ P ≈ 1.4 times the atmospheric pressure.
Answer:
The average force and average pressure experienced by the surface due to the firing is 140 N and 1.4 × 105 N m-2 respectively.

Question 56.
A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s-1, what is the recoil speed of the gun? (NCERT)
Solution:
Given: m1 = 0.02 kg, m2 = 100 kg, v1 = 80 m s-1
To find: Recoil speed (v2)
Formula: m1u1 + m2u2 = m1v1 + m2v2
Calculation: Initially gun and shell are at rest.
∴ m1u1 + m2u2 = 0
Final momentum = m1v1 – m2v2
Using formula,
0 = 0.02 (80) – 100(v2)
∴ v2 = \frac{0.02 \times 80}{100} = 0.016 ms-1
Answer:
The recoil speed of the gun is 0.016 m s-1.

Question 57.
Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m s-1 collide and rebound with the same speed. What is the impulse imparted to each bail due to the other? (NCERT)
Solution:
Given: m = 0.05 kg. u = 6 m/s, v = -6 m/s
To find: Impulse (J)
Formula: J = m (v – u)
calculation: From formula,
J = 0.05 (-6 – 6) = -0.6 kg m s-1
Answer:
Impulse received by each ball is -0.6 kg m s-1.

Question 58.
A bullet of mass 0.1 kg moving horizontally with a velocity of 20 m/s strikes a target and brought to rest in 0.1 s. Find the impulse and average force of impact.
Solution:
Given: m = 0.1 kg, u = 20 m/s, t = 0.1 s
To find: Impulse (J), Average force (F)

Formulae:

i. J = mv – mu
ii. F = m \frac{(v-u)}{t}

Calculation:

From formula (i).
J = m(v – u) = 0.1 (0 – 20) = -2 Ns
From formula (ii),
F = \frac{m(v-u)}{t}=\frac{2}{0.1}=20 N
Answer:
Magnitude of impulse is 2 Ns, average force of impact is 20 N.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 59.
A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg) (NCERT)
Answer:
Let the point B represents the position of bat. The ball strikes the bat with velocity v along the path AB and gets deflected with same velocity along BC. such that ∠ABC = 45°
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 31
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 32
Thus, impulse imparted to the ball is 4.157 kg ms-1

Question 60.
A cricket ball of mass 150 g moving with a velocity of 12 m/s is turned back with a velocity of 20 m/s on hitting the bat. The force of the ball lasts for 0.01 s. Find the average force exerted on the ball by the bat.
Solution:
m = 0.150 kg, v = 20 m/s,
u = -12 m/s and t = 0.01 s
To find: Average force (F)
Formula: F = \frac{m(v-u)}{t}
Calculation: From formula,
F = \frac{0.150[20-(-12)]}{0.01} = 480 N
Answer:
The average force exerted on the ball by the bat is 480 N.

Question 61.
Mass of an Oxygen molecule is 5.35 × 10-26 kg and that of a Nitrogen molecule is 4.65 × 10-26 kg. During their Brownian motion (random motion) in air, an Oxygen molecule travelling with a velocity of 400 m/s collides elastically with a nitrogen molecule travelling with a velocity of 500 m/s in the exactly opposite direction. Calculate the impulse received by each of them during collision. Assuming that the collision lasts for
1 ms, how much is the average force experienced by each molecule?
Solution:
Let, m1 = mO = 5.35 × 10-26 kg,
m2 = mN = 4.65 × 10-26 kg,
∴ u1 = 400 ms-1 and u2 = -500 ms-1 taking direction of motion of oxygen molecule as the positive direction.
For an elastic collision,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 33
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 34
Hence, the net impulse or net change in momentum is zero.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 35
Answer:
The average force experienced by the nitrogen molecule and the oxygen molecule are
-4.478 × 10-20 N and 4.478 × 10-20 N.

Question 62.
Explain rotational analogue of the force. On what factors does it depend? Represent it in vector form.
Answer:

  1. Rotational analogue of the force is called as moment of force or torque.
  2. It depends on the mass of the object, the point of application of the force and the angle between direction of force and the line joining the axis of rotation with the point of application.
  3. In its mathematical form, torque or moment of a force is given by
    \vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}
    where \overrightarrow{\mathrm{F}} is the applied force and \overrightarrow{\mathrm{r}} is the position vector of the point of application of the force from the axis of rotation.

Question 63.
Illustrate with an example how direction of the torque acting on any object is determined.
Answer:
i. Consider a laminar object with axis of rotation perpendicular to it and passing through it as shown in figure (a).
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 36

ii. Figure (b) indicates the top view of the object when the rotation is in anticlockwise direction
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 37

iii. Figure (c) shows the view from the top, if rotation is in clockwise direction.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 38

iv. The applied force \vec{F} and position vector \vec{r} of the point of application of the force are in the plane of these figures.

v. Direction of the torque is always perpendicular to the plane containing the vectors \vec{r} and \vec{F} and can be obtained from the rule of cross product or by using the right-hand thumb rule.

vi. In Figure (b), it is perpendicular to the plane of the figure and outwards while in the figure (c), it is inwards.

Question 64.
State the equation for magnitude of torque and explain various cases of angle between the direction of \overrightarrow{\mathbf{r}} and \overrightarrow{\mathbf{F}}.
Answer:
Magnitude of torque, \tau = r F sin θ
where θ is the smaller angle between the directions of \overrightarrow{\mathbf{r}} and \overrightarrow{\mathbf{F}}.

Special cases:

  1. If θ = 90°, \tau = \taumax = rF. Thus, the force should be applied along normal direction for easy rotation.
  2. If θ = 0° or 180°, \tau = \taumin = 0. Thus, if the force is applied parallel or anti-parallel to \overrightarrow{\mathrm{r}}, there is no rotation.
  3. Moment of a force depends not only on the magnitude and direction of the force, but also on the point where the force acts with respect to the axis of rotation. Same force can have different torque as per its point of application.

Question 65.
A force \overrightarrow{\mathbf{F}}=\mathbf{3} \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{4} \hat{\mathbf{k}} is applied at a point (3, 4, -2). Find its torque about the point (-1, 2, 4).
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 39

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 66.
Define couple. Show that moment of couple is independent of the points of application of forces.
Answer:
A pair of forces consisting of two forces of equal magnitude acting in opposite directions along different lines of action is called a couple.

  1. Figure shows a couple consisting of two forces \overrightarrow{\mathrm{F}}_{1} and \overrightarrow{\mathrm{F}}_{2} of equal magnitudes and opposite directions acting along different lines of action separated by a distance r.
  2. Position vector of any point on the line of action of force \overrightarrow{\mathrm{F}}_{1} from the line of action of force \overrightarrow{\mathrm{F}}_{2} is \overrightarrow{\mathrm{r}}_{12}. Similarly, the position vector of any point on the line of action of force \overrightarrow{\mathrm{F}}_{2} from the line of action of force \overrightarrow{\mathrm{F}}_{1} is \overrightarrow{\mathrm{r}}_{21}.
  3. Torque or moment of the couple is then given mathematically as
    Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 40
  4. From the figure, it is clear that r12 sinα = r21 sin β = r.
  5. If \left|\overrightarrow{\mathrm{F}}_{1}\right|=\left|\overrightarrow{\mathrm{F}}_{2}\right| = F, the magnitude of torque is given by
    \tau=\mathrm{r}_{12} \mathrm{~F}_{1} \sin \alpha = r_{21} F_{2} \sin \beta=r F
  6. It clearly shows that the torque corresponding to a given couple, i.e., the moment of a given couple is constant, i.e., it is independent of the points of application of forces.

Question 67.
The figure below shows three situations of a ball at rest under the action of balanced forces. Is the bail in mechanical equilibrium? Explain how the three situations differ.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 41
Answer:

  1. In all these cases, as the ball is at rest under the action of balanced forces i.e, there is no net force acting on it. Hence, it is in mechanical equilibrium.
    However, potential energy-wise, the three situations show the different states of mechanical equilibrium.
  2. Stable equilibrium: In situation (a), potential energy of the system is at its local minimum. If it is disturbed slightly from its equilibrium position and released, it tends to recover its position. In this situation, the ball is most stable and is said to be in stable equilibrium.
  3. Unstable equilibrium: In situation (b), potential energy of the system is at its local maximum. If it is slightly disturbed from its equilibrium position, it moves farther from that position. This happens because initially, if disturbed, it tries to achieve the configuration of minimum potential energy. In this situation, the ball is said to be in unstable equilibrium.
  4. Neutral equilibrium: in situation (e), potential energy of the system is constant over a plane and remains same at any position. Thus, even if the ball is disturbed, it still remains in equilibrium, practically at any position. In this situation, the ball is in neutral equilibrium.

Question 68.
Two weights 5 kg and 8 kg are suspended from a uniform rod of length 10 m and weighing 3 kg. The distances of the weights from one end are 2 m and 7 m. Find the point at which the rod balances.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 42
Let the rod balance at a point P, x m from the end A of the rod AB. The suspended weight and the centre of gravity of the rod G is shown in the figure.
P = 5 + 3 + 8 = 16kg
Taking moments about A,
16 × x = 5 × 2 + 3 × 5 + 8 × 7
16x = 10 + 15 + 56 = 81
∴ x = \frac{81}{16} = 5.1 m
Answer:
The rod balances at 5.1 m from end A.

Question69.
A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the metre stick? (NCERT)
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 43
Consider the metre scale AB. Let its mass be concentrated at C at 50 cm. mark. Upon placing coins, balancing point of the scale and the coins system is shifted to C’ at 45 cm mark.
For equilibrium about C’
10(45 – 12) = m (50 – 45)
m = \frac{10 \times 33}{5} = 66g
Answer:
The mass of the metre scale is 66 g.

Question 70.
The diagram shows a uniform beam of length 10 m, used as a balance. The beam is pivoted at its centre. A 5.0 N weight is attached to one end of the beam and an empty pan weighing 0.25 N Is attached to the other end of the beam.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 44
i. What is the moment of couple at pivot?
ii. If pivot is shifted 2 ni towards left, then what will be moment of couple at new position?
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 45
Answer:

  1. The moment of couple at center is 23.75 N-m.
  2. The moment of couple at new position is 13.25 N-m.
    ∴ For equilibrium,
    40 × x = 20 × 0.5
    ∴ x = \frac{1}{4} = 0.25 m

Hence, the total distance walked by the person is 1.25 m.

Ans
The person can walk 1.25 m before the plank topples.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 71.
Define centre of mass.
Answer:
Centre of mass of a body is a point about which the summation of moments of masses in the system is zero.

Question 72.
Derive an expression for the position of centre of mass of a system of n particles and for continuous mass distribution.
Answer:
System of n particles;
i. Consider a system of n particles of masses m1, m2, …, mn having position vectors \overrightarrow{\mathrm{r}_{1}}, \overrightarrow{\mathrm{r}_{2}},….., \overrightarrow{\mathrm{r}_{n}} from the origin O.
The total mass of the system is,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 46
Centre of mass for n particles

ii. Position vector \vec{r} of their centre of mass from the same origin is then given by
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 47

iii. If the origin is at the centre of mass, \overrightarrow{\mathbf{r}} = 0
\sum_{1}^{\mathrm{n}} \mathrm{m}_{\mathrm{i}} \overrightarrow{\mathrm{r}}_{\mathrm{i}} = 0,

iv. In this case, \sum_{1}^{n} m_{i} \vec{r}_{i} gives the moment of masses (similar to moment of force) about the centre of mass.

v. If (x1, x2, …… xn), (y1, y2, …..yn), (z1, z2, …. zn) are the respective x, y and z – coordinates of (r1, r2,…….. rn) then x,y and z – coordinates of the centre of mass are given by,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 48

vi. Continuous mass distribution: For a continuous mass distribution with uniform density, the position vector of the centre of mass is given by,
r = \frac{\int \vec{r} d m}{\int d m}=\frac{\int \vec{r} d m}{M}
Where \int \mathrm{dm}=\mathrm{M} is the total mass of the object.

vii. The Cartesian coordinates of centre of mass are
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 49

Question 73.
State the expression for velocity of the centre of mass of a system of n particles and for continuous mass distribution.
Answer:
Let v1, v2,…..vn be the velocities of a system of point masses m1, m2, … mn. Velocity of the centre of mass of the system is given by
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 50
x, y and z components of \overrightarrow{\mathbf{v}} can be obtained similarly.
For continuous distribution, \overrightarrow{\mathrm{v}}_{\mathrm{cm}} = \frac{\int \vec{v} \mathrm{dm}}{\mathrm{M}}

Question 74.
State the expression for acceleration of the centre of mass of a system of n particles and for continuous mass distribution.
Answer:
Let a1, a2,…. an be the accelerations of a system of point masses m1, m2 … mn.
Acceleration of the centre of mass of the system is given by
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 51
x, y and z components of can be obtained similarly.
For continuous distribution, \overrightarrow{\mathrm{a}}_{\mathrm{cm}} = \frac{\int \vec{a} d m}{\mathrm{M}}

Question 75.
State the characteristics of centre of mass.
Answer:

  1. Centre of mass is a hypothetical point at which entire mass of the body can be assumed to he concentrated.
  2. Centre of mass is a location, not a physical quantity.
  3. Centre of mass is particle equivalent of a given object for applying laws of motion.
  4. Centre of mass is the point at which applied force causes only linear acceleration and not angular acceleration.
  5. Centre of mass is located at the centroid, for a rigid body of uniform density.
  6. Centre of mass is located at the geometrical centre, for a symmetric rigid body of uniform density.
  7. Location of centre of mass can be changed only by an external unbalanced force.
  8. Internal forces (like during collision or explosion) never change the location of centre of mass.
  9. Position of the centre of mass depends only upon the distribution of mass, however, to describe its location we may use a coordinate system with a suitable origin.
  10. For a system of particles, the centre of mass need not coincide with any of the particles.
  11. While balancing an object on a pivot, the line of action of weight must pass through the centre of mass and the pivot. Quite often, this is an unstable equilibrium.
  12. Centre of mass of a system of only two particles divides the distance between the particles in an inverse ratio of their masses, i.e., it is closer to the heavier mass.
  13. Centre of mass is a point about which the summation of moments of masses in the system is zero.
  14. If there is an axial symmetry for a given object, the centre of mass lies on the axis of symmetry.
  15. If there are multiple axes of symmetry for a given object, the centre of mass is at their point of intersection.
  16. Centre of mass need not be within the body.
    Example: jumper doing fosbury flop.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 76.
The mass of moon is 0.0 123 times the mass of the earth and separation between them is 3.84 × 108 m. Determine the location of C.M as measured from the centre of the earth.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 52
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 53
Answer:
The location of centre of mass as measured from the center of the earth is 4.67 × 106 m.

Question 77.
Three particles of masses 3 g, 5 g and 8 g are situated at point (2, 2, 2), (-3, 1, 4) and (-1, 3, -2) respectively. Find the position vector of their centre of mass.
Solution:
m1 = 3 g, m2 = 5 g, m3 = 8 g, x1 = 2, y1 = 2, z1 = 2
x2 = -3, y2 = 1, z2 = 4,
x3 = -1, y3 = 3, z3 = -2
Let (X, Y, Z) be co-ordinates of C.M., then
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 54
The co-ordinates of the C.M. are \left(-\frac{17}{16}, \frac{35}{16}, \frac{5}{8}\right)
Answer:
The position vector of the C.M. is -\frac{17}{16} \hat{\mathbf{i}}+\frac{35}{16} \hat{\mathbf{j}}+\frac{5}{8} \hat{\mathbf{k}}

Question 78.
In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 Å = 10-10 m). Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus. (NCERT)
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 55
Claculation: From formula
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 56
Answer:
The location of centre of mass from the nucleus of hydrogen atom is 1.235 A.

Question 79.
Three thin walled uniform hollow spheres of radii 1 cm, 2 cm and 3 cm are so located that their centres are on the three vertices of an equilateral triangle ABC having each side 10 cm. Determine centre of mass of the system.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 57
Solution:
Mass of a thin walled uniform hollow sphere is proportional to its surface area. (as density is constant) hence proportional to r2.

Thus, if mass of the sphere at A is mA = m, then mB = 4m and mC = 9m. By symmetry of the spherical surface, their centres of mass are at their respective centres, i.e., at A, B and C. Let us choose the origin to be at C, where the largest mass 9m is located and the point B with mass 4m on the positive x-axis. With this, the co-ordinates of C are (0, 0) and that of B are (10, 0). If A of mass m is taken in the first quadrant, its co-ordinates will be [5,5 \sqrt{3}]
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 58

Question 80.
Locate the centre of mass of three particles of mass m1 = 1 kg, m2 = 2 kg and m3 = 3 kg at the corner of an equilateral triangle of each side of 1 m.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 59
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 60
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 61
Answer:
The centre of mass of the system of three particles lies at \left(\frac{2}{3} m, \frac{\sqrt{3}}{6} m\right) with respect to the particle of mass 1 kg as the origin.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 81.
A letter ‘E’ is prepared from a uniform cardboard with shape and dimensions as shown in the figure. Locate its centre of mass.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 62
Solution:
As the sheet is uniform, each square can be taken to be equivalent to mass m concentrated at its respective centre. These masses will then be at the points labelled with numbers 1 to 10, as shown in figure. Let us select the origin to be at the left central mass m5, as shown and all the co-ordinates to be in cm.

By symmetry, the centre of mass of m1, m2 and m3 will be at m2 (1, 2) having effective mass 3m. Similarly, effective mass 3m due to m8, m9 and m10 will be at m9 (1, -2). Again, by symmetry, the centre of mass of these two (3m each) will have co-ordinates (1, 0). Mass m6 is also having co-ordinates (1, 0). Thus, the
effective mass at (1, 0) is 7m.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 63
Using symmetry for m4, m5 and m7, there will be effective mass 3m at the origin (0, 0). Thus, effectively, 3m and 7m are separated by 1 cm along X-direction. Y-coordinate is not required.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 64

Question 82.
A hole of radius r is cut from a uniform disc of radius 2r. Centre of the hole is at a distance r from centre of the disc. Locate centre of mass of the remaining part of the disc.
Solution:
Before cutting the hole, c.în. of the full disc was at its centre. Let this be our origin O. Centre of mass of the cut portion is at its centre D. Thus, it is at a distance x1 = r form the origin. Let C be the centre of mass of the
remaining disc, which will he on the extension of the line DO at a distance x2 = x from the origin. As the disc is uniform, mass of any of its part is proportional to the area of that part.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 65
Thus, if m is the mass of the cut disc, mass of the entire disc must be 4m and mass of the remaining disc will be 3m.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 66

Alternate method: (Using negative mass):

Let \overrightarrow{\mathrm{R}} be the position vector of the centre of mass of the uniform disc of mass M. Mass m is with centre of mass at position vector \overrightarrow{\mathrm{r}} from the centre of the disc be cut out from the complete disc. Position vector of the centre of mass of the remaining disc is then given by
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 67

Question 83.
Define centre of gravity of a body. Under what conditions the centre of gravity and centre of mass coincide?
Answer:

  1. centre of gravity of a body is the point around which the resultant torque due to force of gravity on the body is zero.
  2. The centre of mass coincides with centre of gravity when the body is in a uniform gravitational field.

Question 84.
Explain how to find the location of centre of mass or centre of gravity of a laminar object.
Answer:

  1. A laminar object is suspended from a rigid support at two orientations.
  2. Lines are drawn on the object parallel to the plumb line as shown in the figure.
  3. Plumb line is always vertical, i.e., parallel to the line of action of gravitational force.
  4. Intersection of the lines drawn is then the point through which line of action of the gravitational force passes for any orientation. Thus, it gives the location of the c.g. or c.m.
    Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 68

Question 85.
Why do cricketers wear helmet and pads while playing? Is it related with physics?
Answer:
Helmet and pads used by cricketers protects the head, using principles of physics.

  1. The framing between the interior of the helmet and pads increases the time over which the impulse acts on the head resulting into reduction of force.
    (Impulse = force × time = constant)
  2. The pads spread the force applied by the ball over a wider area reducing pressure at a point.

Question 86.
The diagram shows four objects placed on a flat surface.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 69
The centre of mass of each object is marked M. Which object is likely to fall over?
Answer:
Object C will fall because its centre of mass is not exactly at centre, in turn applying more force on one side of the object resulting in to unbalance force. Whereas, in other objects center of mass is exactly at center resulting into zero rotational or translational motion maintaining their equilibrium.

Question 87.
A boy is about to close a large door by applying force at A and B as shown. State with a reason, which of the two positions, A or B, will enable him to close the door with least force.
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 70
Answer:
Boy has to apply more force at point B as compared to point A, because point B is at least distance from the hinge of the door while point A is at maximum distance from hinge of the door. Opening of door applies a moment, which is. given by,
M = F × perpendicular distance
F ∝ \frac{1}{\text { distance }}
More is the distance from the axis of rotation less will be the force.

Question 88.
How is a seat belt useful for safety?
Answer:
When car hits another car or an object with high speed it applies a high impulse on the driver and due to inertia driver tends to move in forward direction towards the steering. Seat belts spreads the force over large area of the body and holds the driver and protects him from crashing at the steering.

Question 89.
According to Newton’s third law of motion for every action there is equal and opposite reaction, why two equal and opposite forces don’t cancel each other?
Answer:
Forces of action and reaction always act on different bodies, hence they never cancel each other.

Question 90.
Linear momentum depends on frame of reference, but principle of conservation of linear momentum is independent of frame of reference. Why?
Answer:
Observers in different frame find different values of linear momentum of a system, hence linear momentum depends upon frame of reference, but each would observe that the value of linear momentum does not change with time (provided the system is isolated), hence principle of conservation of linear momentum is independent of frame of reference.

Question 91.
Multiple choice Questions

Question 1.
A body of mass 2 kg moving on a horizontal surface with initial velocity of 4 m s-1 comes to rest after two seconds. If one wants to keep this body moving on the same surface with a velocity of 4 m s-1, the force required is
(A) 2 N
(B) 4 N
(C) 0
(D) 8 N
Answer:
(B) 4 N

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 2.
What force will change the velocity of a body of mass 1 kg from 20 m s-1 to 30 m s-1 in two seconds?
(A) 1N
(B) 5 N
(C) 10 N
(D) 25 N
Answer:
(B) 5 N

Question 3.
A force of 5 newton acts on a body of weight 9.80 newton. What is the acceleration produced in m/s2?
(A) 0.51
(B) 1.96
(C) 5.00
(D) 49.00
Answer:
(C) 5.00

Question 4.
A body of mass m strikes a wall with velocity v and rebounds with the same speed. Its change in momentum is
(A) 2 mv
(B) mv/2
(C) – mv
(D) Zero
Answer:
(A) 2 mv

Question 5.
A force of 6 N acts on a body of mass 1 kg initially at rest and during this time, the body attains a velocity of 30 m/s. The time for which the force acts on a body is
(A) 10 second
(B) 8 second
(C) 7 second
(D) 5 second
Answer:
(D) 5 second

Question 6.
A bullet of mass 10 g is fired from a gun of mass 1 kg with recoil velocity of gun = 5 m/s. The muzzle velocity will be
(A) 30 km/min
(B) 60 km/min
(C) 30 m/s
(D) 500 m/s
Answer:
(D) 500 m/s

Question 7.
The velocity of rocket with respect to ground is v1 and velocity of gases ejecting from rocket with respect to ground is v2 Then velocity of gases with respect to rocket is given by
(A) v2
(B) v1 + v2
(C) v1 × v2
(D) v1
Answer:
(B) v1 + v2

Question 8.
Two bodies A and B of masses 1 kg and 2 kg moving towards each other with velocities 4 m/s and 1 m/s suffers a head on collision and stick together. The combined mass will
(A) move in direction of motion of lighter mass.
(B) move in direction of motion of heavier mass.
(C) not move.
(D) move in direction perpendicular to the line of motion of two bodies.
Answer:
(A) move in direction of motion of lighter mass.

Question 9.
Which of the following has maximum momentum?
(A) A 100 kg vehicle moving at 0.02 m s-1.
(B) A 4 g weight moving at 1000 cm s-1’.
(C) A 200 g weight moving with kinetic energy of 10-6 J
(D) A 200 g weight after falling through one kilometre.
Answer:
(D) A 200 g weight after falling through one kilometre.

Question 10.
A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. What is conserved?
(A) Momentum alone.
(B) K.E. alone.
(C) Momentum and K.E. both.
(D) P.E. alone.
Answer:
(A) Momentum alone.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 11.
The force exerted by the floor of an elevator on the foot of a person standing there, is more than his weight, if the elevator is
(A) going down and slowing down.
(B) going up and speeding up.
(C) going up and slowing down.
(D) either (A) and (B).
Answer:
(D) either (A) and (B).

Question 12.
If E, G and N represents the magnitudes of electromagnetic, gravitational and nuclear forces between two electrons at a given separation, then,
(A) N = E = G
(B) E < N < G (C) N > G < E (D) E > G > N
Answer:
(D) E > G > N

Qestion 13.
For an inelastic collision, the value of e is
(A) greater than 1
(B) less than 1
(C) equal to 1
(D) none of these
Answer:
(B) less than 1

Question 14.
A perfect inelastic body collides head on with a wall with velocity y. The change in momentum is
(A) mv
(B) 2mv
(C) zero
(D) none of these.
Answer:
(A) mv

Question 15.
Two masses ma and rnb moving with velocitics va and vb in opposite direction collide
elastically and after the collision ma and mb move with velocities vb and va respectively. Then the ratio mamb is
(A) \frac{v_{a}-v_{b}}{v_{a}+v_{b}}
(B) \frac{\mathrm{m}_{\mathrm{a}}+\mathrm{m}_{\mathrm{b}}}{\mathrm{m}_{\mathrm{a}}}
(C) 1
(D) \frac{1}{2}
Answer:
(C) 1

Question 16.
The frictional force acts _____.
(A) in direction of motion
(B) against the direction of motion
(C) perpendicular to the direction of motion
(D) at any angle to the direction of motion
Answer:
(B) against the direction of motion

Question 17.
A marble of mass X collides with a block of mass Z, with a velocity Y. and sticks to it. The final velocity of the system is
(A) \frac{\mathrm{Y}}{\mathrm{X}+\mathrm{Y}} \mathrm{Y}
(B) \frac{X}{X+Z} Y
(C) \frac{X+Y}{Z}
(D) \frac{X+Z}{X}
Answer:
(B) \frac{X}{X+Z} Y

Question 18.
Two balls lying on the same plane collide. Which of the following will be always conserved?
(A) heat
(B) velocity
(C) kinetic energy
(D) linear momentum.
Answer:
(D) linear momentum.

Question 19.
A body is moving with uniform velocity of 50 km h-1, the force required to keep the body in motion in SI unit is
(A) zero
(B) 10
(C) 25
(D) 50
Answer:
(A) zero

Question 20.
A coolie holding a suitcase on his head of 20 kg and travels on a platform. then work done in joule by the coolie is
(A) 198
(B) 98
(C) 49
(D) zero
Answer:
(D) zero

Question 21.
Out of the following forces, which force is non-conservative?
(A) gravitational
(B) electrostatic
(C) frictional
(D) magnetic
Answer:
(C) frictional

Question 22.
The work done in conservative force is ____.
(A) negative
(B) zero
(C) positive
(D) infinite
Answer:
(B) zero

Question 23.
The angle between the line of action of force and displacement when no work done (in degree) is
(A) zero
(B) 45
(C) 90
(D) 120
Answer:
(C) 90

Question 24.
If the momentum of a body is doubled, its KE. increases by
(A) 50%
(B) 300%
(C) 100%
(L)) 400%
Answer:
(B) 300%

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 25.
In perfectly inelastic collision, which is conserved?
(A) P.E. only
(B) K.E. only
(C) momentum only
(D) K.E. and momentum
Answer:
(C) momentum only

Question 26.
In case of elaine collision, which s
(A) Momentum and K.E. is conserved.
(B) Momentum conserved and K.E. not conserved,
(C) Momentum not conserved and K.E. conserved.
(D) Momentum and K.E. both not conserved,
Answer:
(A) Momentum and K.E. is conserved.

Question 27.
Pseudo force is true only in
(A) frame of reference which is at rest
(B) inertial frame of reference.
(C) frame of reference moving with constant velocity.
(D) non-inertial frame of reference
Answer:
(D) non-inertial frame of reference

Question 28.
A men weighing 90kg carries a stone of 20 kg to the top of the building 30m high. The work done by hint is (g = 9.8 m/s2)
(A) 80 J
(B) 100 J
(C) 980 J
(D) 29,400 J
Answer:
(D) 29,400 J

Question 29.
A weight lifter is holding a weight of 100 kg on his shoulders for 45 s, the amount of work done by him in joules is
(A) 4500
(B) 100
(C) 45
(D) zero
Answer:
(D) zero

Question 30.
If m is the mass of a body and E its K.E..then its linear momentum is
(A) \mathrm{m} \sqrt{\mathrm{E}}
(B) 2 \sqrt{\mathrm{m}} \mathrm{E}
(C) \sqrt{m} E
(D) \sqrt{2 \mathrm{mE}}
Answer:
(D) \sqrt{2 \mathrm{mE}}

Question 31.
Torque applied is masimum when the angle between the directions of \overrightarrow{\mathrm{r}} and \overrightarrow{\mathrm{F}} is
(A) 90°
(B) 180°
(C) 0°
(D) 45°
Answer:
(A) 90°

Question 92.
A particle moving with velocity \vec{v} is acted by three forces shown by the vector triangle PQR. The velocity of the particle will:
(A) remain constant
(B) change according to the smallest force \overrightarrow{\mathrm{QR}}
(C) increase
(D) decrease
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 71
Hint: As the three forces acting on a particle represents a triangle (i.e., a closed loop)
∴ Fnet = 0
∴ m \vec{a} = 0
∴ m\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}
∴ v remains constant
Answer:
(A) remain constant

Question 93.
A force F = 20 + 10y acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from y = 0 to y = 1 m is:
(A) 25J
(B) 20J
(C) 30J
(D) SJ
Hint: Work done by variable force, W = \int_{y_{\text {initial }}}^{y_{\text {final }}} \mathrm{Fdy}
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 72
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 73
Answer:
(A) 25J

Question 94.
Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is:
(A) \frac{4}{9}
(B) \frac{5}{9}
(C) \frac{1}{9}
(D) \frac{8}{9}
Hint:
Fractional loss of K.E. of colliding bodies,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 74
Answer:
(D) \frac{8}{9}

Question 95.
An object of mass 500 g, initially at rest, is acted upon by a variable force whose X-component varies with X in the manner shown. The velocities of the object at the points X = 8 m and X = 12 m, would have the respective values of
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 75
(A) 18m/s and 20.6 m/s
(B) 18 m/s and 24.4 m/s
(C) 23 m/s and 24.4 m/s
(D) 23 m/s and 20.6 m/s
Hint: From work-energy theorem
∆ K.E. = work = area under F-x graph
From x = 0 to x = 8m
\frac{1}{2} \mathrm{mv}^{2} = (5 × 20) + (3 × 10)
\frac{1}{2} \mathrm{mv}^{2} = 100 + 30
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 76
Answer:
(D) 23 m/s and 20.6 m/s

Question 96.
The centre of mass of two particles system lies
(A) at the midpoint on the line joining the two particles.
(B) at one end of line joining the two particles.
(C) on the line perpendicular in the line joining two particles.
(D) on the line joining the Iwo particles.
Answer:
(D) on the line joining the two particles.

Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion

Question 97.
A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration ‘a’ towards the right. The relation between a and θ for the block to remain stationary on the wedge is
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 77
Hint:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 78
The mass of block is given to be m. It will remain stationary if forces acting on it are in equilibrium i.e., ma cos θ = mg sin θ
Here, ma = Pseudo force on block.
∴ a = g tan θ
Answer:
a = g tan θ

Question 98.
A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision, When the initial velocity of the lighter block is v, then the value of coefficient of restitution
(e) will
(A) 0.5
(B) 0.25
(C) 0.8
(D) 0.4
Hint:
Given: m1 = m, m2 = 4m, u1 = v, u2 = 0, v1 = 0 According to law of conservation of momentum,
m1u1 + m2u2 = m1v1 + m2v2
mv + 4m × 0 = m × 0 + 4mv2
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 79
Answer:
(B) 0.25

Question 99.
In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 80
Hint:
According to law of conservation of momentum,
mv0 = mv1 + mv2
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 81
Answer:
(D) \sqrt{2} \mathbf{v}_{0}

Question 100.
The mass of a hydrogen molecule is 3.32 × 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45° to the normal and rebound elastically with a speed of 103 m/s, then the pressure on the wall is nearly:
(A) 2.35 × 102 N/m2
(B) 4.70 × 102 N/m2
(C) 2.35 × 103 N/m2
(D) 4.70 × 103 N/m2
Hint:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 82
Answer:
(C) 2.35 × 103 N/m2

Question 101.
A bomb at rest explodes into 3 parts of same mass. The momentum of two parts is -3P\hat{\mathrm{i}} and 2P\hat{\mathrm{j}} respectively. The magnitude of momentum of the third part is
(A) P
(B) \sqrt{5} \mathrm{P}
(C) \sqrt{11} \mathrm{P}
(D) \sqrt{13} \mathrm{P}
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 83
Answer:
(D) \sqrt{13} \mathrm{P}

Question 102.
A sphere of mass ‘m’ moving with velocity V collides head-on on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is (e is coefficient of restitution and collision is inelastic)
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 84
Hint:
Initial momentum = mv
Final momentum = mv1 + mv2
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 85
Answer:
(C) \frac{\mathrm{e}+1}{2}

Question 103.
Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively:
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 86
Hint:
Tension in spring before cutting the strip,
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 87
Answer:
(B) \frac{\mathrm{g}}{3}, g

Question 104.
A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be
(A) 9 J
(B) 18 J
(C) 4.5 J
(D) 22 J
Hint:
F = 6t
m = 1 kg
∴ a = 6t
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 88
Answer:
(C) 4.5 J

Question 105.
Consider a drop of rain water having mass Ig falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take ‘g’ constant with a value 10 m/s2. The work done by the
(i) gravitational force and the
(ii) resistive force of air is:
(A) (i) -10 J
(ii) -8.25 J
(B) (i) 1.25 J
(ii) -8.25 J
(C) (i) 100 J
(ii) 8.75 J
(D) (i) 10 J
(ii) -8.75 J
Hint: Work done by gravitation force is given by (Wg)
Maharashtra Board Class 11 Physics Important Questions Chapter 4 Laws of Motion 89
Answer:
(D) (i) 10 J
(ii) -8.75 J

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Balbharti Maharashtra State Board 11th Physics Important Questions Chapter 2 Mathematical Methods Important Questions and Answers.

Maharashtra State Board 11th Physics Important Questions Chapter 2 Mathematical Methods

Question 1.
Explain representation of a vector graphically and symbolically.
Answer:

  1. Graphical representation:
    A vector is graphically represented by a directed line segment or an arrow.
    eg.: displacement of a body from P to Q is represented as P → Q.
  2. Symbolic representation:
    Symbolically a vector is represented by a single letter with an arrow above it, such as \overrightarrow{\mathrm{A}}. The magnitude of the vector \overrightarrow{\mathrm{A}} is denoted as |A| or | \overrightarrow{\mathrm{A}} | or A.

Question 2.
A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector?
Answer:

  1. For a physical quantity, only having magnitude and direction is not a sufficient condition to be a vector.
  2. A physical quantity also has to obey vectors law of addition to be termed as vector.
  3. Hence, anything that has magnitude and direction is not necessarily a vector.
    Example: Though current has definite magnitude and direction, it is not a vector.

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 3.
Define and explain the following terms:
i. Zero vector (Null vector)
ii. Resultant vector
iii. Negative vectors
iv. Equal vectors
v. Position vector
Answer:
i. Zero vector (Null vector):
A vector having zero magnitude and arbitrary direction is called zero vector. It is denoted as \overrightarrow{0}.
Example: Velocity vector of stationary particle, acceleration vector of a body moving with uniform velocity.

ii. Resultant vector:
The resultant of two or more vectors is defined as that single vector, which produces the same effect as produced by all the vectors together.

iii. Negative vectors:
A negative vector of a given vector is a vector of the same magnitude but opposite in direction to that of the given vector.
Negative vectors are antiparallel vectors.
In figure, \vec{b} = – \vec{a}
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 1

iv. Equal vectors:
Two vectors A and B representing same physical quantity are said to be equal if and only if they have the same magnitude and direction.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 2
In the given figure |\overrightarrow{\mathrm{P}}| = |\overrightarrow{\mathrm{Q}}| = |\overrightarrow{\mathrm{R}}| = |\overrightarrow{\mathrm{S}}|

v. Position vector:
A vector which gives the position of a particle at a point with respect to the origin of chosen co-ordinate system is called position vector.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 3
In the given figure \overrightarrow{\mathrm{OP}} represents position vector of \vec{P} with respect to O.

Question 4.
Whether the resultant of two vectors of unequal magnitude be zero?
Answer:
The resultant of two vectors of different magnitude cannot give zero resultant.

Question 5.
Define unit vector and give its physical significance.
Answer:
Unit vector: A vector having unit magnitude in a given direction is called a unit vector in that direction.
If \vec{p} is a non zero vector (P ≠ 0) then the unit vector \hat{\mathrm{u}}_{\mathrm{p}} in the direction of \overrightarrow{\mathrm{P}} is given by,
\hat{\mathrm{u}}_{\mathrm{p}} = \frac{\overrightarrow{\mathrm{P}}}{\mathrm{P}}
\overrightarrow{\mathrm{P}} = \hat{u}_{p} P

Significance of unit vector:

i. The unit vector gives the direction of a given vector.

ii. Unit vector along X, Y and Z direction of a rectangular (three dimensional) coordinate is represented by \hat{\mathrm{i}}, \hat{\mathrm{j}} and \hat{\mathrm{k}} respectively Such that \hat{\mathbf{u}}_{x} = \hat{\mathrm{i}}, \hat{\mathbf{u}}_{y} = \hat{\mathrm{j}} and \hat{\mathbf{u}}_{z} = \hat{\mathrm{k}}
This gives \hat{\mathrm{i}} = \frac{\overrightarrow{\mathrm{X}}}{\mathrm{X}}, \hat{\mathrm{j}} = \frac{\overrightarrow{\mathrm{Y}}}{\mathrm{X}} and \hat{\mathrm{k}} = \frac{\overrightarrow{\mathrm{Z}}}{\mathrm{Z}}

Question 6.
Explain multiplication of a vector by a scalar.
Answer:

  1. When a vector \overrightarrow{\mathrm{A}} is multiplied by a scalar ‘s’, it becomes ‘s\overrightarrow{\mathrm{A}}’ whose magnitude is s times the magnitude of \overrightarrow{\mathrm{A}}.
  2. The unit of \overrightarrow{\mathrm{A}} is different from the unit of ‘s \overrightarrow{\mathrm{A}}’.
    For example,
    If \overrightarrow{\mathrm{A}} = 10 newton and s = 5 second, then s\overrightarrow{\mathrm{A}} = 10 newton × 5 second = 50 Ns.

Question 7.
Explain addition of vectors.
Answer:

  1. The addition of two or more vectors of same type gives rise to a single vector such that the effect of this single vector is the same as the net effect of the original vectors.
  2. It is important to note that only the vectors of the same type (physical quantity) can be added.
  3. For example, if two vectors, \overrightarrow{\mathrm{P}} = 3 unit and \overrightarrow{\mathrm{Q}} = 4 unit are acting along the same line, then they can be added as, |\overrightarrow{\mathrm{R}}| = |\overrightarrow{\mathrm{P}}| + |\overrightarrow{\mathrm{Q}}|
    |\overrightarrow{\mathrm{R}}| = 3 + 4 = 7
    Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 4
    [Note: When vectors are not in the same direction, then they can be added using triangle law of vector addition.]

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 8.
State true or false. If false correct the statement and rewrite.
It is possible to add two vectors representing physical quantities having different dimensions.
Answer:
False.
It is not possible to add two vectors representing physical quantities having different dimensions.

Question 9.
Explain subtraction of vectors.
Answer:

  1. When two vectors are anti-parallel (in the opposite direction) to each other, the magnitude
  2. It is important to note that only vectors of the same type (physical quantity) can be subtracted.
  3. For example, if two vectors \overrightarrow{\mathrm{P}} = 3 unit and \overrightarrow{\mathrm{Q}} = 4 unit are acting in opposite direction, they are subtracted as, |\overrightarrow{\mathrm{R}}| = ||\overrightarrow{\mathrm{P}}| – |\overrightarrow{\mathrm{Q}}||
    = |3 – 4| = 1 unit, directed along \overrightarrow{\mathrm{Q}}
    Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 5

Question 10.
How can resultant of two vectors of a type inclined with each other be determined?
Answer:
When two vectors of a type are inclined with each other, their resultant can be determined by using triangle law of vector addition.

Question 11.
What is triangle law of vector addition?
Answer:
Triangle law of vector addition:
If two vectors describing the same physical quantity are represented in magnitude and direction, by the two sides of a triangle taken in order, then their resultant is represented in magnitude and direction by the third side of the triangle drawn in the opposite sense, i.e., from the starting point (tail) of the first vector to the end point (head) of the second vector.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 6
Let \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}} be the two vectors of same type taken in same order as shown in figure.
∴ Resultant vector will be given by third side taken in opposite order, i.e., \overline{\mathrm{OA}} + \overline{\mathrm{AB}} = \overline{\mathrm{OB}}
\overrightarrow{\mathrm{P}} + \overrightarrow{\mathrm{Q}} = \overrightarrow{\mathrm{R}}

Question 12.
Using triangle law of vector addition, explain the process of adding two vectors which are not lying in a straight line.
Answer:
i. Two vectors in magnitude and direction are drawn in a plane as shown in figure (a)
Let these vectors be \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}}
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 7

ii. Join the tail of \overrightarrow{\mathrm{Q}} to head of \overrightarrow{\mathrm{P}} in the given direction. The resultant vector will be the line which is obtained by joining tail of \overrightarrow{\mathrm{P}} to head of \overrightarrow{\mathrm{Q}} as shown in figure (b).
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 8

iii. If \overrightarrow{\mathrm{R}} is the resultant vector of \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}} then using triangle law of vector addition, we have, \overrightarrow{\mathrm{R}} = \overrightarrow{\mathrm{P}} + \overrightarrow{\mathrm{Q}}

Question 13.
Is it possible to add two velocities using triangle law?
Answer:
Yes, it is possible to add two velocities using triangle law.

Question 14.
Explain, how two vectors are subtracted. Find their resultant by using triangle law of vector addition.
Answer:

  1. Let \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}} be the two vectors in a plane as shown in figure (a).
    Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 10
  2. To subtract \overrightarrow{\mathrm{Q}} from \overrightarrow{\mathrm{P}}, vector \overrightarrow{\mathrm{Q}} is reversed so that we get the vector –\overrightarrow{\mathrm{Q}} as shown in figure (b).
  3. The resultant vector is obtained by –\overrightarrow{\mathrm{R}} joining tail of \overrightarrow{\mathrm{P}} to head of – \overrightarrow{\mathrm{Q}} as shown in figure (c).
  4. From triangle law of vector addition, \overrightarrow{\mathrm{R}} = \overrightarrow{\mathrm{P}} + (-\overrightarrow{\mathrm{Q}}) = \overrightarrow{\mathrm{P}}\overrightarrow{\mathrm{Q}}

Question 15.
Prove that: Vector addition is commutative.
Answer:
Commutative property of vector addition:
According to commutative property, for two
vectors \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}}, \overrightarrow{\mathrm{P}} + \overrightarrow{\mathrm{Q}} = \overrightarrow{\mathrm{Q}} + \overrightarrow{\mathrm{p}}

Proof:

i. Let two vectors \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}} be represented in magnitude and direction by two sides \overrightarrow{\mathrm{OA}} and \overrightarrow{\mathrm{AB}} respectively.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 11

ii. Complete a parallelogramOABC such that
\overrightarrow{\mathrm{OA}} = \overrightarrow{\mathrm{CB}} = \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{AB}} = \overrightarrow{\mathrm{OC}} = \overrightarrow{\mathrm{Q}} then join OB.

iii. In △OAB, \overrightarrow{\mathrm{OA}} + \overrightarrow{\mathrm{AB}} = \overrightarrow{\mathrm{OB}}
(By triangle law of vector addition)
\overrightarrow{\mathrm{P}} + \overrightarrow{\mathrm{Q}} = \overrightarrow{\mathrm{R}} … (1)
In △OCB, \overrightarrow{\mathrm{OC}} + \overrightarrow{\mathrm{CB}} = \overrightarrow{\mathrm{OB}}
(By triangle law of vector addition)
\overrightarrow{\mathrm{Q}} + \overrightarrow{\mathrm{P}} = \overrightarrow{\mathrm{R}} … (2)

iv. From equation (1) and (2),
\overrightarrow{\mathrm{P}} + \overrightarrow{\mathrm{Q}} = \overrightarrow{\mathrm{Q}} + \overrightarrow{\mathrm{P}}
Hence, addition of two vectors obeys commutative law.

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 16.
Prove that: Vector addition is associative.
Answer:
Associative property of vector addition:
According to associative property, for three vectors \overrightarrow{\mathrm{P}}, \overrightarrow{\mathrm{Q}} and \overrightarrow{\mathrm{R}},
(\overrightarrow{\mathrm{P}} + \overrightarrow{\mathrm{Q}}) + \overrightarrow{\mathrm{R}} = \overrightarrow{\mathrm{P}} + (\overrightarrow{\mathrm{Q}} + \overrightarrow{\mathrm{R}})
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 12
Proof:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 13
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 14
On comparing, equation (2) and (4), we get,
(\overrightarrow{\mathrm{P}} + \overrightarrow{\mathrm{Q}}) + \overrightarrow{\mathrm{R}} = \overrightarrow{\mathrm{P}} + (\overrightarrow{\mathrm{Q}} + \overrightarrow{\mathrm{R}})
Hence, associative law is proved.

Question 17.
State true or false. If false correct the statement and rewrite.
The subtraction of given vectors is neither commutative nor associative.
Answer:
True.

Question 18.
State and prove parallelogram law of vector addition and determine magnitude and direction of resultant vector.
Answer:

i. Parallelogram law of vector add addition;
If two vectors of same type starting from the same point (tails cit the same point), are represented in magnitude and direction by the two adjacent sides of a parallelogram then, their resultant vector is given in magnitude and direction, by the diagonal of the parallelogram starting from the same point.

ii. Proof:

a. Consider two vectors \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}} of the same type, with their tails at the point O’ and θ’ is the angle between \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}} as shown in the figure below.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 15
b. Join BC and AC to complete the parallelogram OACB, with \overline{\mathrm{OA}} = \overrightarrow{\mathrm{P}} and \overline{\mathrm{AC}} = \overrightarrow{\mathrm{Q}} as the adjacent sides. We have to prove that diagonal \overline{\mathrm{OC}} = \overrightarrow{\mathrm{R}}, the resultant of sum of the two given vectors.

c. By the triangle law of vector addition, we have,
\overrightarrow{\mathrm{OA}} + \overrightarrow{\mathrm{AC}} = \overrightarrow{\mathrm{OC}} … (1)
As \overrightarrow{\mathrm{AC}} is parallel to \overrightarrow{\mathrm{OB}},
\overrightarrow{\mathrm{AC}} = \overrightarrow{\mathrm{OB}} = \overrightarrow{\mathrm{Q}}
Substituting \overrightarrow{\mathrm{OA}} and \overrightarrow{\mathrm{OC}} in equation (1) we have,
\overrightarrow{\mathrm{P}} + \overrightarrow{\mathrm{Q}} = \overrightarrow{\mathrm{R}}
Hence proved.

iii. Magnitude of resultant vector:

a. To find the magnitude of resultant vector \overrightarrow{\mathrm{R}} = \overrightarrow{\mathrm{OC}}, draw a perpendicular from C to meet OA extended at S.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 16

c. Using Pythagoras theorem in right angled triangle, OSC
(OC)2 = (OS)2 + (SC)2
= (OA + AS)2 + (SC)2
∴ (OC)2 = (OA)2 + 2(OA).(AS) + (AS2) + (SC)2 . . . .(4)

d. From right angle trianle ASC,
(AS)2 + (SC)2 = (AC)2 …. (5)

e. From equation (4) and (5), we get
(OC)2 = (OA)2 + 2(OA) (AS) + (AC)2
… .(6)

f. Using (2) and (6), we get
(OC)2 = (OA)2 + (AC)2 + 2(OA)(AC) cos θ
∴ R2 = P2 + Q2 + 2 PQ cos θ
∴ R = \sqrt{\mathrm{P}^{2}+\mathrm{Q}^{2}+2 \mathrm{PQ} \cos \theta} ….(7)
Equation (7) gives the magnitude of resultant vector \overrightarrow{\mathrm{R}}.

iv. Direction of resultant vector:
To find the direction of resultant vector \overrightarrow{\mathrm{R}}, let \overrightarrow{\mathrm{R}} make an angle α with \overrightarrow{\mathrm{P}}.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 17
Equation (9) represents direction of resultant vector.
[Note: If β is the angle between \overrightarrow{\mathrm{R}} and \overrightarrow{\mathrm{Q}}, it can be similarly derived that
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 18

Question 19.
Complete the table for two vectors \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}} inclined at angle θ.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 19
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 20

Question 20.
The diagonal of the parallelogram made by two vectors as adjacent sides is not passing through common point of two vectors. What does it represent?
Answer:
The diagonal of the parallelogram made by two vectors as adjacent sides not passing through common point of two vectors represents triangle law of vector addition.

Question 21.
If | \overrightarrow{\mathbf{A}} + \overrightarrow{\mathbf{B}} | = | \overrightarrow{\mathbf{A}}\overrightarrow{\mathbf{B}} | then what can be the
angle between \overrightarrow{\mathbf{A}} and \overrightarrow{\mathbf{B}} ?
Answer:
Let θ be the angle between \overrightarrow{\mathbf{A}} and \overrightarrow{\mathbf{B}}, then
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 21

Thus, if |\overrightarrow{\mathrm{A}} + \overrightarrow{\mathrm{B}}| = |\overrightarrow{\mathrm{A}}\overrightarrow{\mathrm{B}} |, then vectors \overrightarrow{\mathrm{A}} and \overrightarrow{\mathrm{B}} must be at right angles to each other.

Question 22.
Express vector \overrightarrow{\mathbf{A C}} in terms of vectors \overrightarrow{\mathbf{A B}} and \overrightarrow{\mathbf{C B}} shown in the following figure.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 22
Solution:
Using the triangle law of addition of vectors,
\overrightarrow{\mathbf{A C}} + \overrightarrow{\mathbf{C B}} = \overrightarrow{\mathbf{A B}}
\overrightarrow{\mathbf{A C}} = \overrightarrow{\mathbf{A B}}\overrightarrow{\mathbf{C B}}

Question 23.
From the following figure, determine the resultant of four forces \overrightarrow{\mathbf{A}}_{1}, \overrightarrow{\mathbf{A}}_{2}, \overrightarrow{\mathbf{A}}_{3}, \overrightarrow{\mathbf{A}}_{4}.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 23
Solution:
Join \overrightarrow{\mathrm{OB}} to complete ∆OAB as shown in figure below
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 24
Now, using triangle law of vector addition,
\overrightarrow{\mathrm{OB}} = \overrightarrow{\mathrm{OA}} + \overrightarrow{\mathrm{AB}} = \overrightarrow{\mathrm{A}}_{1} + \overrightarrow{\mathrm{A}}_{2}
Join \overrightarrow{\mathrm{OC}} to complete triangle OBC as shown figure below
Similarly, \overrightarrow{\mathrm{OC}} = \overrightarrow{\mathrm{OB}} + \overrightarrow{\mathrm{BC}} = \overrightarrow{\mathrm{A}}_{1} + \overrightarrow{\mathrm{A}}_{2} + \overrightarrow{\mathrm{A}}_{3}
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 25
Answer:
\overrightarrow{O D} is the resultant of the four vectors.

Question 24.
Find the vector that should be added to the sum of (2\hat{\mathbf{i}} – 5\hat{\mathbf{j}} + 3\hat{\mathbf{k}}) and (4\hat{\mathbf{i}} + 7\hat{\mathbf{j}} – 4\hat{\mathbf{k}}) to give a unit vector along the X-axis.
Solution:
Let vector \overrightarrow{\mathrm{p}} be added to get unit vector (\hat{\mathbf{i}}) along X-axis.
Sum of given vectors is given as,
(2\hat{\mathbf{i}} – 5\hat{\mathbf{j}} + 3\hat{\mathbf{k}} ) + (4\hat{\mathbf{i}} + 7\hat{\mathbf{j}} – 4\hat{\mathbf{k}}) = 6\hat{\mathbf{i}} + 2\hat{\mathbf{j}}\hat{\mathbf{k}}
According to given condition, (6\hat{\mathbf{i}} + 2\hat{\mathbf{j}}\hat{\mathbf{k}}) + \hat{\mathbf{P}} = \hat{\mathbf{i}}
\overrightarrow{\mathrm{P}} = \hat{\mathbf{i}} – (6\hat{\mathbf{i}} + 2\hat{\mathbf{j}}\hat{\mathbf{k}}) = \hat{\mathbf{i}} – 6\hat{\mathbf{i}} – 2\hat{\mathbf{j}} + \hat{\mathbf{k}} = -5\hat{\mathbf{i}} – 2\hat{\mathbf{j}} + \hat{\mathbf{k}}
Answer:
The required vector is -5\hat{\mathbf{i}} – 2\hat{\mathbf{j}} + \hat{\mathbf{k}}.

Question 25.
If \overrightarrow{\mathbf{P}} = 2\hat{\mathbf{i}} + 3\hat{\mathbf{j}}\hat{\mathbf{k}} and \overrightarrow{\mathbf{Q}} = 2\hat{\mathbf{i}} – 5\hat{\mathbf{j}} + 2\hat{\mathbf{k}}.Find
i. \overrightarrow{\mathbf{P}} + \overrightarrow{\mathbf{Q}}
ii. 3\overrightarrow{\mathbf{P}} – 2\overrightarrow{\mathbf{Q}}
Solution:
Given \overrightarrow{\mathbf{P}} = 2\hat{\mathbf{i}} + 3\hat{\mathbf{j}}\hat{\mathbf{k}}, \overrightarrow{\mathbf{Q}} = 2\hat{\mathbf{i}} – 5\hat{\mathbf{j}} + 2\hat{\mathbf{k}}
To find:

i. \overrightarrow{\mathbf{P}} + \overrightarrow{\mathbf{Q}}
ii. 3\overrightarrow{\mathbf{P}} – 2\overrightarrow{\mathbf{Q}}

Calculation:

i. \overrightarrow{\mathbf{P}} + \overrightarrow{\mathbf{Q}} = (2\hat{\mathbf{i}} + 3\hat{\mathbf{j}} – k) + (2\hat{\mathbf{i}} – 5\hat{\mathbf{j}} + 2k)
= (2 + 2)\hat{\mathbf{i}} + (3 – 5)\hat{\mathbf{j}} + (-1 + 2)\hat{\mathbf{k}}
= 4\hat{\mathbf{i}} – 2\hat{\mathbf{j}} + \hat{\mathbf{k}}

ii. 3\overrightarrow{\mathbf{P}} = 3(2\hat{\mathbf{i}} + 3\hat{\mathbf{j}}\hat{\mathbf{k}}) = 6\hat{\mathbf{i}} + 9\hat{\mathbf{j}} – 3\hat{\mathbf{k}}
2\overrightarrow{\mathbf{Q}} = 2(2\hat{\mathbf{i}} – 5\hat{\mathbf{j}} + 2\hat{\mathbf{k}}) = 4\hat{\mathbf{i}} – 10\hat{\mathbf{j}} + 4\hat{\mathbf{k}}
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 26

Question 26.
Find unit vector parallel to the resultant of the vectors \overrightarrow{\mathbf{A}} = \hat{\mathbf{i}} + 4\hat{\mathbf{j}} – 2\hat{\mathbf{k}} and \overrightarrow{\mathbf{B}} = 3\hat{\mathbf{i}} – 5\hat{\mathbf{j}} + \hat{\mathbf{k}}.
Solution:
The resultant of \overrightarrow{\mathrm{A}} and \overrightarrow{\mathrm{B}} is,
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 27
Answer:
The required unit vector is \frac{1}{3 \sqrt{2}}(4\hat{\mathbf{i}}\hat{\mathbf{j}}\hat{\mathbf{k}})

Question 27.
Two forces, F1 and F2, each of magnitude 5 N are inclined to each other at 60°. Find the magnitude and direction of their resultant force.
Solution:
Given: F1 = 5 N, F2 = 5 N, θ = 60°
To find: Magnitude of resultant force (R),
Direction of resultant force (α)
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 28
Answer:
i. The magnitude of resultant force is 8.662 N.

ii. The direction of resultant force is 30° w.r.t. \overrightarrow{\mathrm{F}_{1}}.

Question 28.
Water is flowing in a stream with velocity 5 km/hr in an easterly direction relative to the shore. Speed of a boat relative to still water is 20 km/hr. If the boat enters the stream heading north, with what velocity will the boat actually travel?
Answer:
The resultant velocity \overrightarrow{\mathrm{R}} of the boat can be obtained by adding the two velocities using ∆ OAB shown in the figure.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 29
The direction ot the resultant velocity is
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 30
Answer: The velocity of the boat is 20.616 km/hr in a direction 14.04° east of north. .
[Note: tan-1 (0.25) ≈ 14.04° which equals 14°2]

Question 29.
Rain is falling vertically with a speed of 35 m/s. Wind starts blowing at a speed of 12 m/s in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella? (NCERT)
Solution:
Let the velocity of rain and wind be \overrightarrow{\mathbf{V}_{\mathrm{R}}} and \overrightarrow{\mathbf{V}_{\mathrm{W}}}, then resultant velocity \overrightarrow{\mathrm{v}} has magnitude of
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 31
If \overrightarrow{\mathrm{v}} makes an angle θ with vertical then, from the figure
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 32
Answer: The boy should hold his umbrella in vertical plane at an angle of about 19° with vertical towards the east.

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 30.
What are components of a vector?
Answer:

  1. The given vector can be written as sum of two or more vectors along certain fixed directions. The vectors into which the given single vector is splitted are called components of the vector.
  2. Let \overrightarrow{\mathrm{A}} = \mathrm{A}_{1} \hat{\alpha} + \mathrm{A}_{2} \hat{\beta} + \mathrm{A}_{3} \hat{\gamma} where, \hat{\alpha}, \hat{\beta} and \hat{\gamma} are unit vectors along chosen directions. Then, A1, A2 and A3 are known as components of \overrightarrow{\mathrm{A}} along three directions \hat{\alpha}, \hat{\beta} and \hat{\gamma}.
  3. It two vectors are equal then, their corresponding components are also equal and vice-versa.
    Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 33

[Note: The magnitude of a vector is a scalar while each component of a vector is always a vector.]

Question 31.
What is meant by resolution of vector?
Answer:

  1. The process of splitting a given vector into its components is called resolution of the vector.
  2. Resolution of vector is equal to replacing the original vector with the sum of the component vectors.

Question 32.
That are rectangular components of vectors? Explain their uses.
Answer:
i. Rectangular components of a vector:
If components of a given vector are mutually perpendicular to each other then they are called rectangular components of that vector.

ii. Consider a vector \overrightarrow{\mathrm{R}} = \overrightarrow{\mathrm{OC}} originating from the origin O’ of a rectangular co-ordinate system as shown in figure.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 34

iii. Draw CA ⊥ OX and CB ⊥ OY.
Let component of \overrightarrow{\mathrm{R}} along X-axis \overrightarrow{\mathrm{R}}_{\mathrm{x}} and component of \overrightarrow{\mathrm{R}} along Y-axis = \overrightarrow{\mathrm{R}}_{\mathrm{y}}
By parallelogram law of vectors,
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 35
where, \hat{i} and \hat{j} are unit vectors along positive direction of X and Y axes respectively.

iv. If θ is angle made by \overrightarrow{\mathrm{R}} with X-axis, then
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 36

v. Squaring and adding equation (1) and (2) we get,
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 37
Equation (3) gives the magnitude of \overrightarrow{\mathrm{R}} .

vi. Direction of \overrightarrow{\mathrm{R}} can be found out by dividing equation (2) by (1),
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 38
Equation (4) gives direction of \overrightarrow{\mathrm{R}}

vii. When vectors are noncoplanar, it becomes necessary to use the third dimension. If \overrightarrow{\mathrm{R}}_{\mathrm{x}} , \overrightarrow{\mathrm{R}}_{\mathrm{y}} and \overrightarrow{\mathrm{R}}_{\mathrm{z}} are three rectangular components of \overrightarrow{\mathrm{R}} along X, Y and Z axes of a three dimensional rectangular cartesian co-ordinate system then.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 39
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 40

Question 33.
Find a unit vector in the direction of the vector 3 \hat{i} + 4 \hat{j} .
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 41

Question 34.
Given \overrightarrow{\mathbf{a}} = \hat{\mathbf{i}} + 2 \hat{\mathbf{j}} and \overrightarrow{\mathbf{b}} = 2 \hat{\mathbf{i}} + \hat{\mathbf{j}} , what are the magnitudes of the two vectors? Are these two vectors equal?
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 42
The magnitudes of \vec{a} and \vec{b} are equal. However, their corresponding components are not equal, i.e., ax ≠ bx and ay ≠ by. Hence, the two vectors are not equal.
Answer:
Magnitudes of two vectors are equal, but vectors are unequal.

Question 35.
Find the vector drawn from the point (-4, 10, 7) to the point (3, -2, 1). Also find its magnitude.
Solution:
If \overrightarrow{\mathrm{A}} is a vector drawn from the point (x1, y1, z1) to the point (x2, y2, z2), then
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 43

Question 36.
In a cartesian co-ordinate system, the co-ordinates of two points P and Q are (2, 4, 4) and (-2, -3, 7) respectively, find \overrightarrow{\mathbf{P Q}} and its magnitude.
Solution:
Given: Position vector of P = (2,4,4)
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 44
∴ | \overrightarrow{\mathrm{PQ}} | = 8.6 units
Answer: Vector \overrightarrow{\mathrm{PQ}} is -4 \hat{\mathbf{i}} – 7 \hat{\mathbf{j}} + 3 \hat{\mathbf{k}} and its magnitude is 8.6 units.

Question 37.
If \overrightarrow{\mathbf{A}} = 3 \hat{i} + 4[/latex] = 3 \hat{j} and \overrightarrow{\mathbf{B}} = 7 \hat{i} + 24 \hat{j} , find a vector having the same magnitude as \overrightarrow{\mathbf{B}} and parallel to \overrightarrow{\mathbf{A}} .
Solution:
The magnitude of vector \overrightarrow{\mathrm{A}} is | \overrightarrow{\mathrm{A}} |
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 45
Answer: The required vector is 15 \hat{\mathbf{i}} + 20 \hat{\mathbf{j}} .

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 38.
Complete the table.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 46
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 47

Question 39.
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful.
i. Adding any two scalars,
ii. Adding a scalar to a vector of the same dimensions,
iii. Multiplying any vector by any scalar,
iv. Multiplying any two scalars,
v. Adding any two vectors. (NCERT)
Answer:

  1. Not any two scalars can be added. To add two scalars it is essential that they represent same physical quantity.
  2. This operation is meaningless. Only a vector can be added to another vector.
  3. This operation is possible. When a vector is multiplied with a dimensional scalar, the resultant vector will have different dimensions.
    eg.: acceleration vector is multiplied with mass (a dimensional scalar), the resultant vector has the dimensions of force.
    When a vector is multiplied with non – dimensional scalar, it will be a vector having dimensions as that of the given vector.
    eg.: \overrightarrow{\mathrm{A}} × 3 = 3 \overrightarrow{\mathrm{A}}
  4. This operation is possible. Multiplication of non-dimensional scalars is simply algebraic multiplication. Multiplication of non dimensional scalars will result into scalar with different dimensions.
    eg.: Volume × density = mass.
  5. Not any two vectors can be added. To add two vectors it is essential that they represent same physical quantity.

Question 40.
Explain scalar product of two vectors with the help of suitable examples.
Answer:
Scalar product of two vectors:

  1. The scalar product of two non-zero vectors is defined as the product of the magnitude of the two vectors and cosine of the angle θ between the two vectors.
  2. The dot sign is used between the two vectors to be multiplied therefore scalar product is also called dot product.
  3. The scalar product of two vectors \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}} is given by, \overrightarrow{\mathrm{P}} . \overrightarrow{\mathrm{Q}} = PQ cos θ
    where, p = magnitude of \overrightarrow{\mathrm{P}} , Q = magnitude of \overrightarrow{\mathrm{Q}}
    θ = angle between \overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{Q}}
  4. Examples of scalar product:
    1. Power (P) is a scalar product of force ( \overrightarrow{\mathrm{F}} ) and velocity ( \overrightarrow{\mathrm{v}} )
      ∴ P = \overrightarrow{\mathrm{F}} . \overrightarrow{\mathrm{v}}
    2. Work is a scalar product of force ( \overrightarrow{\mathrm{F}} ) and displacement ( \overrightarrow{\mathrm{s}} ).
      ∴ W = \overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{s}}

Question 41.
Discuss characteristics of scalar product of two vectors.
Answer:
Characteristics of the scalar product of two vectors:
i. The scalar product of two vectors is equivalent to the product of magnitude of one vector with component of the other in the direction of the first.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 48
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 49
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 50
vi. Scalar product of two vectors is expressed in terms of rectangular components as
\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}} = Ax + Bx + AyBy + AzBz

vii. For \vec{a} \neq 0, \vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c} does not necessarily mean \vec{b} = \vec{c}

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 42.
Complete the table vector given below:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 51
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 52

Question 43.
Define and explain vector product of two vectors with suitable examples.
Answer:
i. The vector product of two vectors is a third vector whose magnitude is equal to the product of magnitude of the two vectors and sine of the smaller angle θ between the two vectors.

ii. Vector product is also called cross product of vectors because cross sign is used to represent vector product.

iii. Explanation:

a. The vector product of two vectors \overrightarrow{\mathrm{A}} and \overrightarrow{\mathrm{B}} , is a third vector \overrightarrow{\mathrm{R}} and is written as, \overrightarrow{\mathrm{R}} = \overrightarrow{\mathrm{A}} × \overrightarrow{\mathrm{B}} = AB sin θ \hat{\mathrm{u}}_{\mathrm{r}} where, \hat{\mathrm{u}}_{\mathrm{r}} is unit vector in direction of \overrightarrow{\mathrm{R}} , i.e., perpendicular to plane containing two vectors. It is given by right handed screw rule.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 53
c. Examples of vector product:

1. Force experienced by a charge q moving with velocity \overrightarrow{\mathrm{V}} in uniform magnetic field of induction (strength) \overrightarrow{\mathrm{B}} is given as \overrightarrow{\mathrm{F}} = q\overrightarrow{\mathrm{V}} × \overrightarrow{\mathrm{B}}

2. Moment of a force or torque (\begin{aligned} &\rightarrow\\ &\tau \end{aligned}) is the vector product of the position vector (\vec{r}) and the force (\overrightarrow{\mathrm{F}}).
i.e., \begin{aligned} &\rightarrow\\ &\tau \end{aligned} = \overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}

3. The instantaneous velocity (\overrightarrow{\mathrm{v}}) of a rotating particle is equal to the cross product of its angular velocity (\vec{\omega}) and its position (\overrightarrow{\mathrm{r}}) from axis of rotation.
\overrightarrow{\mathrm{v}} = \overrightarrow{\mathrm{r}} × \vec{\omega}

Question 44.
State right handed screw rule.
Answer:
Statement of Right handed screw rule: Hold a right handed screw with its axis perpendicular to the plane containing vectors and the screw rotated from first vector to second vector through a small angle, the direction in which the screw tip would advance is the direction of the vector product of two vectors.

Question 45.
State the characteristics of the vector product (cross product) of two vectors.
Answer:
Characteristics of the vector product (cross product):
i. The vector product of two vectors does not obey the commutative law of multiplication.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 54
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 55
vi. The magnitude of cross product of two vectors is numerically equal to the area of a parallelogram whose adjacent sides represent the two vectors.

Question 46.
Derive an expression for cross product of two vectors and express it in determinant form.
Answer:
Expression for cross product of two vectors:
i. Let two vectors \overrightarrow{\mathrm{R}} and \overrightarrow{\mathrm{Q}} be represented in magnitude and direction by,
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 56
ii.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 57
iii. Determinant form of cross product of two vectors \overrightarrow{\mathrm{R}} and \overrightarrow{\mathrm{Q}} is given by,
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 58

Question 47.
Show that magnitude of vector product of two vectors is numerically equal to the area of a parallelogram formed by the two
vectors.
Answer:
Suppose OACB is a parallelogram of adjacent sides, \overrightarrow{\mathrm{OA}}=\overrightarrow{\mathrm{P}} and \overrightarrow{\mathrm{OB}}=\overrightarrow{\mathrm{Q}}.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 59
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 60

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 48.
Distinguish between scalar product (dot product) and vector product (cross product).
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 61

Question 49.
Given \overrightarrow{\mathbf{P}} = 4\hat{\mathbf{i}}\hat{\mathbf{j}} + 8\hat{\mathbf{k}} and \overrightarrow{\mathbf{Q}} = 2\hat{\mathbf{i}} – m\hat{\mathbf{j}} + 4\hat{\mathbf{k}} find m if \overrightarrow{\mathbf{P}} and \overrightarrow{\mathbf{Q}} have the same direction. Solution:
Since \overrightarrow{\mathbf{P}} and \overrightarrow{\mathbf{Q}} have the same direction, their corresponding components must be in the same proportion, i.e.,
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 62

Question 50.
Find the scalar product of the two vectors \overrightarrow{\mathbf{v}}_{1} = \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}} and \overrightarrow{\mathbf{v}}_{2} = 3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-\mathbf{5} \hat{\mathbf{k}}
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 63
Answer: Scalar product of two given vectors is – 4.

Question 51.
A force \overrightarrow{\mathbf{F}} = 4 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}+3 \hat{\mathbf{k}} acting on a particle produces a displacement of \overrightarrow{\mathbf{S}} = \overrightarrow{\mathrm{s}}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\mathbf{5} \hat{\mathbf{k}} where F is expressed in newton and s in metre. Find the work done by the force.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 64
Answer: The work done by the force is 41 J.

Question 52.
Find ‘a’ if \overrightarrow{\mathbf{A}} = 3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} and \overrightarrow{\mathbf{B}} = \mathbf{a} \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}} are perpendicular to one another.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 65

Question 53.
If \overrightarrow{\mathbf{A}} = 5 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} and \overrightarrow{\mathbf{B}} = 2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}} determine the angle between and . Solution:
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 66

Question 54.
Find the angle between the vectors
\overrightarrow{\mathbf{A}} = \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}} and \overrightarrow{\mathbf{B}} = -\hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{2} \hat{\mathbf{k}}.
Solution:
Let angle between the vectors be θ
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 67
Answer: The angle between the vectors is 60°.

Question 55.
If \overrightarrow{\mathbf{A}} = 2 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+3 \hat{\mathbf{k}} and \vec{B} = 3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\mathbf{5} \hat{\mathbf{k}}, find the component of \overrightarrow{\mathbf{A}} along \overrightarrow{\mathbf{B}}.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 68

Question 56.
\hat{\mathbf{i}} and \hat{\mathbf{j}} are unit vectors along X-axis and Y-axis respectively. What is the magnitude and direction of the vector \hat{\mathbf{i}}+\hat{\mathbf{j}} and \hat{\mathbf{i}}-\hat{\mathbf{j}}? What are the components of a vector
\overrightarrow{\mathbf{A}}=2 \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}} along the directions of (\hat{\mathbf{i}}+\hat{\mathbf{j}}) and (\hat{\mathbf{i}}-\hat{\mathbf{j}})? (NCERT)
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 69
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 70

Question 57.
The angular momentum \overrightarrow{\mathrm{L}}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}}, where \overrightarrow{\mathbf{r}} is a position vector and \overrightarrow{\mathrm{p}} is linear momentum of a body.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 71
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 72

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 58.
If \overrightarrow{\mathbf{A}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}} and \overrightarrow{\mathbf{B}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}} are two vectors, find |\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}|
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 73

Question 59.
Find unit vectors perpendicular to the plane of the vectors, \overrightarrow{\mathbf{A}} = and
\overrightarrow{\mathbf{B}} = 2 \hat{\mathbf{i}}-\hat{\mathbf{k}}
Solution:
Let required unit vector be \hat{\mathrm{u}}.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 74
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 75

Question 60.
\overrightarrow{\mathbf{P}} = \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{k}} and \overrightarrow{\mathbf{Q}} = 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}} are two vectors, find the unit vector parallel to \overrightarrow{\mathbf{P}} \times \overrightarrow{\mathbf{Q}}. Also find the vector perpendicular to P and Q of magnitude 6 units.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 76

Question 61.
Find the area of a triangle formed by \overrightarrow{\mathbf{A}} = \hat{3} \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+2 \hat{\mathbf{k}} and \overrightarrow{\mathbf{B}} = \hat{\mathbf{i}}+\hat{\mathbf{j}}-\boldsymbol{2} \hat{\mathbf{k}} as adjacent sides measure in metre. Solution:
Given: Two adjacent sides of triangle,
\overrightarrow{\mathrm{A}} = 3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overrightarrow{\mathrm{B}} = \hat{i}+\hat{j}-2 \hat{k}
To find: Area of triangle
Formula: Area of triangle =
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 77
Answer:
Area of the triangle is 6.1 m2.

Question 62.
Find the derivatives of the functions,
i. f(x) = x8
ii. f(x) = x3 + sin x
Solution:
i. Using \frac{\mathrm{dx}^{\mathrm{n}}}{\mathrm{dx}} = nxn-1,
\frac{d\left(x^{8}\right)}{d x} = 8x7

ii.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 78

Question 63.
Find derivatives of e2x – tan x
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 79

Question 64.
Find the derivatives of the functions.
f(x) = x3 sin x
Solution:
Using,
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 80

Question 65.
Find derivatives of \frac{d}{d x}(x \times \ln x)
Solution:
Using,
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 81

Question 66.
Evaluate the following integrals.

i. \int x^{8} d x
Solution:
Using formula \int x^{n} d x = \frac{x^{n+1}}{n+1},
\int x^{8} d x = \frac{x^{9}}{9}

ii. \int_{2}^{5} x^{2} d x
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 82

iii) \int(x+\sin x) d x
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 83

iv) \int\left(\frac{10}{x}+e^{x}\right) d x
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 84

v) \int_{1}^{4}\left(x^{3}-x\right) d x
Answer:
Using,
f1(x) – f2(x) = \int f_{1}(x)-\int f_{2}(x)
Here,
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 85

Question 67.
A man applies a force of 10 N on a garbage crate. If another man applies a force of 8 N on the same crate at an angle of 60° with respect to previous, then what will be the resultant force and direction of the crate, if crate is stationary.
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 86
Answer:
A resultant force of 15.62 N is applied on a crate at an angle of 26.56°.

Question 68.
A lady dropped her wallet in the parking lot of a super market. A boy picked the wallet up and ran towards the lady. He set off at 60° to the verge, heading towards the lady with a speed of 10 m s-1, as shown in the diagram.
Find the component of velocity of boy directly across the parking strip.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 87
Answer:
The angle between velocity vector and the direction of path is 60°.
∴ Component of velocity across the parking strip
= v × cos 60°
= 10-1 × cos 60°
= 5 m s-1

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 69.
On an open ground, a biker follows a track that turns to his left by an angle of 60° after every 600 m. Starting from a given turn, specify the displacement of the biker at the third and sixth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
Answer:
The path followed by the biker will be a closed hexagonal path. Suppose the motorist starts his journey from the point O.
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 88
= 1200 m
= 1.2 km
∴ Total path length = |\overrightarrow{\mathrm{OA}}|+|\overrightarrow{\mathrm{AB}}|+|\overrightarrow{\mathrm{BC}}|
= 600 + 600 + 600
= 1800 m
= 1.8 km
The ratio of the magnitude of displacement to the total path-length = \frac{1.2}{1.8} = \frac{2}{3} = 0.67

ii. The motorist will take the sixth turn at O.
Displacement is zero.
path-length is = 3600 m or 3.6 km.
Ration of magnitude of displacement and path-length is zero.

Question 70.
What is the resultant of vectors shown in the figure below?
Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods 89
Answer:
If number of vectors are represented by the various sides of a closed polygon taken in one order then, their resultant is always zero.

Question 71.
If \overrightarrow{\mathbf{P}} is moving away from a point and \overrightarrow{\mathbf{Q}} is moving towards a point then, can their resultant be found using parallelogram law of vector addition?
Answer:
No. Resultant cannot be found by parallelogram law of vector addition because to apply law of parallelogram of vectors the two vectors and should either act towards a point or away from a point.

Question 72.
Which of the throwing is a vector?
(A) speed
(B) displacement
(C) mass
(D) time
Answer:
(B) displacement

Question 73.
The equation \vec{a}+\vec{a}=\vec{a} is
(A) meaningless
(B) always truc
(C) may he possible for limited values of a’
(D) true only when \overrightarrow{\mathrm{a}}=0
Answer:
(D) true only when \overrightarrow{\mathrm{a}}=0

Question 74.
The minimum number of numerically equal vectors whose vector sum can be zero is
(A) 4
(B) 3
(C) 2
(D) 1
Answer:
(C) 2

Question 75.
If \vec{A}+\vec{B}=\vec{A}-\vec{B} then vector \overrightarrow{\mathrm{B}} must be
(A) zero vector
(B) unit vector
(C) Non zero vector
(D) equal to \overrightarrow{\mathrm{A}}
Answer:
(A) zero vector

Question 76.
If \hat{\mathrm{n}} is the unit vector in the direction of \overrightarrow{\mathrm{A}}, then,
(A) \hat{n}=\frac{\vec{A}}{|\vec{A}|}
(B) \hat{\mathrm{n}}=\overrightarrow{\mathrm{A}}|\overrightarrow{\mathrm{A}}|
(C) \hat{\mathrm{n}}=\frac{|\overrightarrow{\mathrm{A}}|}{\overrightarrow{\mathrm{A}}}
(D) \hat{\mathrm{n}}=\hat{\mathrm{n}} \times \overrightarrow{\mathrm{A}}
Answer:
(A) \hat{n}=\frac{\vec{A}}{|\vec{A}|}

Question 77.
Two quantities of 5 and 12 unit when added gives a quantity 13 unit. This quantity is
(A) time
(B) mass
(C) linear momentum
(D) speed
Answer:
(C) linear momentum

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 78.
A force of 60 N acting perpendicular to a force of 80 N, magnitude of resultant force is
(A) 20N
(B) 70N
(C) 100 N
(D) 140 N
Answer:
(C) 100 N

Question 79.
A river is flowing at the rate of 6 km h-1. A man swims across it with a velocity of 9 km h-1. The resultant velocity of the man will be
(A) \sqrt{15} \mathrm{~km} \mathrm{~h}^{-1}
(B) \sqrt{45} \mathrm{~km} \mathrm{~h}^{-1}
(C) \sqrt{117} \mathrm{~km} \mathrm{~h}^{-1}
(D) \sqrt{225} \mathrm{~km} \mathrm{~h}^{-1}
Answer:
(C) \sqrt{117} \mathrm{~km} \mathrm{~h}^{-1}

Question 80.
If \overrightarrow{\mathrm{A}}=\overrightarrow{\mathrm{B}}+\overrightarrow{\mathrm{C}} and magnitudes of \overrightarrow{\mathrm{A}}, \overrightarrow{\mathrm{B}} and \overrightarrow{\mathrm{C}} are 5, 4 and 3 unit respectively, then angle between \overrightarrow{\mathrm{A}} and \overrightarrow{\mathrm{B}} is
(A) sin-1 (3/4)
(B) cos-1 (4/5)
(C) tan-1 (5/3)
(D) cos-1 (3/5)
Answer:
(B) cos-1 (4/5)

Question 81.
If \vec{A}=\hat{i}+2 \hat{j}+3 \hat{k} and \overrightarrow{\mathrm{B}}=3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}, then the area of parallelogram formed from these vectors as the adjacent sides will be
(A) 2\sqrt{3} square units
(B) 4\sqrt{3} square units
(C) 6\sqrt{3} square units
(D) 8\sqrt{3} square units
Answer:
(D) 8\sqrt{3} square units

Question 82.
A person moves from a point S and walks along the path which is a square of each side 50 m. He runs east, south, then west and finally north. Then the total displacement covered is
(A) 200m
(B) 100 m
(C) 50\sqrt{2} m
(D) zero
Answer:
(D) zero

Question 83.
The maximum value of magnitude of (\vec{A}-\vec{B}) is
(A) A – B
(B) A
(C) A + B
(D) \sqrt{\left(A^{2}+B^{2}\right)}
Answer:
(C) A + B

Question 84.
The magnitude of the X and Y components of \overrightarrow{\mathrm{A}} are 7 and 6. Also the magnitudes of the X and Y components of \vec{A}+\vec{B} are 11 and 9 respectively. What is the magnitude of
(A) 5
(B) 6
(C) 8
(D)
Answer:
(A) 5

Question 85.
What is the maximum n Limber of components into which a force can be resolved?
(A) Two
(B) Three
(C) Four
(D) Any number
Answer:
(D) Any number

Question 86.
The resultant of two vectors of magnitude |\overrightarrow{\mathrm{P}}| is also |\overrightarrow{\mathrm{P}}|. They act at an angle
(A) 60°
(B) 90°
(C) 120°
(D) 180°
Answer:
(C) 120°

Question 87.
The vectors \overrightarrow{\mathrm{A}} and \overrightarrow{\mathrm{B}} are such that \overrightarrow{\mathrm{A}} + \overrightarrow{\mathrm{B}} = \overrightarrow{\mathrm{C}} and A2 + B2 = C2. Angle θ between positive directions of \overrightarrow{\mathrm{A}} and \overrightarrow{\mathrm{B}} is
(A) \frac{\pi}{2}
(B) 0
(C) π
(D) \frac{2 \pi}{3}
Answer:
(A) \frac{\pi}{2}

Maharashtra Board Class 11 Physics Important Questions Chapter 2 Mathematical Methods

Question 88.
The expression \frac{1}{\sqrt{2}}(\hat{\mathrm{i}}+\hat{\mathrm{j}}) is a
(A) unit vector
(B) null vector
(C) vector of magnitude \sqrt{2}
(D) scalar
Answer:
(A) unit vector

Question 89.
What is the angle between \hat{i}+\hat{j}+\hat{k} and \hat{\mathrm{i}}?
(A) 0°
(B) \frac{\pi}{6}
(C) \frac{\pi}{3}
(D) None of the above
Answer:
(D) None of the above

Question 90.
(\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}) is a unit vector along X-axis. If \overrightarrow{\mathrm{P}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}} then \overrightarrow{\mathrm{Q}} is
(A) \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}
(B) \hat{\mathrm{j}}-\hat{\mathrm{k}}
(C) \hat{i}+\hat{j}+\hat{k}
(D) \hat{\mathrm{j}}+\hat{\mathrm{k}}
Answer:
(B) \hat{\mathrm{j}}-\hat{\mathrm{k}}

Question 91.
The magnitude of scalar product of the vectors \overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+5 \hat{\mathrm{k}} and \overrightarrow{\mathrm{B}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}} is
(A) 20
(B) 22
(C) 26
(D) 29
Answer:
(C) 26

Question 92.
Three vectors \overrightarrow{\mathrm{A}}, \overrightarrow{\mathrm{B}} and \overrightarrow{\mathrm{C}} satisfy the relation \overrightarrow{\mathrm{A}} . \overrightarrow{\mathrm{B}} = 0 and \overrightarrow{\mathrm{A}}. \overrightarrow{\mathrm{C}} = 0, then \overrightarrow{\mathrm{A}} is parallel to
(A) \overrightarrow{\mathrm{B}}
(B) \overrightarrow{\mathrm{C}}
(C) \overrightarrow{\mathrm{B}} × \overrightarrow{\mathrm{C}}
(D) \overrightarrow{\mathrm{A}} . \overrightarrow{\mathrm{C}}
Answer:
(C) \overrightarrow{\mathrm{B}} × \overrightarrow{\mathrm{C}}

Question 93.
What vector must be added to the sum of two vectors 2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}} and 3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}} so that the resultant is a unit vector along Z axis?
(A) 5 \hat{\hat{i}}+\hat{\mathrm{k}}
(B) -5 \hat{i}+3 \hat{j}
(C) 3 \hat{j}+5 \hat{k}
(D) -3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}
Answer:
(B) -5 \hat{i}+3 \hat{j}

Question 94.
\overrightarrow{\mathrm{A}}=5 \overrightarrow{\mathrm{i}}-2 \overrightarrow{\mathrm{j}}+3 \overrightarrow{\mathrm{k}} and \overrightarrow{\mathrm{B}}=2 \overrightarrow{\mathrm{i}}+\overrightarrow{\mathrm{j}}+2 \overrightarrow{\mathrm{k}}, then component of \overrightarrow{\mathrm{B}} along \overrightarrow{\mathrm{A}} is
(A) \frac{\sqrt{28}}{38}
(B) \frac{28}{\sqrt{38}}
(C) \frac{\sqrt{28}}{48}
(D) \frac{14}{\sqrt{38}}
Answer:
(D) \frac{14}{\sqrt{38}}

Question 95.
Choose the WRONG statement
(A) The division of vector by scalar is valid.
(B) The multiplication of vector by scalar is valid.
(C) The multiplication of vector by another vector is valid by using vector algebra.
(D) The division of a vector by another vector is valid by using vector algebra.
Answer:
(D) The division of a vector by another vector is valid by using vector algebra.

Question 96.
The resultant of two forces of 3 N and 4 N is 5 N, the angle between the forces is
(A) 30°
(B) 60°
(C) 90°
(D) 120°
Answer:
(C) 90°

Question 97.
The unit vector along \hat{\mathrm{i}}+\hat{\mathrm{j}} is
(A) \hat{\mathrm{k}}
(B) \hat{\mathrm{i}}+\hat{\mathrm{j}}
(C) \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}
(D) \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{2}
Answer:
(C) \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Balbharti Maharashtra State Board 11th Physics Important Questions Chapter 3 Motion in a Plane Important Questions and Answers.

Maharashtra State Board 11th Physics Important Questions Chapter 3 Motion in a Plane

Question 1.
Explain the term: Displacement.
Answer:
Displacement:

  1. Displacement of a particle for a time interval is the difference between the position vectors of the object in that time interval.
  2. Let \overrightarrow{\mathrm{x}_{1}} and \overrightarrow{\mathrm{x}_{2}} be the position vectors of a particle at time t1 and t2 respectively. Then the displacement \overrightarrow{\mathrm{S}} in time ∆t = (t2 – t\overrightarrow{\mathrm{s}}=\Delta \overrightarrow{\mathrm{x}}=\overrightarrow{\mathrm{x}}_{2}-\overrightarrow{\mathrm{x}}_{1}) is given by \overrightarrow{\mathrm{s}}=\Delta \overrightarrow{\mathrm{x}}=\overrightarrow{\mathrm{x}}_{2}-\overrightarrow{\mathrm{x}}_{1}
  3. Dimensions of displacement are equal to that of length i.e.. [L1M0T0].
  4. Displacement is a vector quantity.
  5. Example:
    • For an object has travelled through 1 m from time t1 to t2 along the positive X-direction, the magnitude of its displacement is I m and its direction is along the positive X-axis.
    • On the other hand, for an object has travelled through I m from time t1 to t1 along the positive Y-direction, the magnitude of its displacement remains same i.e., I m but the direction of the displacement is along the positive Y-axis.

Question 2.
Explain the term: Path length.
Answer:

  1. Path length is the actual distance travelled by the particle during its motion.
  2. It is a scalar quantity.
  3. Dimensions of path length are equal to that of length i.e.. [L1M0T0]
  4. Example:
    • If an object travels along the X-axis from x = 3 m to x = 6 m then the distance travelled is 3 m. In this case the displacement is also 3 m and its direction is along the positive X-axis.
    • However, if the object now comes back to x 5, then the distance through which the object has moved increases to 3 + I = 4 m. Its initial position was x 3 m and the final position is now x = 5 m and thus, its displacement is ∆x = 5 – 3 = 2 m, i.e., the magnitude of the displacement is 2 m and its direction is along the positive X-axis.
    • If the object now moves to x =1, then the distance travelled, i.e., the path length increases to 4 + 4 = 8 m while the magnitude of displacement becomes 3 – 1 = 2 m and its direction is along the negative X-axis.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 3.
Explain the terms:
i. Average velocity
ii. Instantaneous velocity
iii. Average speed
iv. Instantaneous speed
Answer:
i) Average velocity:

  1. Average velocity (\overrightarrow{\mathrm{v}}_{\mathrm{av}}) of an object is the displacement (\Delta \overrightarrow{\mathrm{x}}) of the object during the time interval (∆t) over which average velocity is being calculated, divided by that time interval.
  2. Average velocity = (\frac{\text { Displacement }}{\text { Time interval }})
    \overrightarrow{\mathrm{V}_{\mathrm{av}}}=\frac{\overrightarrow{\mathrm{x}}_{2}-\overrightarrow{\mathrm{x}}_{1}}{\mathrm{t}_{2}-\mathrm{t}_{1}}=\frac{\Delta \overrightarrow{\mathrm{x}}}{\Delta \mathrm{t}}
  3. Average velocity is a vector quantity.
  4. Its SI unit is m/s and dimensions are [M0L1T-1]
  5. For example, if the positions of an object are x +4 m and x = +6 m at times t = O and t = 1 minute respectively, the magnitude of its average velocity during that time is Vav = (6 – 4)1(1 – 0) = 2 m per minute and its direction will be along the positive X-axis.
    \overrightarrow{\mathrm{v}}_{\mathrm{av}} = 2 i m/min
    Where, i = unit vector along X-axis.

ii) Instantaneous velocity:

  1. The instantaneous velocity (\overrightarrow{\mathrm{V}}) is the limiting value of ¡he average velocity of the object over a small time interval (∆t) around t when the value of lime interval goes to zero.
  2. It is the velocity of an object at a given instant of time.
  3. \overrightarrow{\mathrm{v}}=\lim _{\Delta t \rightarrow 0} \frac{\Delta \overrightarrow{\mathrm{x}}}{\Delta \mathrm{t}}=\frac{\mathrm{d} \overrightarrow{\mathrm{x}}}{\mathrm{dt}}
    where \frac{\mathrm{d} \overrightarrow{\mathrm{x}}}{\mathrm{dt}} derivative of \overrightarrow{\mathrm{x}} with respect to t.

iii) Average speed:

  1. Average speed of an object is the total path length (distance) travelled by the object during the time interval over which average speed is being calculated, divided by that time interval.
  2. Average speed = \frac{\text { Total path length }}{\text { Total time interval }}
  3. Average speed is a scalar quantity.
  4. Its S.I. unit is m/s and dimensions are [M0V1T-1].
  5. In rectilinear motion;
    • If the motion of the object is only in one direction, then the magnitude of displacement will be equal to the path length and hence the magnitude of average velocity will be equal to the average speed.
    • If the motion of the object reverses its direction, then the magnitude of displacement will be less then the path length and hence the magnitude of average velocity will be less than the average speed.

iv) Instantaneous speed:
The instantaneous speed is the limiting value of the average speed of the object over a small time interval ‘∆t’ around t when the value of time interval goes to zero.

Question 4.
Distinguish between uniform rectilinear motion and non-uniform rectilinear motion.
Answer:

No. Uniformly rectilinear motion Non-uniform rectilinear motion
i. The object is moving with constant velocity. The object is moving with variable velocity.
ii. The average and instantaneous velocities are same. The average and instantaneous velocities are different.
iii. The average and instantaneous speeds are the same. The average and instantaneous speeds are different.
iv. The average and instantaneous speeds are equal to the magnitude of the velocity. The average speed will be different from the magnitude of average velocity.

Question 5.
Explain the terms:

  1. Acceleration
  2. Average acceleration
  3. Instantaneous acceleration

Answer:

  1. Acceleration:
    • Acceleration is the rate of change of velocity with respect to time.
    • It is a vector quantity.
    • Dimension: [M0L1T-2]
    • If a particle moves with constant velocity, its acceleration is zero.
  2. Average acceleration:
    • Average acceleration is the change in velocity divided by the total time required for the change.
    • If \overrightarrow{\mathrm{v}_{\mathrm{1}}} and \overrightarrow{\mathrm{v}_{\mathrm{2}}} are the velocities of the T particle at time t1 and t2 respectively, then the change in velocity is and time required for this change is ∆t = t2 – t1
      \vec{a}_{a v}=\frac{\vec{v}_{2}-\vec{v}_{1}}{t_{2}-t_{1}}=\frac{\Delta \vec{v}}{\Delta t}
  3. Instantaneous acceleration:
    • The instantaneous acceleration a is the limiting value of the average acceleration of the object over a small time interval ‘∆t’ around t when the value of time interval goes to zero.
      \overrightarrow{\mathrm{a}}_{\text {inst }}=\lim _{\Delta t \rightarrow 0} \frac{\Delta \overrightarrow{\mathrm{v}}}{\Delta \mathrm{t}}=\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{d} \mathrm{t}}
    • Instantaneous acceleration is the slope of the tangent to the velocity-time graph at a position corresponding to given instant of time.
      [Note: Generally, when the term acceleration is used, it is an instantaneous acceleration.]

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 6.
Draw and explain the position-time graph of:

  1. An object at rest.
  2. An object moving with uniform velocity along positive x-axis.
  3. An object moving with uniform velocity along negative x-axis.
  4. An object moving with non-uniform velocity.
  5. An object performing oscillatory motion with constant speed.

Answer:

  1. The position-time graph of an object at rest:
    • For an object at rest, the position-time graph is a horizontal straight line parallel to time axis.
    • The displacement of the object is zero as there is no change in the object’s position.
    • Slope of the graph is zero, which indicates that velocity of the particle is zero.
      Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 1
  2. The position-time graph of an object moving with uniform velocity along positive x-axis:
    • When an object moves, the position of the particle changes with respect to time.
    • Since velocity is constant, displacement is proportional to elapsed time.
    • The graph is a straight line with positive slope, showing that the velocity is along the positive x-axis.
    • In this case, as the motion is uniform, the average velocity and instantaneous velocity are equal at all times.
    • Speed is equal to the magnitude of the velocity.
      Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 2
  3. Position-time graph of an object moving with uniform velocity along negative x- axis:
    • The graph is a straight line with negative slope, showing that the velocity is along the negative x-axis.
    • Displacement decreases with increase in time.
      Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 3
  4. Position-time graph of a particle moving with non-uniform velocity;
    • When the velocity of an object changes with time, slope of the graph is different at different points. Therefore, the average and instantaneous velocities are different.
    • Average velocity over time interval from t1 to t4 around time t0 = slope of line AB.
    • Average velocity over time interval from t2 to t3 = slope of line CD
    • On further reducing the time interval around t0, it can be deduced that, instantaneous interval at t0 = the slope of the tangent PQ at t0.
      Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 4
  5. Position-time graph of an object performing oscillatory motion with constant speed:
    For an object performing oscillatory motion with constant speed, the direction of velocity changes from positive to negative and vice versa over fixed intervals of time.
    Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 5

Question 7.
Explain the velocity-tune graphs of an object:
i) Moving with zero acceleration.
ii) Moving with constant positive acceleration.
iii) Moving with constant negative acceleration.
iv) Moving with non-uniform acceleration.
Answer:
i) Object is moving with zero acceleration:

  1. Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 6
  2. As the acceleration is zero, the graph will be a straight line parallel to time axis.
  3. Velocity of the particle is constant as the acceleration is zero.
  4. Magnitude of displacement of object from t1 to t2 = v0 × (t2 – t1) shaded area under velocity-time graph.

ii) Object is moving with constant positive acceleration:

  1. The velocity-time graph is linear.
  2. Velocity increases with increase in time. as acceleration is positive (along the direction of velocity).
  3. The area under the velocity-time graph between two instants of time t1 and t2 gives the displacement of the object during that time interval.
  4. Slope of the graph is \frac{\Delta \mathrm{v}}{\Delta \mathrm{t}} = positive acceleration
    Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 7

iii) Object is moving with constant negative acceleration:

  1. The velocity-time graph is linear.
  2. Velocity decreases with increase in time as acceleration is negative (opposite to the direction of velocities).
  3. The area tinder the velocity-time graph between two instants of time t1 and t2 gives the displacement 0f the object during that time interval.
  4. Slope of the graph is \frac{\Delta \mathrm{v}}{\Delta \mathrm{t}} negative acceleration
    Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 8

iv. Object is moving with non-uniform acceleration:

  1. Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 9
  2. Velocity-time graph is non-linear.
  3. The area under the velocity-time graph between two instants of time t1 and t2 gives the displacement of the object during that time interval area under the velocity-time curve =
    Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 10
    = x(t2) – x(t1)
    = displacement of the object from t1 to t2.

Question 8.
A ball thrown vertically upwards from a point P on earth reaches a point Q and returns back to earth striking at a point R. Draw speed-time graph to depict the motion of the ball (Neglect air resistance).
Answer:

  • Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 11
  • A ball which is thrown up with a certain initial speed goes up with decreasing speed to a certain height where its speed becomes zero.
  • Now, during its downward motion, the speed goes on increasing from zero and reaches its initial value when it strikes the ground.
  • The speed-time graph for the motion of a ball is as shown in the figure.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 9.
Figure shows velocity-time graph for various situations. What does each graph indicate?
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 12
Answer:

  1. Initial velocity, u > 0. Also, velocity is constant with time. Hence, acceleration is zero.
  2. As finite initial velocity is increasing with time, acceleration, a > 0 and is constant.
  3. Initial velocity, u = 0. Velocity is increasing with time so, acceleration a is positive. But it is decreasing in magnitude with time.
  4. Initial velocity, u = 0. Velocity is linearly increasing with time. Hence, starting from rest acceleration is constant.
  5. Initial velocity, u = 0. Acceleration and velocity is increasing with time.
  6. Initial velocity u > 0. Velocity decreases and ultimately comes to rest. Hence, acceleration a < 0.

Question 10.
‘The distances travelled by an object starting from rest and having a positive uniform acceleration in successive seconds are in the ratio 1:3:5:7….’ Prove it.
Answer:

  1. Consider an object under free fall, Initial velocity u = 0, acceleration a = g
  2. The distance travelled by the object in equal time intervals t0 can be given by the second law of motion as,
    s = ut0 + \frac{1}{2} gt02
  3. Distance travelled in the first time interval to,
    s1 = 0 + \frac{1}{2}gt02 = \frac{1}{2} gt02
    Substituting \frac{\mathrm{g}}{2} = A, we have s1 = At02
  4. Distance travelled in the time interval 2t0 = A (2t0)2
    ∴ The distance travelled in the second t0 interval, s2 = A(4t02 – t02) = 3At0\frac{\mathrm{g}}{2} = 3s1
  5. Distance travelled in the time interval 3t0 = A(3t0)2
    ∴ The distance travelled in the third to interval,
    s3 = A (9t02 – 4t02) = 5 At02 = 5s1
  6. On continuing, it can be seen that the distances travelled, (s1 : s2 : s3 ….) are in the ratio (1 : 3 : 5 :….)

Question 11.
Explain the concept of relative velocity along a straight line with the help of an example.
Answer:

  1. Consider two trains A and B moving on two parallel tracks in the same direction.
  2. Case 1: Train B overtakes train A.
    For a passenger in train A, train B appears to be moving slower than train A. This happens because the passenger in train A perceives the velocity of train B with respect to him/her i.e., the difference in the velocities of the two trains which is much smaller than the velocity of train A.
  3. Case 2: Train A overtakes train B.
    For a passenger in train A, train B appears to be moving faster than train A. This happens because the passenger in train A perceives the velocity of the train B w.r.t. to him/her i.e., the difference in the velocities of the two trains which is larger than the velocity of train A.
  4. If \vec{v}_{\mathrm{A}} and \vec{v}_{\mathrm{B}} be the velocities of two bodies then relative velocity of A with respect to B is given by \vec{v}_{A B}=\vec{v}_{A}-\vec{v}_{B}.
  5. Similarly the velocity of B with respect to A is given by, \vec{v}_{A B}=\vec{v}_{B}-\vec{v}_{A}.
    Thus, relative velocity of an object w.r.t. another object is the difference in their velocities
  6. If two objects start form the same point at t = 0, with different velocities, distance between them increases with time in direct proportion to the relative velocity between them.

Solved Problems

Question 12.
A person walks from point P to point Q along a straight road ¡n 10 minutes, then turns back and returns to point R which ¡s midway between P and Q after further 4 minutes. If PQ is 1 km, find the average speed and velocity of the person in going from P to R.
Solution:
Given: time taken (t) = 10 + 4 = 14 minutes,
distance (s) = PQ + QR = 1 + 0.5 = 1.5 km,
displacement = PQ – QR = 1 – 0.5 = 0.5km
To find: Average speed, average velocity (v)
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 13
The average speed and average velocity of the person is 6.42 km/hr and 2.142 km/hr respectively.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 13.
A car moves at a constant speed of 60 km/hr for 1 km and 40 km/hr for next 1 km. What ¡s the average speed of the car?
Solution:
Given. v1 = 60 km/hr, x1 = 1 km,
v2 = 40 km/hr, x2 = 1 km
To find: Average speed of car (Vav)
Formula: vav = \frac{\text { total path length }}{\text { total time interval }}
Calculation: From given data,
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 14
∴ Average speed of car = 48 km/hr
The average speed of the car is 48 km/hr

Question 14.
A stone is thrown vertically upwards from the ground with a velocity 15 m/s. At the same instant a ball is dropped from a point directly above the stone from a height of 30 m. At what height from the ground will the stone and the ball meet and after how much time? (Use g = 10 m/s2 for ease of calculation).
Solution:
Let the stone and the ball meet after time t0. From second equation of motion, the distances travelled by the stone and the ball in that time is given as,
Sstone = 15 t0\frac{1}{2} gt02
Sball = \frac{1}{2} gt02
When they meet. Sstone + Sball = 30
∴ 15t0\frac{1}{2} gt02 + \frac{1}{2} gt02 = 30
t0 = \frac{30}{15} = 2 s
∴ Sstone = 15 (2) – \frac{1}{2} (10) (2)2 = 30 – 20 = 10 m
The stone and the ball meet at a height of 10 m after time 2s.

Question 15.
A ball is dropped from the top of a building 122.5 m high. How long will it take to reach the ground? What wilt be its velocity when it strikes the ground?
Solution:
Given: s = h = 122.5 m, u = 0,
a = g = 9.8 ms2
To find: i) Time taken to reach the ground (t)
ii) Velocity of ball when it strikes ground (v)

Formulae: i) s = ut + \frac{1}{2} at2
ii) v = u + gt
Calculation: From formula (i),
122.5 = 0 + \frac{1}{2} × 9.8 t2
t2 = \frac{122.5}{4.9} = 25
t = \sqrt {25} = 5 second
From formula (ii),
v = u + gt
v = 0 + 9.8 × 5 = 49 m/s

i) Time taken to reach the ground is 5 s.
ii) Velocity of the ball when it strikes the ground is 49 m/s.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 16.
The position vectors of three particles are given by
\overrightarrow{\mathrm{x}}_{1}=(5 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}) \mathrm{m}, \overrightarrow{\mathrm{x}}_{2}=(5 \mathrm{t} \hat{\mathrm{i}}+5 \mathrm{t} \hat{\mathrm{j}}) \mathrm{m} and \overrightarrow{\mathrm{x}}_{3}=\left(5 \mathrm{t} \hat{\mathrm{i}}+10 \mathrm{t}^{2} \hat{\mathrm{j}}\right) \mathrm{m} as a function of time t.
Determine the velocity and acceleration for each, in SI units.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 15
v2 = \sqrt{5^{2}+5^{2}} = 5\sqrt{2} m/s
tan θ = \frac{5}{5} = 1
∴ θ = 45°
Direction of v2 makes an angle of 45° to the horizontal.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 16
Thus, third particle is getting accelerated along the y-axis at 20 m/s2.

Question 17.
The initial velocity of an object is \overrightarrow{\mathrm{u}}=5 \hat{\mathrm{i}}+10 \hat{\mathrm{j}} \mathrm{m} / \mathrm{s}. Its constant acceleration is \vec{a}=2 \hat{i}+3 \hat{j} \mathrm{~m} / \mathrm{s}^{2}. Determine the velocity and the displacement after 5 s.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 17
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 18

Question 18.
An aeroplane A, is travelling in a straight line with a velocity of 300 km/hr with respect to Earth. Another aeroplane B, is travelling in the opposite direction with a velocity of 350 km/hr with respect to Earth. What is the relative velocity of A with respect to B? What should be the velocity of a third aeroplane C moving parallel to A, relative to the Earth if it has a relative velocity of 100 km/hr with respect to A?
Solution:
Given: vA = 300 km/hr, vB = 350 km/hr,
vCA = 100 km/hr
To find: i) Velocity of plane A relative to B (vA – vB)
ii) Velocity of aeroplane C (vC)

Formula: i) vAB = vA – vB
ii) vCA = vC – vA

Calculations: From formula (i),
vAB = vA – vB = 300 – (-350)
∴ vAB = 650 km/hr
From formula (ii),
vC = vCA + vA = 100 + 300 = 400 km/hr

i) The relative velocity of A with respect to B is 650 km/hr.
ii) The velocity of plane C relative to Earth is 400 km/hr.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 19.
A car moving at a speed 10 m/s on a straight road is ahead of car B moving in the same direction at 6 m/s. Find the velocity of A relative to B and vice-versa.
Solution:
Given: vA = 10 m/s, vB = 6 m/s,
To find: i) Velocity of A relative to B (vA – vB)
ii) Velocity of B relative to A (vB – vA)

Formulae: i) vAB = vA – vB
ii) vBA = vB – vA

Calculation: From formula (i),
vAB = 10 – 6 = 4 m/s
From formula (ii),
vBA = 6 – 10 = -4 m/s
-ve sign indicates that driver of car A sees the car B lagging behind at the rate of 4 m/s.
∴ vAB = 4 m/s, vBA = -4 m/s

i) Velocity of A relative to B is 4 m/s.
ii) Velocity of B relative to A is -4 m/s.

Question 20.
Two trains 120 m and 80 m in length are running in opposite directions with velocities 42 km/h and 30 km/h respectively. In what time will they completely cross each other?
Solution:
Given: l1 = 120 m, l2 = 80 m,
vA = 42 km/h = 42 × \frac{5}{18} = \frac{35}{3} m/s,
vB = -30km/h= -30 × \frac{5}{18} = \frac{-25}{3} m/s
To find: Time taken by trains to cross each other (t)
Formula: Time = \frac{\text { Distance }}{\text { speed }}

Calculation :
Total distance to be travelled
= sum of lengths of two trains
= 120 + 80 = 200m
Relative velocity of A with respect to B is vAB,
vAB = vA – vB
= \frac{35}{3} – (\frac{-25}{3})
= \frac{60}{3}
∴ vAB = 20m/S
From formula,
∴ Time taken to cross each other (t) = \frac{\text { Distance }}{\text { speed }}
= \frac{200}{20}
= 10 s
Time taken by the two trains to cross each other is 10 s.

Question 21.
A jet aeroplane travelling at the speed of 500 km/hr ejects its products of combustion at speed of 1500 km/hr relative to jet plane. What is the relative velocity of the latter with respect to an observer on the ground?
Solution:
Let us consider the positive direction of motion towards the observer on the ground.
Suppose \vec{v}_{\mathrm{a}} and \vec{v}_{\mathrm{cj}} be the velocities of the aeroplane and relative velocity of combustion products w.r.t. aeroplane respectively.

\vec{v}_{\mathrm{cj}} = 1,500 km/hr (towards the observer on the ground) and \vec{v}_{\mathrm{a}} = 500 km/hr (away from the observer on the ground)
∴ – \vec{v}_{\mathrm{a}} = -500 km/ hr (towards the observer on the ground)

Let \vec{v}_{\mathrm{c}} be the velocity of the combustion products towards the observer on ground then,
\vec{v}_{\mathrm{c} j}=\vec{v}_{\mathrm{c}}-\vec{v}_{\mathrm{a}}
\vec{v}_{\mathrm{c} }=\vec{v}_{\mathrm{cj}}-\vec{v}_{\mathrm{a}}
= 1500 + (-500)
= 1000 km/hr
\vec{v}_{\mathrm{c}} = 1000 km/hr
The relative velocity of the combustion products w.r.t. the observer is 1000 km/hr.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 22.
Derive the expression for average velocity and instantaneous velocity for the motion of an object in x-y plane.
Answer:
i) Consider an object to be at point A at time t1 in an x—y plane.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 19
ii) At time t1, the position vector of the object is given as,
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 20
vii) The instantaneous velocity of the object at point A along the trajectory is along the tangent to the curve at A. This is shown by the vector AB.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 21
Equation (3) is the slope of the tangent to the curve at the point at which we are calculating the instantaneous velocity.

Question 23.
Derive the expression for average acceleration and instantaneous acceleration for the motion of an object in x-y plane.
Answer:
i) Consider an object moving in an x-y plane.
Let the velocity of the particle be \vec{v}_{1} and \vec{v}_{2} at time t1 and t2 respectively.
ii) The average acceleration (\overrightarrow{\mathrm{a}}_{\mathrm{av}}) of the particle between t1 and t2 is given as,
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 22
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 23
Equation (1) is the slope of the tangent to the curve at the point at which we are calculating the instantaneous acceleration.

Question 24.
Explain relative velocity between two objects moving in a plane.
Answer:

  1. If \vec{v}_{A} and \vec{v}_{B} be the velocities of two bodies then relative velocity of A with respect to B is given by, \vec{v}_{A B}=\vec{v}_{A}-\vec{v}_{B}
  2. Similarly, the velocity of B with respect to A is given by, \vec{v}_{\text {BA }}=\vec{v}_{\text {B }}-\overrightarrow{v_{A}}
  3. Thus, the magnitudes of the two relative velocities are equal and their directions are opposite.
  4. For a number of objects A, B, C, D—Y, Z, moving with respect to the other. The velocity of A relative to Z can be given as, \overrightarrow{\mathrm{v}}_{\mathrm{AZ}}=\overrightarrow{\mathrm{v}}_{\mathrm{AB}}+\overrightarrow{\mathrm{v}}_{\mathrm{BC}}+\overrightarrow{\mathrm{v}}_{\mathrm{CD}}+\ldots+\overrightarrow{\mathrm{v}}_{\mathrm{XY}}+\overrightarrow{\mathrm{v}}_{\mathrm{YZ}}
    The order of subscripts is: A → B → C → D → Z

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 25.
Write a note on projectile motion.
Answer:

  1. An object in flight after being thrown with some velocity is called a projectile and its motion is called projectile motion.
  2. Example: A bullet fired from a gun, football kicked in air, a stone thrown obliquely in air etc.
  3. In projectile motion, the object is moving freely under the influence of Earth’s gravitational field.
  4. The projectile has two components of velocity, one in the horizontal i.e., along the x- direction and the other in the vertical i.e., along the y-direction.
  5. As acceleration due to gravity acts only along the vertically downward direction, the vertical component changes in accordance with the laws of motion with ax = 0 and ay = -g.
  6. As no force is acting in the horizontal direction, the horizontal component of velocity remains unchanged.
    [Note: Retarding forces like air resistance etc. are neglected in projectile motion unless otherwise stated.]

Question 26.
Obtain an expression for the time of flight of a projectile.
Answer:
Expression for time of flight:

  1. Consider a body projected with velocity \vec{u}, at an angle θ of projection from point O in the co-ordinate system of the X-Y plane, as shown in figure.
    Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 24
  2. The initial velocity \vec{u} can be resolved into two rectangular components:
    ux = u cos θ (Horizontal component)
    uy = u sin θ (Vertical component)
  3. Thus, the horizontal component remains constant throughout the motion due to the absence of any force acting in that direction, while the vertical component changes according to, vy = uy + ay t with ay = – g and uy = u sin θ
  4. The components of velocity of the projectile at time t are given by, vx = ux = u cos θ
    vy = uy – gt = u sin θ – gt ………….. (1)
  5. At maximum height.
    vy = 0, t = tA = time of ascent = time taken to reach maximum height.
    ∴ 0 = u sin θ – gtA ……..[From(l)]
    u sin θ = gtA
    tA = \frac{\mathrm{u} \sin \theta}{\mathrm{g}} ………….. (2)
    This is time of ascent of projectile.
  6. The total time in air i.e., time of flight T is given as,
    T = 2tA ………… [From(2)]
    = \frac{2 \mathrm{u} \sin \theta}{\mathrm{g}} ………… (3)
    Equation (3) represents time of flight of projectile.

Question 27.
Define Horizontal range of projectile:
Answer:
The maximum horizontal distance travelled by the projectile is called the horizontal range (R) of the projectile.

Solved Examples

Question 28.
An aeroplane Is travelling northward with a velocity of 300 km/hr with respect to the Earth. Wind is blowing from east to west at a speed of 100 km/hr. What is the velocity of the aeroplane with respect to the wind?
Solution:
Given:
velocity of aeroplane w.r.t Earth,
\vec{v}_{A E}=300 \hat{j}
velocity of wind w.r.t Earth,
\vec{v}_{w E}=-100 \hat{i}
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 25

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 29.
A hiker stands on the edge of a cliff 490 m above the ground and throws a stone horizontally with an initial speed of 15 ms-1. Neglecting air resistance, find the time taken by the stone to reach the ground, and the speed with which it hits the ground. Take = 9.8 m/s2.
Solution:
Given: h = 490m, ux = 15 ms-1, ay = 9.8 ms-1,
ax = 0
To find: i) Time taken (t)
ii) Velocity (v)

Formulae: i) t = \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}
ii) v = \sqrt{v_{x}^{2}+v_{y}^{2}}

Calculation: t = \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}=\sqrt{\frac{2 \times 490}{9.8}} = 10 s
vx = ux + axt= 15 + 0 × 10 = 15 m/s
uy = uy + ayt = 0 + 9.8 × 10 = 98 m/s
∴ v = \sqrt{\mathrm{v}_{\mathrm{x}}^{2}+\mathrm{v}_{\mathrm{y}}^{2}}=\sqrt{15^{2}+98^{2}}
= 99.1 m/s
The stone taken 10 s to reach the ground and hits the ground with 99.1 m/s.

Question 30.
A body is projected with a velocity of 40 ms-1. After 2 s it crosses a vertical pole of height 20.4 m. Find the angle of projection and horizontal range of projectile, (g = 9.8 ms-2).
Solution:
Given: u = 40 ms-1, t = 2 s, y = 20.4 m,
ay = -9.8 m/s2

To find: i) Angle of projection (θ)
ii) Horizontal range of projectile (R)

Formulae: i) y = uy t + \frac{1}{2} ay t2
ii) R = \frac{\mathrm{u}^{2} \sin 2 \theta}{\mathrm{g}}

Calculation: Taking vertical upward motion of the projectile from point of projection up to the top of vertical pole we have
uy = 40 sinθ,
From formula (i),
∴ 20.4 = 40 sinθ × 2 + \frac{1}{2} (-9.8) × 22
∴ 20.4 = 80 sinθ – 19.6
or sinθ = \frac{(20.4+19.6)}{80}=\frac{1}{2}
or θ = 30°.
From formula (ii),
Horizontal range = \frac{40^{2}}{9.8} sin 2 × 30°
= 141.4 m
The angle of projection is 30°. The horizontal range of projection is 141.4m

Question 31.
A stone is thrown with an initial velocity components of 20 m/s along the vertical, and 15 m/s along the horizontal direction. Determine the position and velocity of the stone after 3 s. Determine the maximum height that it will reach and the total distance travelled along the horizontal on reaching the ground. (Assume g = 10 m/s2)
Solution:
The initial velocity of the stone in x-direction = u cos θ = 15 m/s and in y-direction = u sin θ = 20 m/s
After 3 s, vx = u cos θ = 15 m/s
vy = u sin θ – gt
= 20 – 10(3)
= -10 m/s
10 m/s downwards.
∴ v = \sqrt{\mathrm{v}_{x}^{2}+\mathrm{v}_{\mathrm{y}}^{2}}=\sqrt{15^{2}+10^{2}}=\sqrt{225+100}=\sqrt{325}
∴ v = 18.03m/s
tan α = vy/vx = 10/15 = 2/3
∴ α = tan-1 (2/3) = 33° 41’ with the horizontal.
Sx = (u cos θ)t = 15 × 3 = 45m,
Sy = (u sin θ)t – \frac{1}{2}gt2 = 2o × 3 – 5(3)2
∴ Sy = 15m
The maximum vertical distance travelled is given by,
H = \frac{(\mathrm{u} \sin \theta)^{2}}{(2 \mathrm{~g})}=\frac{20^{2}}{(2 \times 10)}
∴ H = 20m
Maximum horizontal distance travelled
R = \frac{2 \cdot u_{x} \cdot u_{y}}{g}=\frac{2(15)(20)}{10} = 60 m

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 32.
A body is projected with a velocity of 30 ms-1 at an angle of 300 with the vertical.
Find
i) the maximum height
ii) time of flight and
iii) the horizontal range
Solution:
Given:
30 ms-1, θ = 90° – 30° = 60°

To find: i) The maximum height reached (H)
ii) Time of flight (T)
iii) The horizontal range (R)
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 26
i) The maximum height reached by the body is 34.44 m.
ii) The time of flight of the body is 5.3 s.
iii) The horizontal range of the body is 79.53 m.

Question 33.
A projectile has a range of 50 m and reaches a maximum height of 10 m. What is the e1eation of the projectile?
Solution:
Given: R = 50m, H = 10 m
To find: Elevation of the projectile (θ)
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 27
∴ θ = tan-1 (0.8)
∴ θ = 38.66°
The elevation of the projectile is 38.66°

Question 34.
A bullet fired at an angle of 300 with the horizontal hits the ground 3 km away. By adjusting the angle of projection, can one hope to hit a target 5 km away? Assume the muzzle speed to be fixed and neglect air resistance.
Solution:
R = 3km = 3000m, θ = 30°,
Distance of target R’ = 5km
Horizontal range, R = \frac{\mathrm{u}^{2} \sin 2 \theta}{\mathrm{g}}
∴ 3000 = \frac{\mathrm{u}^{2} \sin 60^{\circ}}{\mathrm{g}}
\frac{\mathrm{u}^{2}}{\mathrm{~g}}=\frac{3000}{\sin 60^{\circ}}=\frac{3000 \times 2}{\sqrt{3}} = 2000\sqrt {3}
Maximum horizontal range,
Rmax = \frac{\mathrm{u}^{2}}{\mathrm{~g}} = 2000 \sqrt {3} m
= 2000 × 1.732 = 3464m = 3.46km
Since R’ > Rmax, Target cannot be hit.

Question 35.
Q.54. A ball is thrown at an angle θ and another ball ¡s thrown at an angle (90° – θ) with the horizontal direction from the same point with velocity 39.2 ms-1. The second ball reaches 50 m higher than the first balL find their individual heights. [Take g = 9.8 ms-2]
Solution:
For the first ball: Angle of projection = θ,
u = 39.2 ms-1
H = \frac{\mathrm{u}^{2} \sin ^{2} \theta}{2 \mathrm{~g}}
H = \frac{(39.2)^{2} \sin ^{2} \theta}{2 \times 9.8} …………… (i)
For the second ball: Angle of projection
= 90° – θ,
u = 39.2 ms-1,
maximum height reached = (H + 50) m
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 28
or 2H = 78.4 – 50 = 28.4
∴ H = 14.2 m
∴ Height of first ball = H = 14.2 m
Height of second ball = H + 50 = 14.2 + 50 = 64.2 m

i) Height reached by the first ball is 14.2 m.
ii) Height reached by the second ball is 64.2m.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 36.
A body is thrown with a velocity of 49 m/s at an angle of 30° with the horizontal. Find
i) the maximum height attained by it
ii) the time of flight and
iii) the horizontal range.
Solution:
Given: u = 49 m/s. θ = 30°
To find: i) The maximum height attained (H)
ii) The time of flight (T)
iii) The horizontal range (R)
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 29
i) The maximum height attained by the body is 30.625 m
ii) The time of flight of the body is 5 s.
iii) The horizontal range of the body is 212.2 m.

Question 37.
A fighter plane flying horizontally at a altitude of 1.5 km with a speed of 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with a muzzle velocity of 600 m/s to hit the plane? At what minimum altitude should the pilot fly to avoid being hit? [Take g = 10 m /s2]
Solution:
Given: h = 1.5 km = 1500 m,
u = 600 m/s,
y = 720 km/h = 720 × \frac{5}{18} = 200 m/s

To find: i) Angle of firing (θ)
ii) Minimum altitude (H)

Formula: H = \frac{u^{2} \sin ^{2} \theta}{2 g}

Calculation:
Let the shell hit the plane t seconds after firing,
∴ 600 cos(90 – θ) × t = 200 t
∴ cos(90 – θ) = \frac{1}{6}
∴ 90° – θ = cos-1(\frac{1}{3})
cos -1(\frac{1}{3}) = 90° – θ
∴ 70°28’ = 90° – θ
∴ θ = 90° – cos-1 (\frac{1}{3})
∴ θ = 19°47’ with vertical
To avoid being hit, the plane must be at a minimum height, i.e., maximum height reached by the shell.
From formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 30
∴ H = 15.9 km

i) Angle made by gun with the vertical is 19°47′.
ii) Minimum altitude at which the pilot should fly is 15.9 km.

Question 38.
A both is thrown with a velocity of 40 m/s in a direction making an angle of 30° with the horizontal. Calculate
i) Horizontal range
ii) Maximum height and
iii) Time taken to reach the maximum height.
Solution:
Given: u = 40 m/s, θ = 30°
To find: i) Horizontal range (R)
ii) Maximum height (Hmax)
iii) Time to reach max. height (tA)
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 31
i) Horizontal range of the body is 141.4 m.
ii) Maximum height reached by the body is 20.41 m.
iii) Time taken by the body to reach the maximum height is 2.041 s.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 39.
If a child launches paper plane with a velocity of 6 m/s2 at an angle θ with vertical.
i) What will be the maximum range of the projectile?
ii) What will be the maximum height of the projectile?
iii) Will the plane hit a lady standing at a distance of 6m?
Solution:
i) Range of projectile to given by.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 32
Hmax = 1.63 m
iii) As maximum range of projectile is 6.53 m and lady is standing 6m away, plane will hit the lady.

Question 40.
Explain the term uniform circular motion.
Answer:

  1. The motion of a body along the circumference of a circle with constant speed is called uniform circular motion.
  2. The magnitude of velocity remains constant and its direction is tangential to its circular path.
  3. The acceleration is of constant magnitude and it is perpendicular to the tangential velocity. It is always directed towards the centre of the circular path. This acceleration is called centripetal acceleration.
  4. The centripetal force provides the necessary centripetal acceleration.
  5. Examples of U.C.M:
    • Motion of the earth around the sun.
    • Motion of the moon around the earth.
    • Revolution of electron around the nucleus of atom.

Question 41.
What is meant by period of revolution of U.C.M. Obtain an expression for the period of revolution of a particle performing uniform circular motion.
Answer:
The time taken by a particle performing uniform circular motion to complete one revolution is called as period of revolution. It is denoted by T.

Expression for time period:
During period T, particle covers a distance equal to circumference 2πr of circle with uniform speed v.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 33

Question 42.
For a particle performing uniform circular motion, derive an expression for angular speed and state its unit.
Answer:

  1. Consider an object of mass m, moving with a uniform speed v, along a circle of radius r. Let T be the time period of revolution of the object, i.e., the time taken by the object to complete one revolution or to travel a distance of 2πr.
    Thus, T = 2πr/v
    ∴ Speed, v = \frac{\text { Distance }}{\text { Time }}=\frac{2 \pi \mathrm{r}}{\mathrm{T}} …………….. (1)
  2. During circular motion of a point object, the position vector of the object from centre of the circle is the radius vector r. Its magnitude is radius r and it is directed away from the centre to the particle, i.e., away from the centre of the circle.
  3. As the particle performs UCM, this radius vector describes equal angles in equal intervals of time.
  4. The angular speed gives the angle described by the radius vector.
  5. During one complete revolution, the angle described is 2π and the time taken is period T. Hence, the angular speed ω is given as, ….[From (1)]
    ω = \frac{\text { Angle }}{\text { time }}=\frac{2 \pi}{\mathrm{T}}=\frac{\left(\frac{2 \pi \mathrm{r}}{\mathrm{T}}\right)}{\mathrm{r}} …………….. [From (1)]
    = \frac{\mathrm{v}}{\mathrm{r}}
  6. The unit of angular speed is radian/second.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 43.
Derive an expression for centripetal acceleration of a particle performing uniform circular motion.
Answer:
Expression for centripetal acceleration by calculus method:
i) Suppose a particle is performing U.C.M in anticlockwise direction.
The co-ordinate axes are chosen as shown in the figure.
Let,
A = initial position of the particle which lies on positive X-axis
P = instantaneous position after time t
θ = angle made by radius vector
ω = constant angular speed
\overrightarrow{\mathrm{r}} = instantaneous position vector at time t

ii) From the figure,
\vec{r}=\hat{i} x+\hat{j} y
where, \hat{i} and \hat{j} are unit vectors along X-axis and Y-axis respectively.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 34
iii) Also, x = r cos θ and y = r sin θ
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 35

iv) Velocity of the particle is given as rate of change of position vector.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 36

vi) From equation (1) and (2),
\overrightarrow{\mathrm{a}}=-\omega^{2} \overrightarrow{\mathrm{r}} ……….. (3)
Negative sign shows that direction of acceleration is opposite to the direction of position vector. Equation (3) is the centripetal acceleration.

vii) Magnitude of centripetal acceleration is given by,
a = ω2r

viii) The force providing this acceleration should also be along the same direction, hence centripetal.
\overrightarrow{\mathrm{F}}=\mathrm{m} \overrightarrow{\mathrm{a}}=-\mathrm{m} \omega^{2} \overrightarrow{\mathrm{r}}
This is the expression for the centripetal force on a particle undergoing uniform circular motion.

ix) Magnitude of F = mω2r = \frac{\mathrm{mv}^{2}}{\mathrm{r}} = mωv

Question 44.
Discuss the factors on which time period of conical pendulum depends.
Answer:
Time period of conical pendulum is given by,
T = 2π \sqrt{\frac{\cos \theta}{\mathrm{g}}} …………. (i)
where, l = length of the string
g = acceleration due to gravity
θ = angle of inclination
From equation (i), it is observed that period of conical pendulum depends on following factors.
i) Length of pendulum (l): Time period of conical pendulum increases with increase in length of pendulum, i.e., T ∝ \sqrt {l}
ii) Acceleration due to gravity (g): Time period of conical pendulum decreases with increase in g. i.e., T ∝ \frac{1}{\sqrt{g}}
iii) Angle of inclination (θ): As θ increases, cos θ decreases, hence, time period of conical pendulum decreases with increase in θ. (For 0 < θ < π) i.e., T ∝ \sqrt{\cos \theta}

Question 45.
Is there any limitation on semi vertical angle in conical pendulum? Give reason.
Answer:
Yes.

  1. For a conical pendulum, Period T ∝ \sqrt{\cos \theta}
    ∴ Tension F ∝ \frac{1}{\cos \theta}
    Speed v ∝ \sqrt{\tan \theta}
    With increase in angle θ, cos θ decreases and tan θ increases. For θ = 90°, T = 0, F = ∞ and v = ∞ which cannot be possible.
  2. Also, θ depends upon breaking tension of string, and a body tied to a string cannot be resolved in a horizontal circle such that the string is horizontal. Hence, there is limitation of semi vertical angle in conical pendulum.

Solved Examples

Question 46.
An object of mass 50 g moves uniformly along a circular orbit with an angular speed of 5 rad/s. If the linear speed of the particle is 25 m/s, ¡s the radius of the circle? Calculate the centripetal force acting on the particle.
Solution:
Given: ω = 5 rad/s, v = 25 m/s,
m = 50 g = 0.05 kg
To find: radius (r), centipetal force (F)
Formula: i) v = ωr
ii) F = \frac{\mathrm{mv}^{2}}{\mathrm{r}}

Calculation: From formula (i),
r = v/ω = 25/5 m = 5 m.
From formula (ii),
F = \frac{0.05 \times 25^{2}}{5} = 6.25 N.

i) Radius of the circle is 5 m.
ii) Centripetal force acting on the particle is 6.25 N.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 47.
An object is travelling in a horizontal circle with uniform speed. At t = 0, the velocity is given by \overrightarrow{\mathbf{u}}=20 \hat{\mathbf{i}}+35 \hat{\mathbf{j}} km/s. After one minute the velocity becomes \overrightarrow{\mathbf{v}}=-20 \hat{\mathbf{i}}-35 \hat{\mathbf{j}}. What is the magnitude of the acceleration?
Solution:
Magnitude of initial and final velocities,
u= \sqrt{(20)^{2}+(35)^{2}} m/s
∴ u = \sqrt{1625} m/s
∴ u = 40.3 m/s
As the velocity reverses in 1 minute, the time period of revolution is 2 minutes.
T = \frac{2 \pi \mathrm{r}}{\mathrm{u}}, giving r = \frac{\text { uT }}{2 \pi}
Now,
a = \frac{\mathrm{u}^{2}}{\mathrm{r}}=\frac{\mathrm{u}^{2} 2 \pi}{\mathrm{uT}}=\frac{2 \pi \mathrm{u}}{\mathrm{T}}=\frac{2 \times 3.142 \times 40.3}{2 \times 60}
= {antilog[log(3.142) + log(40.3) – log(60)]}
= {antilog(0.4972 + 1.6053 – 1.7782)}
= {antilog(0.3243)}
= 2.110.
∴ a = 2.11 m/s2
The magnitude of acceleration is 2.11 m/s2.

Question 48.
A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track if the car has uniform centripetal acceleration of π2/s2.
Solution:
Given: 5 rounds = 2πr(5),
t = 2minutes = 120s
To find: Radius (r)
Formula: acp = ω2r
Calculation: From formula,
acp = ω2r
∴ π2 = \frac{\mathrm{v}^{2}}{\mathrm{r}}
But v = \frac{2 \pi r(5)}{t}=\frac{10 \pi r}{t}
∴ π2 = \frac{100 \pi^{2} \mathrm{r}^{2}}{\mathrm{rt}^{2}}
∴ r = \frac{120 \times 120}{100} =144m
The radius of the track is 144 m.

Question 49.
A car of mass 1500 kg rounds a curve of radius 250m at 90 km/hour. Calculate the centripetal force acting on it.
Solution:
Given: m= 1500 kg, r = 250m,
v = 90 km/h = 90 × \frac{5}{18} = 25m/s
To find: Centripetal force (FCP)
Formula: FCP = \frac{\mathrm{mv}^{2}}{\mathrm{r}}
Calculation: From formula,
FCP = \frac{1500 \times(25)^{2}}{250}
∴ FCP = 3750 N
The centripetal force acting on the car is 3750 N.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 50.
A one kg mass tied at the end of the string 0.5 m long is whirled ¡n a horizontal circle, the other end of the string being fixed. The breaking tension in the string is 50 N. Find the greatest speed that can be given to the mass.
Solution:
Given: Breaking tension, F = 50 N,
m = 1 kg, r = 0.5m
To find: Maximum speed (vmax)
Formula: B.T (F) = max. C.F \frac{m v_{\max }^{2}}{r}
Calculation: From formula,
v2max = \frac{F \times r}{m}
∴ v2max = \frac{50 \times 0.5}{1}
∴ vmax = \sqrt{50 \times 0.5} = 5 m/s
The greatest speed that can be given to the mass is 5 m/s.

Question 51.
A mass of 5 kg is tied at the end of a string 1.2 m long revolving in a horizontal circle. If the breaking tension in the string is 300 N, find the maximum number of revolutions per minute the mass can make.
Solution:
Given: Length of the string, r = 1.2 m,
Mass attached. m = 5 kg,
Breaking tension, T = 300 N
To find: Maximum number of revolutions per minute (nmax)
Formula: Tmax = Fmax = mrω2max
Calculation: From formula,
∴ 5 × 1.2 × (2πn)2 = 300
∴ 5 × 1.2 × 4π2n2 = 300
∴ n2max = \frac{300}{4 \times(3.142)^{2} \times 6.0} = 1.26618
∴nmax = \sqrt{1.26618} = 1.125 rev/s
∴ nmax = 1.125 × 60
∴ nmax = 67.5 rev/min
The maximum number of revolutions per minute made by the mass is 67.5 rev /min.

Question 52.
A coin placed on a revolving disc, with its centre at a distance of 6 cm from the axis of rotation just slips off when the speed of the revolving disc exceeds 45 r.p.m. What should be the maximum angular speed of the disc, so that when the coin is at a distance of 12 cm from the axis of rotation, it does not slip?
Solution:
Given. r1 = 6cm, r2 = 12cm, n1 = 45 r.p.m
To Find: Maximum angular speed (n2)
Formula: Max. C.F = mrω2
Calculation: Since, mr1ω12 mr2ω22 [As mass is constant]
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 37
The maximum angular speed of the disc should be 31.8 r.p.m.

Question 53.
A stone of mass 0.25 kg tied to the end of a string is whirled in a circle of radius 1.5 m with a speed of 40 revolutions/min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?
Solution:
Given: m = 0.25 kg, r.= 1.5 m, Tmax = 200 N,
n = 40 rev. min-1 = \frac{40}{60} rev s-1
To find: i) Tension (T)
ii) Maximum speed (vmax)
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 38
i) The tension in the string is 6.55 N.
ii) The maximum speed with which the stone can be whirled around is 34.64 m s-1.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 54.
In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a vertical axis, calculate tension in the string. (g = 9.8 m/s2)
Solution:
Given: l = 120 cm = 1.2rn, r = 0.2m,
m = 150 g = 0.15 kg
To find: Tension in the string (T)
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 39
∴ Substituting in formula,
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 40
Tension in the string is 1.491 N.

Question 55.
A conical pendulum has length 50 cm. Its bob of mass 100 g performs uniform circular motion in horizontal plane, so as to have radius of path 30 cm. Find
i) The angle made by the string with vertical
ii) The tension in the supporting thread and
iii) The speed of bob.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 41
Given: l = 150 cm = 0.5 m, r = 30 cm = 0.3 m,
m = 100 g = 100 × 10-3 kg = 0.1 kg
To find: i) Angle made by the string with vertical (θ)
ii) Tension in the supporting thread (T)
iii) Speed of bob (y)

Formulae: i) tan θ = –\frac{r}{\mathrm{~h}}
ii) tan θ = \frac{\mathrm{v}^{2}}{\mathrm{rg}}

Calculation: By Pythagoras theorem, l2 = r2 + h2
h2 = l2 – r2
h2 = 0.25 – 0.09 = 0.16
h = 0.4m
i) From formula (1),
tan θ = \frac{0.3}{0.4} = 0.75
∴ θ = tan-1 (0.75)
θ = 36°52’

ii) The weight of bob is balanced by vertical component of tension T
∴ T cos θ = mg
cos θ = \frac{\mathrm{h}}{l}=\frac{0.4}{0.5} = 0.8
∴ T = \frac{\mathrm{mg}}{\cos \theta}=\frac{0.1 \times 9.8}{0.8}
∴ T = 1.225 N

iii) From formula (2),
v2 = rg tan θ
∴ v2 = 0.3 × 9.8 × 0.75 = 2.205
∴ v = 1.485 m/s

i) Angle made by the string with vertical is 36°52′. ‘
ii) Tension in the supporting thread is 1.225 N.
iii) Speed of the bob is 1.485 m/s

Apply Your Knowledge

Question 56.
Explain the variation of acceleration, velocity and distance with time for an object under free fall.
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 42
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 43

  1. For a free falling object, considering the downward direction as negative, the object is released from rest.
    ∴ initial velocity u = 0 and a = -g = -9.8 m/s2
    ∴ The kinematical equations become,
    v = u + at = 0 – gt = -gt = -9.8t
    s = ut + \frac{1}{2}at2 = o + \frac{1}{2}(-g)t2 = –\frac{1}{2} 9.8t2
    = -4.9t2
    v2 = u2 + 2as = 0 + 2(-g)s
    = -2gs = -2 × 9.8s
    = -19.6s
  2. These equations give the velocity and the distance travelled as a function of time and also the variation of velocity with distance.
  3. The variation of acceleration, velocity and distance with the time is as shown in figure a, b and c respectively.

Question 57.
The position-time (x – t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in figure. Choose the correct entries in the brackets below.
i) (A/B) lives closer to the school than (B/A)
ii) (A/B) starts from the school earlier than (B/A)
iii) (A/B) walks faster than (B/A)
iv) A and B reach home at the (same/different) time
v) (A/B) overtakes (B/A) on the road (once/twice)
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 44
Answer:

  1. A lives closer to the school than B. This is because, OQ > OP, hence B has to cover larger distance than A.
  2. A starts from the school earlier than B. This is because, A starts at t = 0 whereas B starts at some finite time greater than zero.
  3. As slope of B is greater than that of A, hence B walks faster than A. iv. A and B reach home at different times.
  4. This is because the value of ‘t’ corresponding to P and Q for A and B respectively is different.
  5. B overtakes A on the road once. This is because A and B meet each other only once on their way back home. As B starts from school later than A and walks faster than A, hence B overtakes A once on his way home.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 58.
A bowler throws the ball up to correct distance by controlling his velocity and angle of throw, as shown in the figure given below
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 45
i) What will be the range of the projectile?
ii) What will be the height of the projectile from ground?
Answer:

  1. Range of projectile is given by,
    R = \frac{u^{2} \sin 2 \theta}{g}=\frac{6^{2} \times \sin (2 \times 30)}{9.8}
    R = 3.18 m
  2. Height of projectile is given by,
    H = \frac{\mathrm{u}^{2} \sin ^{2} \theta}{2 \mathrm{~g}}=\frac{6^{2} \times \sin ^{2} 30}{2 \times 9.8} = 0.46m
    Height achieved by ball from ground is
    H = 0.46 + 1 = 1.46m

i) The range of the projectile is 3.18 m.
ii) The height of the projectile is 1.46 m.

Question 59.
A child takes reading of two cars running on highway, for his school project. He draws a position-time graph of the two cars as shown in the figure
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 46
i) What is the velocity of two cars when they meet together?
ii) What is the difference in velocities of the two cars when they cover their maximum distance?
iii) What will be acceleration of the two cars in first 20 s?
Solution:
i) According to graph, the velocity of two cars when they meet each other are,
x = 70m
t = 308
v = \frac{x}{t}=\frac{70}{30} = 2.33 m/s

ii) According to graph, for maximum distance.
For 1st car,
x1 = 120m
t1 = 50 s
v1 = \frac{x_{1}}{t_{1}}=\frac{120}{50}
v1 = 2.4 m/s

For 2nd car,
x2 = 90 m
t2 = 60 s
v2 = \frac{x_{2}}{t_{2}}=\frac{90}{60}
v2 = 1.5 m/s
Difference in velocities is given by,
v1 – v2 = 2.4 – 1.5 = 0.9 m/s

iii) According to graph,
Acceleration of 1st car in first 20 s
v1 = \frac{\mathrm{x}_{1}}{\mathrm{t}}
v1 = \frac{60}{20}
v1 = 3 m/s
a1 = \frac{\mathrm{v}_{1}}{\mathrm{t}}=\frac{3}{20}
a1 = 0.15 m/s2
Acceleration of 2nd car in first 20 s
v2 = \frac{\mathrm{x}_{2}}{\mathrm{t}}
v2 = \frac{40}{20}
v2 = 2 m/s
a2 = \frac{\mathrm{v}_{2}}{\mathrm{t}}=\frac{2}{20}
a2 = 0.1 m/s2
Now,
a1 – a2 = 0.15 – 0.1
= 0.05 m/s2

i) The velocity of two cars when they meet together is 2.33 m/s.
ii) The difference in velocities of two cars when they cover maximum distance is 0.9 m/s.
iii) The accelerator of two cars in 20 s is 0.05 m/s2.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 60.
The speed of a projectile u reduces by 50% on reaching maximum height. What is the range on the horizontal plane?
Solution:
If θ is the angle of projection, then velocity of projectile at height point = u cos θ
u cos θ = \frac{50}{100} u = \frac{1}{2} u
or cos θ = \frac{1}{2} cos 60°
or θ = 60°
Horizontal range,
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 47

Question 61.
In projectile motion, vertical motion and horizontal motion are dependent of each other. Yes or No? Justify your answer.
Answer:
No. In projectile motion, the horizontal and vertical motion are independent of each other because both motions don’t affect each other.

Question 62.
In angular projection of a projectile, at highest point, what will be the components of horizontal and vertical velocities?
Answer:
At highest point of angular projection of a projectile, the horizontal component of its velocity is non zero and the vertical component of its velocity is momentarily zero.

Question 63.
What angle will be described between velocity and acceleration at highest point of projectile path?
Answer:
At highest point of projectile path, the angle between velocity and acceleration is 90°.

Quick Review

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 48
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 49
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 50

Multiple Choice Questions

Question 1.
The velocity-time relation of a particle starting from rest is given by v = kt where k = 2 m/s2. The distance travelled in 3 sec is
(A) 9 m
(B) 16 m
(C) 27 m
(D) 36 m
Answer:
(A) 9 m

Question 2.
If the particle is at rest, then the x – t graph can be only
(A) parallel to position – axis
(B) parallel to time – axis
(C) inclined with acute angle
(D) inclined with obtuse angle
Answer:
(B) parallel to time – axis

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 3.
A body is thrown vertically upwards, maximum height is reached, then it will have
(A) zero velocity and zero acceleration.
(B) zero velocity and finite acceleration.
(C) finite velocity and zero acceleration.
(D) finite velocity and finite acceleration.
Answer:
(B) zero velocity and finite acceleration.

Question 4.
Which of the following is NOT a projectile?
(A) A bullet fired from gun.
(B) A shell fired from cannon.
(C) A hammer thrown by athlete.
(D) An aeroplane in flight.
Answer:
(D) An aeroplane in flight.

Question 5.
The range of projectile is 1 .5 km when it is projected at an angle of 15° with horizontal. What will be its range when it is projected at an angle of 45° with the horizontal?
(A) 0.75 km
(B) 1.5 km
(C) 3 km
(D) 6 km
Answer:
(C) 3 km

Question 6.
Which of the following remains constant for a projectile fired from the earth?
(A) Momentum
(B) Kinetic energy
(C) Vertical component of velocity
(D) Horizontal component of velocity
Answer:
(D) Horizontal component of velocity

Question 7.
In case of a projectile, what is the angle between the instantaneous velocity and acceleration at the highest point?
(A) 45°
(B) 1800
(C) 90°
(D) 0°
Answer:
(C) 90°

Question 8.
A player kicks up a ball at an angle θ with the horizontal. The horizontal range is maximum when θ is equal to
(A) 30°
(B) 45°
(C) 60°
(D) 90°
Answer:
(B) 45°

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 9.
The greatest height to which a man can throw a stone is h. The greatest distance to which he can throw it will be
(A) h/2
(B) 2h
(C) h
(D) 3h
Answer:
(B) 2h

Question 10.
Two balls are projected at an angle θ and (90° – θ) to the horizontal with the same speed. The ratio of their maximum vertical
heights is
(A) 1 : 1
(B) tan θ : 1
(C) 1 : tan θ
(D) tan2 θ : 1
Answer:
(D) tan2 θ : 1

Question 11.
When air resistance is taken into account while dealing with the motion of the projectile, to achieve maximum horizontal range, the angle of projection should be,
(A) equal to 45°
(B) less than 45°
(C) greater than 90°
(D) greater than 45°
Answer:
(D) greater than 45°

Question 12.
The maximum height attained by projectile is found to be equal to 0.433 of the horizontal range. The angle of projection of this projectile is
(A) 30°
(B) 45°
(C) 60°
(D) 75°
Answer:
(C) 60°

Question 13.
A projectile is thrown with an initial velocity of 50 m/s. The maximum horizontal distance which this projectile can travel is
(A) 64m
(B) 128m
(C) 5m
(D) 255m
Answer:
(D) 255m

Question 14.
A jet airplane travelling at the speed of 500 kmh-1 ejects the burnt gases at the speed of 1400 kmh-1 relative to the jet airplane. The speed of burnt gases relative to stationary observer on the earth is
(A) 2.8 kmh-1
(B) 190 kmh-1
(C) 700 kmh-1
(D) 900 kmh-1
Answer:
(D) 900 kmh-1

Question 15.
A projectile projected with certain angle reaches ground with
(A) double angle
(B) same angle
(C) greater than 90°
(D) angle between 90° and 180°
Answer:
(B) same angle

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 16.
The time period of conical pendulum is _________.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 51
Answer:
(C) 2 \pi \sqrt{\frac{l \cos \theta}{\mathrm{g}}}

Question 17.
A projectile projected with certain velocity reaches ground with (magnitude)
(A) zero velocity
(B) smaller velocity
(C) same velocity
(D) greater velocity
Answer:
(C) same velocity

Question 18.
The period of a conical pendulum in terms of its length (l), semivertical angle (θ) and acceleration due to gravity (g) is:
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 52
Answer:
(C) 4 \pi \sqrt{\frac{l \cos \theta}{4 \mathrm{~g}}}

Question 19.
Consider a simple pendulum of length 1 m. Its bob performs a circular motion in horizontal plane with its string making an angle 600 with the vertical. The period of rotation of the bob is(Take g = 10 m/s2)
(A) 2s
(B) 1.4s
(C) 1.98 s
(D) none of these
Answer:
(B) 1.4s

Question 20.
The period of a conical pendulum is
(A) equal to that of a simple pendulum of same length l.
(B) more than that of a simple pendulum of same length l.
(C) less than that of a simple pendulum of same length l.
(D) independent of length of pendulum.
Answer:
(C) less than that of a simple pendulum of same length l.

Competitive Corner

Question 1.
Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be:
(A) rB : rA
(B) 1 : 1
(C) rA : rB
(D) vA : vB
Answer:
(B) 1 : 1
Hint:
Time period of rotation (A and B) is same
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 53

Question 2.
When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60° with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30° and the same object is shot with the same velocity, it can travel x2 distance. Then x1 : x2 will be:
(A) 1 : \sqrt {3}
(B) 1 : 2\sqrt {3}
(C) 1 : \sqrt {2}
(D) \sqrt {3} : 1
Answer:
(A) 1 : \sqrt {3}
Hint:
v2 = u2 + 2as
∴ v2 = u2 + 2 g sin θ x
sin θ. x = constant
∴ x ∝ \frac{1}{\sin \theta}
\frac{x_{1}}{x_{2}}=\frac{\sin \theta_{2}}{\sin \theta_{1}}=\frac{1 / 2}{\sqrt{3} / 2} = 1 : \sqrt {3}

Question 3.
A person travelling in a straight line moves with a constant velocity v1 for certain distance x’ and with a constant velocity v2 for next equal distance. The average velocity y is given by the relation
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 54
Answer:
(C) \frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}
Hint:
Let, t’ be the time taken to travel distance ‘x’ with constant velocity ‘v1
∴ t1 = \frac{\mathrm{x}}{\mathrm{v}_{2}}
Let ‘t2’ be the time taken to travel equal distance ‘x’ with constant velocity ‘v2
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 55

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 4.
Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200 m, with the same velocity of 25 m/s. When and where will the two bullets collide? (g = 10 m/s2)
(A) They will not collide
(B) After 2 s at a height of 180 m
(C) After 2 s at a height of 20 m
(D) After 4 s at a height of 120 m
Answer:
(B) After 2 s at a height of 180 m
Hint:
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 56
Let the bullets collide at time t
The horizontal displacement x1 and x2 is given by the equation
x1 = ut and x2 = ut
∴ x1 + x2 = 100
∴ 25t + 25t = 100
∴ t = 2s
Vertical displacement ‘y’ is given by
y = \frac{1}{2} gt2 = \frac{1}{2} × 10 × 22 = 20m
∴ h = 200 – 20= 180m

Question 5.
A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field \vec{E}. Due to the force q\vec{E}, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively
(A) 2 m/s, 4 m/s
(B) 1 m/s, 3 m/s
(C) 1 m/s, 3.5 m/s
(D) 1.5 m/s, 3 m/s
Answer:
(B) 1 m/s, 3 m/s
Hint:
Car at rest attains velocity of 6 m/s in t1 = 1 s.
Now as direction of field is reversed, velocity of car will reduce to 0 m/s in next 1 s. i.e., at t2 = 2 s. But, it continues to move for next one second. This will give velocity of -6 m/s to car at t3 = 3 s.
Using this data, plot of velocity versus time will be
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 57

Question 6.
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 58
Answer:
(D)
Hint:
The graphs (A), (B) and (C) represent the uniformly retarded motion, i.e., velocity decreases uniformly. However, the slope of the curve in graph (D), indicates increasing velocity. Hence, graph (D) is incorrect.

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 7.
A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then:
(A) T ∝ R(n+1)/2
(B) T ∝ Rn/2
(C) T ∝ R3/2 for any n
(D) T ∝ R\frac{n}{2}+1
Answer:
(A) T ∝ R(n+1)/2
Hint:
The centripetal force acting on the particle is provided by the central force,
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 59

Question 8.
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be:
(A) \frac{\mathrm{t}_{1}+\mathrm{t}_{2}}{2}
(B) \frac{t_{1} t_{2}}{t_{2}-t_{1}}
(C) \frac{\mathbf{t}_{1} t_{2}}{\mathbf{t}_{2}+t_{1}}
(D) t1 – t2
Answer:
(C) \frac{\mathbf{t}_{1} t_{2}}{\mathbf{t}_{2}+t_{1}}
Hint:
Let velocity of Preeti be v1, velocity of escalator be v2 and distance travelled be L.
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 60

Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane

Question 9.
A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?
Maharashtra Board Class 11 Physics Important Questions Chapter 3 Motion in a Plane 61
Answer:
(A)
Hint:
If a body is projected in vertically upward direction, then its acceleration is constant and negative. If direction of motion is positive i.e.. vertically up) and initial position of body is taken as origin, then the velocity decreases uniformly. At highest point its velocity is equal to zero and then it accelerates uniformly downwards returning to its reference position.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Balbharti Maharashtra State Board 11th Physics Important Questions Chapter 1 Units and Measurements Important Questions and Answers.

Maharashtra State Board 11th Physics Important Questions Chapter 1 Units and Measurements

Question 1.
What is a measurement? How is measured quantity expressed?
Answer:

  1. A measurement is a comparison with internationally accepted standard measuring unit.
  2. The measured quantity (M) is expressed in terms of a number (n) followed by a corresponding unit (u) i.e., M = nu.

Example:
Length of a wire when expressed as 2 m, it means value of length is 2 in the unit of m (metre).

Question 2.
State true or false. If false correct the statement and rewrite. Different quantities are measured in different units.
Answer: True.
[Note: Choice of unit depends upon its suitability for measuring the magnitude of a physical quantity under consideration. Hence, we choose different scales for same physical quantity.]

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 3.
Describe briefly different types of systems of units.
Answer:
System of units are classified mainly into four types:

  1. C.G.S. system:
    It stands for Centimetre-Gram-Second system. In this system, length, mass and time are measured in centimetre, gram and second respectively.
  2. M.K.S. system:
    It stands for Metre-Kilogram-Second system. In this system, length, mass and time are measured in metre, kilogram and second respectively.
  3. F.P.S. system:
    It stands for Foot-Pound-Second system. In this system, length, mass and time are measured in foot, pound and second respectively.
  4. S.I. system:
    It stands for System International. This system has replaced all other systems mentioned above. It has been internationally accepted and is being used all over world. As the SI units use decimal system, conversion within the system is very simple and convenient.

Question 4.
What are fundamental quantities? State two examples of fundamental quantities. Write their S.J. and C.G.S. units.
Answer:
Fundamental quantities:
The physical quantities which do not depend on any other physical quantity for their measurements i.e., they can be directly measured are called fundamental quantities.
Examples: mass, length etc.
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 1

Question 5.
What are fundamental units? State the S.l. units of seven fundamental quantities.
Answer:
Fundamental units:
The units used to measure fundamental quantities are called fundamental units.
S.I. Units of fundamental quantities:
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 2

Question 6.
State and describe the two supplementary units.
Answer:
The two supplementary units are:
i) Plane angle (dθ):
a. The ratio of kngth of arc (ds) of an circle to the radius (r) of the circle is called as Plane angle (dθ)
i.e., dθ = \frac{\mathrm{ds}}{\mathrm{r}}
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 3
b. Thus, dθ is angle subtended by the arc at the centre of the circle.
c. Unit: radian (rad)
d. Denoted as θc
e. Length of arc of circle = Circumference of circle = 2πr.
∴ plane angle subtended by entire circle at its centre is θ = \frac{2 \pi \mathrm{r}}{\mathrm{r}} = 2πc

ii) Solid angle (dΩ):
a. solid angle is 3-dimensional analogue of plane angle.
b. Solid angle is defined as area of a portion of surface of a sphere to the square of radius of the sphere.
i.e., dΩ = \frac{\mathrm{d} \mathrm{A}}{\mathrm{r}^{2}}
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 4
c. Unit: Steradian (sr)
d. Denoted as (Ω)
e. Surface area of sphere = 4πr2
∴ solid angle subtended by entire sphere at its centre is Ω = \frac{4 \pi r^{2}}{r^{2}} = 4π sr

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 7.
Derive the relation between radian and degree. Also find out 1” and 1’ in terms of their respective values in radian. (Take π = 3.1416)
Answer:
We know that, 2 πc = 360°
∴ πc = 180°
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 5

Question 8.
What are derived quantities and derived units? State two examples. State the corresponding S.L. and C.G.S. units of the examples.
Answer:

  1. Derived quantities: Physical qUantities other than fundamental quantities which depend on one or more fundamental quantities for their measurements are called derived quantities.
  2. Derived units: The units of derived quantities which are expressed in terms of fundamental units for their measurements are called derived units.
  3. Examples and units:
    Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 6

Question 9.
Classify the following quantities into fundamental and derived quantities: Length, Velocity, Area, Electric current, Acceleration, Time, Force, Momentum, Energy, Temperature, Mass, Pressure, Magnetic induction, Density.
Answer:
Fundamental Quantities: Length, Electric current, Time, Temperature, Mass.

Derived Quantities: Velocity, Area, Acceleration, Force, Momentum, Energy. Pressure, Magnetic induction, Density

Question 10.
Classify the following units into fundamental, supplementary and derived units:
newton, metre, candela, radian, hertz. square metre, tesla, ampere, kelvin, volt, mol, coulomb, farad, steradian.
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 7

Question 11.
List the conventions followed while using SI units.
Answer:
Following conventions should be followed while writing S.I. units of physical quantities:

  1. Unit of every physical quantity should be represented by its symbol.
  2. Full name of a unit always starts with smaller letter even if it is named after a person, eg.: 1 newton, 1 joule, etc. But symbol for unit named after a person should be in capital letter, eg.: N after scientist Newton, J after scientist Joule, etc.
  3. Symbols for units do not take plural form.
  4. Symbols for units do not contain any full stops at the end of recommended letter.
  5. The units of physical quantities in numerator and denominator should be written as one ratio. For example the SI unit of acceleration is m/s2 or m s-2 but not m/s/s.
  6. Use of combination of units and symbols for units is avoided when physical quantity is expressed by combination of two. For example, The unit J/kg K is correct while joule/kg K is not correct.
  7. A prefix symbol is used before the symbol of the unit.
    • a. Prefix symbol and symbol of unit constitute a new symbol for the unit which can be raised to a positive or negative power of 10.
      For example,
      1 ms = 1 millisecond = 10-3 s
      1 μs = 1 microsecond = 10-6 s
      1 ns = 1 nanosecond = 10-9 s
    • b. Use of double prefixes is avoided when single prefix is available
      10-6 s = 1 μs and not 1 mms
      10-9 s = 1 ns and not 1 mμs
  8. Space or hyphen must be introduced while indicating multiplication of two units e.g., m/s should be written as m s-1 or m-s-1.

Solved Examples

Question 12.
What is the solid angle subtended by the moon at any point of the Earth, given the diameter of the moon is 3474 km and its distance from the Earth 3.84 × 108 m?
Solution:
Given: Diameter (D) = 3474 km
∴ Radius of moon (R) = 1737 km
= 1.737 × 106 m
Distance from Earth r = 3.84 × 108 m
To find: Solid angle (dΩ)
Formula: dΩ = \frac{\mathrm{d} \mathrm{A}}{\mathrm{r}^{2}}

Calculation:
From formula,
dΩ = \frac{\pi \mathrm{R}^{2}}{\mathrm{r}^{2}} ……..( cross-sectional area of disc of moon = πR2)
dΩ = \frac{\pi \times\left(1.737 \times 10^{5}\right)^{2}}{\left(3.84 \times 10^{8}\right)^{2}}
= \frac{3.412 \times(1.737)^{2} \times 10^{10}}{(3.84)^{2} \times 10^{16}}
= antilog{log(3.142) + 2log(1.737) – 2log(3.84)} × 10-6
= antilog {0.4972 + 2(0.2397) – 2(0.5843)} × 10-6
= antilog{0.4972 + 0.4794 – 1.1686} × 10-6
= antilog{\overline{1} .8080} × 10-6
= 6.428 × 10-1 × 10-6
= 6.43 × 10-5 sr
Solid angle subtended by moon at Earth is 6.43 × 10-5 sr
[Note: Above answer is obtained substituting value of r as 3.142]

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 13.
Pluto has mean diameter of 2,300 km and very eccentric orbit (oval shaped) around the Sun, with a perihelion (nearest) distance of 4.4 × 109 km and an aphelion (farthest) distance of 7.3 × 109 km. What are the respective solid angles subtended by Pluto from Earth’s perspective? Assume that distance from the Sun can be neglected.
Solution:
Given: Radius of Pluto. R = \frac{2300}{2} km
= 1150km
Perihelion distance rp = 4.4 × 109 km
Aphelion distance ra = 7.3 × 109 km
To find: Solid angles (dΩp and dΩa)
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 8
Solid angle at perihelion distance is 2.146 × 10-13 sr and at aphelion distance is 7.798 × 10-14 sr.

Question 14.
Define a metre.
Answer:
The metre is the length of the path travelled by light in vacuum during a time interval of 1/299, 792, 458 of a second.
Answer:

Question 15.
What ¡s parallax?
Answer:

  1. Parallax is defined as the apparent change in position of an object due to a change in position of an observer.
  2. Explanation: When a pencil is held in front of our eyes and we look at it once with our left eye closed and then with our right eye closed, pencil appears to move against the background. This effect is called parallax effect.

Question 16.
What is parallax angle?
Answer:
i) Angle between the two directions along which a star or planet is viewed at the two points of observation is called parallax angle (parallactic angle).
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 9
ii) It is given by θ = \frac{b}{D}
where, b = Separation between two points of observation.
D = Distance of source from any point of observation.

Question 17.
Explain the method to determine distance of a planet from the Earth.
Answer:

  1. Parallax method is used to determine distance of different planets from the Earth.
  2. To measure the distance ‘D’ of a far distant planet S, select two different observatories (E1 and E2).
  3. The planet should be visible from E1 and E2 observatories simultaneously i.e. at the same time.
  4. E1 and E2 are separated by distance ‘b’ shown in figure.
    ∴ E1E3 = b
    Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 10
  5. The angle between the two directions along which the planet is viewed, can be measured. It is parallax angle, which in this case is L ∠E1E2 = θ
  6. The planet is far away from the (Earth) observers, hence
    b < <D
    \frac{b}{D} < < 1 and ‘θ’ is also very small.
    Hence, E1E2 can be considered as arc of length b of circle with S as centre and D as radius.
    :. E1S = E2S = D
    ∴ θ = \frac{b}{D} . . . .(θ is taken in radian)
    ∴ D = \frac{b}{\theta}
    Thus, the distance ‘D’ of a far away planet ‘S’ can be determined using the parallax method.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 18.
Explain how parallax method is used to measure distance of a star from Earth.
Answer:

  1. The parallax measured from two farthest distance points on Earth for stars will be too small and hence cannot be measured.
  2. Instead, parallax between two farthest points (i.e., 2 ΔU apart) along the orbit of Earth around the Sun (s) is measured.
    Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 11

Question 19.
Explain how size of a planet or star is measured.
Answer:

  1. To determine the diameter (d) of a planet or star, two diametrically opposite points of the planet are viewed from the same observatory.
  2. If d is diameter of planet or star, angle subtended by it at any single point on the Earth is called angular diameter of planet.
  3. Let angle α be angle between these two directions.
  4. If distance between the Earth and planet or star (D) is known, α = \frac{\mathrm{d}}{\mathrm{D}}
  5. This relation gives, d = α D
    Thus, diameter (d) of planet or star can be determined.

Question 20.
Name the devices used to measure very small distances such as atomic size.
Answer:
Devices used are:
Electron microscope, tunnelling electron microscope.

Question 21.
Just as large distances are measured in AU, parsec or light year, atomic or nuclear distances are measured with the help of microscopic units. Match the units given in column A with their corresponding SI unit given in column B.
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 39
Answer:
i. – (b)
ii. – (a)

Solved Examples

Question 22.
A star is 5.5 light years away from the Earth. How much parallax in arcsec will it subtend when viewed from two opposite points along the orbit of the Earth?
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 12
Solution:
Two opposite points-A and B along the orbit of the Earth are 2 AU apart. The angle subtended by AB at the position of the star is
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 13
= antilog{log(2.992) – log(5.5) – log(9.46)} × 10-4
= antilog {0.4761 – 0.7404 – 0.9759} × 10-4
= antilog {\overline{2}.7598} × 10-4
= 5.751 × 10-2 × 10-4
= 5.75 × 10-6
= 5.75 × 10-6 rad
= 5.75 × 10-6 × 57.297 × 60 × 60 arcsec
…. (converting radian into arcsecond)
= 1.186 arcsec
Parallax is 1.186 arcsec

Question 23.
The moon is at a distance of 3.84 × 108 m from the Earth. If viewed from two diametrically opposite points on the Earth, the angle subtended at the moon is 1° 54′. What is the diameter of the Earth?
Solution:
Given
Distance (D) = 3.84 × 108 m
Subtended angle (α)
= 1° 54′ = (60’+ 54′)= 114′
= 114 × 2.91 × 10-4 rad
= 3.317 × 10-2 rad
To find: Diameter of Earth (d)
Formula: d = αD
Calculation: From formula,
d = 3.317 × 10-2 × 3.84 × 108
= 1.274 × 107 m
Diameter of Earth is 1.274 × 107 m.

Question 24.
Explain the method to measure mass.
Answer:
Method for measurement of mass:

  1. Mass, until recently, was measured with a standard mass of the international prototype of the kilogram (a platinum-iridium alloy cylinder) kept at international Bureau of Weights and Measures, at Serves, near Paris, France.
  2. As platinum – iridium piece was seen to pick up microparticles and found to be affected by atmosphere, its mass could no longer be treated as constant.
  3. Hence, a new definition of mass was introduced in terms of electric current on 20th May 2019.
  4. Now, one kilogram mass is described in terms of amount of current which has to be passed through electromagnet to pull one side of extremely sensitive balance to balance the other side which holds one standard kg mass.
  5. To measure mass of small entities such as atoms and nucleus, atomic mass unit (amu) is used.
    It is defined as (\frac{1}{12})th mass of an unexcited atom of carbon -12(C12).
    1 amu ≈ 1.66 × 10-27 kg.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 25.
That can he the reason for choosing Carbon-12 to define atomic mass unit?
Answer:

  1. Unlike oxygen and hydrogen, which exhibit various isotopes in higher proportions, carbon- 12 is the single most abundant (98% of available carbon) isotope of carbon.
  2. it is also very stable.
    Hence, it makes more accurate unit of measuring mass and is used to define atomic mass unit.

Question 26.
Define mean solar day. Explain the method for measurement of time.
Answer:

  1. A mean solar day is the average time interval from one noon to the next noon.
    Method for measurement of time:
  2. The unit of time, the second, was considered to be \frac{1}{86400} of the mean solar day, where a mean solar day = 24 hours
    = 24 × 60 × 60
    = 86400 s
  3. However, this definition proved to be unsatisfactory to define the unit of time precisely because solar day varies gradually due to gradual slowing down of the Earth’s rotation. Hence, the definition of second was replaced by one based on atomic standard of time.
  4. Atomic standard of time is now used for the measurement of time. In atomic standard of time, periodic vibrations of caesium atom is used.
  5. One second is time required for 9,192.631,770 vibrations of the radiation corresponding to transition between two hyperfine energy states of caesium-133 (Cs- 133) atom.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 27.
Define dimensions and dimensional formula of physical quantities. Give few examples of dimensional formula.
Answer:

  1. Dimensions:
    The dimensions of a physical quantity are the powers to which the fundamental units must be raised in order to obtain the unit of a given physical quantity.
  2. Dimensional formula:
    When any derived quantity is represented with appropriate powers of symbols of the fundamental quantities, SUCh an expression is called dimensional formula.
    It is expressed by square bracket with no comma in between the symbols.
  3. Examples of dimensional formula:
    a. Speed = \frac{\text { Distance }}{\text { time }}
    ∴ Dimensions of speed = \frac{[\mathrm{L}]}{[\mathrm{T}]} = [L1M0T-1]
    [Note: As power of M is zero, it can be omitted from dimensional formula. Therefore, dimensions of speed can be written as [L1T1]
    Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 14

Question 28.
A book with many printing errors contains four different formulae for the displacement y of a particle undergoing a certain periodic function:
i) y = a sin \frac{2 \pi t}{T}
ii) y = a sin v t
iii) y = \frac{\mathrm{a}}{\mathbf{T}} \sin \frac{\mathrm{t}}{\mathrm{a}}
iv) y = \frac{a}{\sqrt{2}}\left[\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right]
Here, a is maximum displacement of particle, y ¡s speed of particle, T is time period of motion. Rule out the wrong formulae on dimensional grounds.
Answer:
The argument of trigonometrical function, i.e., angle is dimensionless. Now,
i) The argument, \left[\frac{2 \pi \mathrm{t}}{\mathrm{T}}\right]=\frac{[\mathrm{T}]}{[\mathrm{T}]} = 1 = [L0M0T0]
which is a dimensionless quantity.
Hence, formula (i) is correct.

ii) The argument,
[vt] = [LT-1] [T] = [L] = [L1M0T0]
which is not a dimensionless quantity.
Hence, formula (ii) is incorrect.

iii) The argument,
\left[\frac{\mathrm{t}}{\mathrm{a}}\right]=\frac{[\mathrm{T}]}{[\mathrm{L}]} = [L-1M0T1]
which is not a dimensionless quantity.
Hence, formula (iii) is incorrect.

iv) The argument,
\left[\frac{2 \pi \mathrm{t}}{\mathrm{T}}\right]=\frac{[\mathrm{T}]}{[\mathrm{T}]} = 1 = [L0M0T0]
which is a dimensionless quantity.
Hence, formula (iv) is correct.

Question 29.
State principle of homogeneity of dimensions.
Answer:
Principle of homogeneity of dimensions: The dimensions of all the terms on the two sides of a physical equation relating different physical quantities must be same.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 30.
State the uses of dimensional analysis.
Answer:
Uses of dimensional analysis:

To check the correctness of a physical equation.
Correctness of a physical equation by dimensional analysis:

  1. A physical equation is correct only if the dimensions of all the terms on both sides of that equations are the same.
  2. For example, consider the equation of motion.
    v = u + at ……………. (1)
  3. Writing the dimensional formula of every term, we get
    Dimensions of LH.S. [v] [L1M0T-1],
    Dimensions of R.H.S. = [u] + [at]
    = [L1M0T-1] + [L1M0T-2] [L1M0T-1]
    = [L1M0T-1] + [L1M0T-1]
    ⇒ [L.HS.] = [R.H.S.]
  4. As dimensions of both side of equation is same, physical equation is dimensionally correct.

To derive the relationship between related physical quantities.
Expression for time period of a simple pendulum by dimensional analysis:

  1. Time period (T) of a simple pendulum depends upon length (l) and acceleration due to gravity (g) as follows:
    T ∝ la gb
    i.e., T = k la gb ………… (1)
    where, k = proportionality constant, which is dimensionless.
  2. The dimensions of T = [L0M0T1)
    The dimensions of l = [L1M0T0]
    The dimensions of g = [L1M0T2]
    Taking dimensions on both sides of equation (1),
    [L0M0T1] = [L1M0T0]a [L1M0T-2]b
    [L0M0T1] = [La+bM0T-2b]
  3. Equating corresponding power of L, M and T on both sides, we get
    a + b = 0 …………. (2)
    and -2b = 1
    ∴ b = –\frac{1}{2}
  4. Substituting ‘b’ in equation (2), we get
    a = \frac{1}{2}
  5. Substituting values of a and b in equation (1),
    we have,
    Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 15
  6. Experimentally, it ¡s found that k = 2π
    ∴ T = 2π \sqrt{\frac{l}{\mathrm{~g}}}
    This is the required expression for time period of a simple pendulum.

To find the conversion factor between the units of the same physical quantity in two different systems of units.
Conversion factor between units of same physical quantity:

  1. let ‘n’ be the conversion factor between the units of work.
    ∴ 1 J = n erg ………….. (1)
  2. Dimensions of work in S.l. system are \left[\mathrm{L}_{1}^{2} \mathrm{M}_{1}^{\prime} \mathrm{T}_{1}^{-2}\right] and in CGS system are \left[\mathrm{L}_{2}^{2} \mathrm{M}_{2}^{1} \mathrm{~T}_{2}^{-2}\right]
  3. From (1),
    1\left[\mathrm{~L}_{1}^{2} \mathrm{M}_{1}^{1} \mathrm{~T}_{1}^{-2}\right]=\mathrm{n}\left[\mathrm{L}_{2}^{2} \mathrm{M}_{2}^{1} \mathrm{~T}_{2}^{-2}\right]
    Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 16
    n= 104 × 103 × 1 = 107
    Hence, the conversion factor, n = 107
    There fore, from equation (1), we have,
    ∴ 1 J = 107 erg.

Question 31.
Explain the use of dimensional analysis to check the correctness of a physical equation.
Answer:
Correctness of a physical equation by dimensional analysis:

  1. A physical equation is correct only if the dimensions of all the terms on both sides of that equations are the same.
  2. For example, consider the equation of motion.
    v = u + at ……………. (1)
  3. Writing the dimensional formula of every term, we get
    Dimensions of LH.S. [v] [L1M0T-1],
    Dimensions of R.H.S. = [u] + [at]
    = [L1M0T-1] + [L1M0T-2] [L1M0T-1]
    = [L1M0T-1] + [L1M0T-1]
    ⇒ [L.HS.] = [R.H.S.]
  4. As dimensions of both side of equation is same, physical equation is dimensionally correct.

Question 32.
Time period of a simple pendulum depends upon the length of pendulum (l) and acceleration due to gravity (g). Using dimensional analysis, obtain an expression for time period of a simple pendulum.
Answer:
Expression for time period of a simple pendulum by dimensional analysis:
i) Time period (T) of a simple pendulum depends upon length (l) and acceleration due to gravity (g) as follows:
T ∝ la gb
i.e., T = k la gb ………… (1)
where, k = proportionality constant, which is dimensionless.

ii) The dimensions of T = [L0M0T1)
The dimensions of l = [L1M0T0]
The dimensions of g = [L1M0T2]
Taking dimensions on both sides of equation (1),
[L0M0T1] = [L1M0T0]a [L1M0T-2]b
[L0M0T1] = [La+bM0T-2b]

iii) Equating corresponding power of L, M and T
on both sides, we get
a + b = 0 …………. (2)
and -2b = 1
∴ b = –\frac{1}{2}

iv) Substituting ‘b’ in equation (2), we get
a = \frac{1}{2}

v) Substituting values of a and b in equation (1),
we have,
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 15

vi) Experimentally, it ¡s found that k = 2π
∴ T = 2π \sqrt{\frac{l}{\mathrm{~g}}}
This is the required expression for time period of a simple pendulum.

Question 33.
Find the conversion factor between the S.I. and the C.OES. units of work using dimensional analysis.
Answer:
Conversion factor between units of same physical quantity:

  1. let ‘n’ be the conversion factor between the units of work.
    ∴ 1 J = n erg ………….. (1)
  2. Dimensions of work in S.l. system are \left[\mathrm{L}_{1}^{2} \mathrm{M}_{1}^{\prime} \mathrm{T}_{1}^{-2}\right] and in CGS system are \left[\mathrm{L}_{2}^{2} \mathrm{M}_{2}^{1} \mathrm{~T}_{2}^{-2}\right]
  3. From (1),
    1\left[\mathrm{~L}_{1}^{2} \mathrm{M}_{1}^{1} \mathrm{~T}_{1}^{-2}\right]=\mathrm{n}\left[\mathrm{L}_{2}^{2} \mathrm{M}_{2}^{1} \mathrm{~T}_{2}^{-2}\right]
    Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 16
    n= 104 × 103 × 1 = 107
    Hence, the conversion factor, n = 107
    There fore, from equation (1), we have,
    ∴ 1 J = 107 erg.

Question 34.
State the limitations of dimensional analysis.
Answer:
Limitations of dimensional analysis:

  • The value of dimensionless constant can be obtained with the help of experiments only.
  • Dimensional analysis cannot be used to derive relations involving trigonometric (sin θ, cos θ, etc.), exponential (ex, ex2, etc.), and logarithmic functions (log x, log x3, etc) as these quantities are dimensionless.
  • This method is not useful if constant of proportionality is not a dimensionless quantity.
  • If the correct equation contains some more terms of the same dimension, it is not possible to know about their presence using dimensional equation.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 35.
If two quantities have same dimensions, do they always represent the same physical content?
Answer:
When dimensions of two quantities are same, they do not always represent the same physical content.
Example:
Force and momentum both have same dimensions but they represent different physical content.

Question 36.
A dimensionally correct equation need not actually be a correct equation but dimensionally incorrect equation is necessarily wrong. Justify.
Answer:
i) To justify a dimensionally correct equation need not be actually a correct equation, consider equation, v2 = 2as
Dimensions of L.H.S. = [v2] = [L2M0T2]
Dimensions of R.H.S. = [as]= [L2M0T2]
⇒ [L.H.S.] = [R.H.S.]
This implies equation v2 = 2as is dimensionally correct.
But actual equation is, v2 = u2 + 2as
This confirms a dimensionally correct equation need not be actually a correct equation.

ii) To justify dimensionally incorrect equation is necessarily wrong, consider the formula,
\frac{1}{2} mv = mgh
Dimensions of L.H.S. = [mv] = [L1M1T-1]
Dimensions of R.H.S. = [mgh] = [L2M1T-2]
Since the dimensions of R.H.S. and L.H.S. are not equal, the formula given by equation must be incorrect.
This confirms dimensionally incorrect equation is necessarily wrong.

Question 37.
State, whether all constants are dimensionless or unitless.
Answer:
All constants need not be dimensionless or unitless.
Planck’s constant, gravitational constant etc., possess dimensions and units. They are dimensional constants.

Solved Examples

Question 38.
If length ‘L’, force ‘F’ and time ‘T’ are taken as fundamental quantities, what would be the dimensional equation of mass and density?
Solution:
i) Force = Mass × Acceleration Force
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 17
∴ Dimensional equation of mass
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 18
= [F1L-4T2]

i) The dimensional equation of mass is [F1L-1T2].
ii) The dimensional equation of density is [F1L-4T2].

Question 39.
A calorie is a unit of heat and it equals 4.2 J, where 1 J = kg m2 s-2. A distant civilisation employs a system of units in which the units of mass, length and time are α kg, β m and δ s. Also J’ is their unit of energy. What will be the magnitude of calorie in their units?
Solution:
1 cal = 4.2 kg m2 s-2
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 19
New unit of energy is J’
Dimensional formula of energy is [L2M1T-2] According to the question,
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 20

Question 40.
Assume that the speed (v) of sound in air depends upon the pressure (P) and density (ρ) of air, then use dimensional analysis to obtain an expression for the speed of sound.
Solution:
It is given that speed (v) of sound in air depends upon the pressure (P) and density (ρ) of the air.
Hence, we can write, v = k Pa ρb ……….. (1)
where, k is a dimensionless constant and a and b are powers to be determined.
Dimensions of y = [L1M0T-1]
Dimensions of P = [L-1M1T-2]
Dimensions of ρ = [L-3M1T0]
Substituting the dimensions of the quantities on both sides of equation (1),
∴ [L1M0T-1] = [L-1M1T-2]a [L-3M1T0]b
∴ [L1M0T-1] = [L-aMaT-2a] [L-3bMbT0]
∴ [L1M0T-1] = [L-a-3bMa+bT-2a]
Comparing the powers of L, M and T on both sides, we get,
-2a = -1
∴ a = \frac{1}{2}
Also, a + b = O
\frac{1}{2} + b = 0 b = – \frac{1}{2}
Substituting values of a and b in equation (1), we get
y = k P\frac{1}{2} ρ\frac{1}{2}
∴ v = k \sqrt{\frac{\mathrm{p}}{\rho}}

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 41.
Density of oil is 0.8 g cm3 in C.G.S. unit. Find its value in S.I. units.
Solution:
Dimensions of density is [L-3M1T0]
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 21
= 0.8 [10-3] [10-2]-3
= 0.8 [10-3] [10]6
n = 0.8 × 103
Substituting the value of ‘n’ in equation (1).
we get, 0.8 g cm3 = 0.8 × 103 kg m-3.
Density of oil in S.l unit is 0.8 × 103 kg m-3.

Question 42.
The value of G in C.G.S system is 6.67 × 10-8 dyne cm2 g-2. Calculate its value in S.l. system.
Solution:
Dimensional formula of gravitational constant
[L3M-1T-2]
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 22
n = 6.67 × 10-8 × 10-6 × 103
n = 6.67 × 10-11
From equation (1),
6.67 × 10-8 dyne cm2 g-2
= 6.67 × 10-11 N-m2 kg-2
Value ofG in S.l. system is 6.67 × 10-11 N-m2 kg-2.

Question 43.
What is accuracy?
Answer:
Accuracy is how close a measurement is to the actual value of that quantity.

Question 44.
What is precision?
Answer:
Precision is a measure of how consistently a device records nearly identical values i.e., reproducible results.

Question 45.
A scale in a lab measures the mass of object consistently more by 500 g than their actual mass. How would you describe the scale in terms of accuracy and precision?
Answer:
The scale is precise but not accurate.
Explanation: Precision measures how consistently a device records the same answer; even though it displays the wrong value. Hence, the scale is precise.

Accuracy is how well a device measures something against its accepted value. As scale in the lab is always off by 500 g, it is not accurate.
[Note: The goal of the observer should be to get accurate as well as precise measurements.]

Question 46.
List reasons that may introduce possible uncertainties in an observation.
Answer:
Possible uncertainties in an observation may arise due to following reasons:

  1. Quality of instrument used,
  2. Skill of the person doing the experiment,
  3. The method used for measurement,
  4. External or internal factors affecting the result of the experiment.

Question 47.
What is systematic error? Classify errors into different categories.
Answer:

  1. Systematic errors are errors that are not determined by chance but are introduced by an inaccuracy (involving either the observation or measurement process) inherent to the system.
  2. Classification of errors:
    Errors are classified into following two groups:
  3. Systematic errors:
    • Instrumental error (constant error),
    • Error due to imperfection in experimental technique,
    • Personal error (human error).
  4. Random error (accidental error)

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 48.
What is instrumental (constant) error?
Answer:
Instrumental error:

  1. It arises due to defective calibration of an instrument.
  2. Example: If a thermometer is not graduated properly, i.e., one degree on the thermometer actually corresponds to 0.99°, the temperature measured by such a thermometer will differ from its value by a constant amount.

Question 49.
What is error due to imperfection in experimental technique?
Answer:
Error due to imperfection in experimental technique:

  • The errors which occur due to defective setting of an instrument is called error due to imperfection in experimental technique.
  • For example the measured volume of a liquid in a graduated tube will be inaccurate if the tube is not held vertical.

Question 50.
What is personal error?
Answer:
Personal error (Human error):

  • The errors introduced due to fault of an observer taking readings are called personal errors.
  • For example, while measuring the length of an object with a ruler, it is necessary to look at the ruler from directly above. If the observer looks at it from an angle, the measured length will be wrong due to parallax.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 51.
What is random error (accidental)?
Answer:

  1. Random error (accidental):
    The errors which are caused due to minute change in experimental conditions like temperature, pressure change in gas or fluctuation in voltage, while the experiment is being performed are called random errors.
  2. They can be positive or negative.
  3. Random error cannot be eliminated completely but can be minimized by taking multiple observations and calculating their mean.

Question 52.
State general methods to minimise effect of systematic errors.
Answer:
Methods to minimise effect of systematic errors:

  1. By using correct instrument.
  2. Following proper experimental procedure.
  3. Removing personal error.

Question 53.
Define the term:
Arithmetic mean
Answer:
Arithmetic mean:
a. The most probable value of a large number of readings of a quantity is called the arithmetic mean value of the quantity. This value can be considered to be true value of the quantity.

b. If a1, a2, a3, …………… an are ‘n’ number of readings taken for measurement of a quantity, then their mean value is given by,
amean = \frac{a_{1}+a_{2}+\ldots \ldots .+a_{n}}{n}
∴ amean = \frac{1}{n} \sum_{i=1}^{n} a_{i}

Question 54.
What does a = amean ± ∆amean signify?
Answer:
a = amean ± ∆ amean signifies that the actual value of a lies between (amean – ∆ amean) and (amean + ∆ amean).

Question 55.
What is meant by the term combination of errors?
Answer:
Derived quantities may get errors due to individual errors of fundamental quantities, such type of errors are called as combined errors.

Question 56.
Explain errors in sum and in difference of measured quantity.
Answer:
Errors in sum and in difference:
i) Suppose two physical quantities A and B have measured values A ± ∆A and B ± ∆B. respectively, where ∆A and ∆B are their mean absolute errors.

ii) Then, the absolute error ∆Z in their sum.
Z = A + B
Z ± ∆Z = (A ± ∆A) + (B ± ∆B)
= (A + B) ± ∆A ± ∆B
∴ ± ∆Z = ± ∆A ± ∆B.

iii) For difference. i.e.. if Z = A – B.
Z ± ∆Z = A ± ∆A) – (B ± ∆B)
= (A – B) ± ∆A ∓ ∆B
∴ ± ∆Z = ± ∆A ∓ ∆B,

iv) There are four possible values for ∆Z. namely (+∆A – ∆B), (+∆A + ∆B), (-∆A -∆B), (-∆A + ∆B). Hence, maximLim value of absolute error is ∆Z = (∆A+ ∆B) in both the cases.

v) Thus. when two quantities are added or subtracted, the absolute error in the final result is the sum of the absolute errors in the individual quantities.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 57.
Explain errors in product of measured quantity.
Answer:
Errors in product:
i) Suppose Z = AB and measured values of A and B are (A ± ∆A) and (B ± ∆B) then,
Z ± ∆Z = (A ± ∆A) (B ± ∆B)
= AB ± A∆B ± B∆A ± ∆A∆B
Dividing L.H.S by Z and R.H.S. by AB we get
\left(1 \pm \frac{\Delta Z}{Z}\right)=\left[1 \pm \frac{\Delta B}{B} \pm \frac{\Delta A}{A} \pm\left(\frac{\Delta A}{A}\right)\left(\frac{\Delta B}{B}\right)\right]
Since ∆A/A and ∆B/B are very small, product is neglected. Hence, maximum relative error in Z is \frac{\Delta Z}{Z}=\frac{\Delta A}{A}+\frac{\Delta B}{B}

ii) Thus, when two quantities are multiplied, the maximum relative error in the result is the sum of relative errors in each quantity.

Question 58.
Explain errors due to power (index) of measured quantity.
Answer:
Errors due to the power (index) of measured quantity:

  1. Suppose
    Z = A3 = A × A × A
    then,
  2. Hence the relative error in Z = A3 is three times the relative error in A.
  3. This means if Z = An
    Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 23
  4. This implies, the quantity in the formula which has large power is responsible for maximum error.

Question 59.
The radius of a sphere measured repeatedly yields values 5.63 m, 5.54 m, 5.44 m, 5.40 m and 5.35 m. Determine the most probable value of radius and the mean absolute, relative and percentage errors.
Solution:
Given: a1 = 5.63 m, a2 = 5.54 m, a3 = 5.44 m
a4 = 5.40 m, a5 = 5.35 m,
To find:
i) Most probable value (Mean value)
ii) Mean absolute error
iii) Relative error
iv) Percentage error
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 24
From formula (ii),
Absolute errors:
∆a1 = |amean – a1| = |5.472 – 5.63| = 0.158
∆a2 = |amean – a2| = |5.472 – 5.54| = 0.068
∆a3 = |amean – a3| = |5.472 – 5.44| = 0.032
∆a4 = |amean – a4| = |5.472 – 5.40| = 0.072
∆a5 = |amean – a5| = |5.472 – 5.35| = 0.122

From formula (ii),
∆amean = \frac{0.158+0.068+0.032+0.072+0.122}{5}
= \frac{0.452}{5}
= 0.0904 m
From formula (iii),
Relative error = \frac{0.0904}{5.472}
= 1.652 × 10-2
(after rounding off to correct significant digits)
= 1.66 × 10-2
= 0.0166
∴ Percentage error = 1.66 × 10-2 × 100 = 1.66%
i) The mean value is 5.472 m.
ii) The mean absolute error is 0.0904 m.
iii) The relative error is 0.0166.
iv) The percentage error is 1.66%
[Note: Answer to relative error is rounded off using rules of significant figures and of rounding off]

Question 60.
Lin an experiment to determine the volume of an object, mass and density are recorded as m = (5 ± 0.15) kg and p = (5 ± 0.2) kg m3 respectively. Calculate percentage error in the measurement of volume.
Solulion:
Given: M = 5kg, ∆M = 0.15 kg, ρ = 5 kg/m3,
∆ρ = 0.2 kg/m3
To find: Percentage error in volume (V)
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 25
The percentage error in the determination of volume is 7%.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 61.
The acceleration due to gravity is determined by using a simple pendulum of length l = (100 ± 0.1) cm. If its time period is T = (2 ± 0.01) s, find the maximum percentage error in the measurement of g.
Solution:
Given: ∆l = 0.1 cm, l = 100 cm, ∆T = 0.01 s,
T = 2s
To find: Percentage error
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 26
Percentage error in measurement of g is 1.1 %.

Question 62.
Find the number of significant figures in the following numbers,
i. 25.42
ii. 0.004567
iii. 35.320
iv. 91.000
Answer:
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 27

Solved Examples

Question 63.
Add 7.21, 12.141 and 0.0028 and express the result to an appropriate number of significant figures.
Solution:
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 28
In the given problem, minimum number of digits after decimal is 2.
∴ Result will be rounded off upto two places of decimal.
Corrected rounded off sum is 19.35.

Question 64.
The mass of a box measured by a grocer’s balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is (i) the total mass of the box? (ii) the difference in the masses of the pieces to correct significant figures?
Solution:
i) Total mass of the box
= (2.3+ 0.02017 + 0.02015) kg
= 2.34032 kg
Since, the last number of significant figure is 2, therefore, the total mass of the box = 2.3 kg

ii) Difference of mass = (20.17 – 20.15) = 0.02g Since, there are two significant figures so the difference in masses to the correct significant figures is 0.02 g.

i) The total mass of the box to correct significant figures is 2.3 kg.
ii) The difference in the masses to correct significant figures is 0.02 g.

Apply Your Knowledge

Question 65.
Write the dimensions of a and b in the relation
E = \frac{b-x^{2}}{a}
Where E is energy, x ¡s distance and t is time.
Answer:
The given relation is E = \frac{b-x^{2}}{a}
As x is subtracted from b,
∴ dimensions of b are x2;
i.e., b = [L2]
∴ We can write equation as E = \frac{\mathrm{L}^{2}}{\mathrm{a}}
Or a = \frac{\mathrm{L}^{2}}{\mathrm{E}}=\frac{\mathrm{L}^{2}}{\left[\mathrm{~L}^{2} \mathrm{MT}^{-2}\right]} = [L0M-1T2]

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 66.
What is the difference between 6.0 and 6.00? which Is more accurate?
Answer:
6.0 indicates the measurement is correct up to first decimal place, whereas 6.00 indicates that the measurement is correct up to second decimal place. Thus, 6.00 is a more accurate value than 6.0.

Question 67.
A child walking on a footpath notices that the width of the footpath is uneven. He reported this to his school principal and the complaint was forwarded to the municipal officer.
i. What is the possible error encountered?
ii. What is the relative error in width of footpath if width of footpath in 10 m length are noted as 5 m, 5.5 m, 5 m, 6 m and 4.5 m?
Answer:
i) The error encountered is personal error.

ii) Mean value of widths
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 29
The relative error in width of footpath is 0.084.

Question 68.
A factory owner kept five identical spheres between two wooden blocks on a ruler as shown in figure. He called all his workers and told them to take reading, to check their efficiency and knowledge.
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 30
i. What is the area of central sphere?
ii. What is the absolute error in reading of diameter of second sphere?
Answer:
i) From above diagram radius of central sphere is
r = 1 cm
∴ Area = πr2 = 3.142 × (1)2= 3.142 cm2
The area of central sphere is 3.142 cm2.

ii) Mean value of all reading of diameters
dmean = \frac{\mathrm{d}_{1}+\mathrm{d}_{2}+\mathrm{d}_{3}+\mathrm{d}_{4}+\mathrm{d}_{5}}{5}=\frac{2+2+2+2+2}{5}
= \frac{10}{5} = 2 cm
Absolute error in reading of second sphere.
∆d2 = |dmean – d2| = 2 – 2 = 0
The absolute error in reading of diameter of second sphere is zero.

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 69.
A potential difference of V = 100 ± 2 volt, when applied across a resistance R gives a current of 10 ± 0.5 ampere. Calculate percentage error in R given by R V/I.
Answer:
Here. V = 100 ± 2 volt and I = 10 ± 0.5 ampere
Expressing limits of error as percentage error,
We have
V = 100 volt ± \frac{2}{100} × 100% = 10 volt ± 2%
and I = 10 ampere ± \frac{0.5}{10} × 100%
= 10 ampere ± 5%
∴ R = \frac{V}{I}
∴ %error in R = %error in V + %error in I
= 2% + 5% = 7%

Quick Review

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 31
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 32

Multiple Choice Questions

Question 1.
A physical quantity may be defined as
(A) the one having dimension.
(B) that which is immeasurable.
(C) that which has weight.
(D) that which has mass.
Answer:
(A) the one having dimension.

Question 2.
Which of the following is the fundamental unit?
(A) Length, force, time
(B) Length, mass, time
(C) Mass, volume, height
(D) Mass, velocity, pressure
Answer:
(B) Length, mass, time

Question 3.
Which of the following is NOT a fundamental quantity?
(A) Temperature
(B) Electric charge
(C) Mass
(D) Electric current
Answer:
(B) Electric charge

Question 4.
The distance of the planet from the earth is measured by __________.
(A) direct method
(B) directly by metre scale
(C) spherometer method
(D) parallax method
Answer:
(D) parallax method

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 5.
The two stars S1 and S2 are located at distances d1 and d2 respectively. Also if d1 > d22 then following statement is true.
(A) The parallax of S1 and S2 are same.
(B) The parallax of S1 is twice as that of S2
(C) The parallax of S1 is greater than parallax of S2
(D) The parallax of S2 is greater than parallax of S1
Answer:
(D) The parallax of S2 is greater than parallax of S1

Question 6.
Which of the following is NOT a unit of time?
(A) Hour
(B) Nano second
(C) Microsecond
(D) parsec
Answer:
(D) parsec

Question 7.
An atomic clock makes use of _________.
(A) cesium-133 atom
(B) cesium-132 atom
(C) cesium-123 atom
(D) cesium-131 atom
Answer:
(A) cesium-133 atom

Question 8.
S.I. unit of energy is joule and it is equivalent to
(A) 106 erg
(B) 10-7 erg
(C) 107 erg
(D) 105 erg
Answer:
(C) 107 erg

Question 9.
[L1M1T-1] is an expression for __________.
(A) force
(B) energy
(C) pressure
(D) momentum
Answer:
(D) momentum

Question 10.
Dimensions of sin θ is
(A) [L2]
(B) [M]
(C) [ML]
(D) [M0L0T0]
Answer:
(D) [M0L0T0]

Question 11.
Accuracy of measurement is determined by
(A) absolute error
(B) percentage error
(C) human error
(D) personal error
Answer:
(B) percentage error

Question 12.
Zero error of an instrument introduces .
(A) systematic error
(B) random error
(C) personal error
(D) decimal error
Answer:
(A) systematic error

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 13.
The diameter of the paper pin is measured accurately by using ________.
(A) Vernier callipers
(B) micrometer screw gauge
(C) metre scale
(D) a measuring tape
Answer:
(B) micrometer screw gauge

Question 14.
The number of significant figures in 11.118 × 10-6 is
(A) 3
(B) 4
(C) 5
(D) 6
Answer:
(C) 5

Question 15.
0.00849 contains ___________ significant figures.
(A) 6
(B) 5
(C) 3
(D) 2
Answer:
(C) 3

Question 16.
3.310 × 102 has ___________ significant figures.
(A) 6
(B) 4
(C) 2
(D) 1
Answer:
(B) 4

Question 17.
The Earth’s radius is 6371 km. The order of magnitude of the Earth’s radius is
(A) 103 m
(B) 109 m
(C) 107 m
(D) 102 m
Answer:
(C) 107 m

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 18.
__________ is the smallest measurement that can be made using the given instrument
(A) Significant number
(B) Least count
(C) Order of magnitude
(D) Relative error
Answer:
(B) Least count

Competitive Corner

Question 1.
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X,
where X = \frac{A^{2} \frac{1}{B^{2}}}{C^{\frac{1}{3}} D^{3}}, will be:
(A) -10 %
(B) 10 %
(C) \left(\frac{3}{13}\right) \%
(D) 16 %
Answer:
(D) 16 %
Hint:
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 33
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 34
∴ Percentage error in x is given as,
\frac{\Delta x}{x} × 100 – (error contributed by A) – (error contributed by B) + (error contributed by C) + (error contributed by D)
= 2% + 1% + 1% + 12%
= 16%

Question 2.
The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n – 1) divisions of main scale. The least count of the vernier callipers is,
(A) \frac{1}{n(n+1)} cm
(B) \frac{1}{(n+1)(n-1)} cm
(C) \frac{1}{n} cm
(D) \frac{1}{n^{2}} cm
Answer:
(D) \frac{1}{n^{2}} cm
Hint:
1 V.S.D. = \frac{(n-1)}{n} M.S.D.
LC. = 1 M.S.D. – 1 V.S.D.
= 1 M.S.D. – \frac{(n-1)}{n} M.S.D.
= \frac{1}{n} M.S.D.
= \frac{1}{n} × \frac{1}{n} cm
∴ L.C. = \frac{1}{n^{2}} cm

Question 3.
A student measures time for 20 oscillations of a simple pendulum as 30 s. 32 s, 35 s and 31 s. 1f the minimum division in the measuring clock is I s, then correct mean time in second is
(A) 32 ± 3
(B) 32 ± 1
(C) 32 ± 2
(D) 32 ± 5
Answer:
(C) 32 ± 2
Hint:
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 35
Hence rounding off,
∆t = ± 2 s
∴ t ± ∆t = 32 ± 2 s

Question 4.
A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference leveL If screw gauge has a zero error of— 0.004 cm, the correct diameter of the ball is
(A) 0.521 cm
(B) 0.525 cm
(C) 0.053 cm
(D) 0.29 cm
Answer:
(D) 0.29 cm

Hint:
Least count of screw gauge = 0.001 cm = 0.01mm
Main scale reading = 5 mm.
Zero error = – 0.004 cm = -0.04 mm
Zero correction = +0.04 mm
Observed reading = Mainscale reading + (Division × least count)
Observed reading = 5 + (25 × 0.01) = 5.25 mm
Corrected reading = Observed reading + Zero correction
Corrected reading = 5.25 + 0.04
= 5.29 mm = 0.529 cm

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 5.
The density of the material in the shape of a cube is determined by measuring three sides of the cube and its mass. 1f the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:
(A) 4.5%
(B) 6%
(C) 2.5°
(D) 3.5%
Answer:
(A) 4.5%
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 36

Question 6.
Let x = \left[\frac{a^{2} b^{2}}{c}\right] be the physical quantity. If the percentage error in the measurement of physical quantities a, b and c is 2, 3 and 4 percent respectively then percentage en-or in the measurement of x is
(A) 7%
(B) 14%
(C) 21%
(D) 28%
Answer:
(B) 14%
Hint:
Given: x = \frac{a^{2} b^{2}}{c}
Percentage error is given by.
\frac{\Delta x}{x}=\frac{2 \Delta a}{a}+\frac{2 \Delta b}{b}+\frac{\Delta c}{c}
= (2 × 2) + (2 × 3) + 4
= 4 + 6 + 4 = 14
\frac{\Delta \mathrm{x}}{\mathrm{x}} \% = 14%

Question 7.
A physical quantity of the dimensions of length that can be formed out of c, G and \frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0}} is [c is velocity of light, G is universal constant of gravitation and e is charge]:
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 37
Answer:
(A) \frac{1}{\mathrm{c}^{2}}\left[\mathrm{G} \frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0}}\right]^{1 / 2}

Hint:
Let the physical quantity formed of the dimensions of length be given as.
[L] = [c]x [G]y \left[\frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0}}\right]^{z} …………….. (i)
Now,
Dimensions of velocity of light [c]x = [LT-1]x
Dimensions of universal gravitational constant
[G]y = [L3T2M-1]y
Dimensions of \left[\frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0}}\right]^{z} = [ML3T-2]z
Substitrning these in equation (i)
[L] [LT-1]x [M-1L3T-2]y [ML3T-2]z
= Lx+3y+3z M-y+z T-x-2y-2z
Solving for x, y, z
x + 3y + 3z = 1
-y + z = 0
x + 2y + 2z = O
Solving the above equation,
x = -2, y = \frac{1}{2}, z = \frac{1}{2}
∴ L = \frac{1}{c^{2}}\left[\mathrm{G} \frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0}}\right]^{1 / 2}

Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements

Question 8.
The following observations were taken for determining surface tension T of water by capillary method:
diameter of capillary, D = 1.25 × 10-2 m
rise of water, h = 1.45 × 10-2 m
Using g = 9.80 m/s2 and the simplified relation
T = \frac{\mathrm{rhg}}{2} × 103 N/m, the possible error in surface tension is closest to:
(A) 0.15%
(B) 1.5%
(C) 2.4%
(D) 10%
Answer:
(B) 1.5%
Hint:
D = 1.25 × 10-2 m; h = 1.45 × 10-2 m
The maximum permissible error in D
= ∆D = 0.01 × 10-2 m
The maximum permissible error in h
= ∆h = 0.01 × 10-2 m
g is given as a constant and is errorless.
Maharashtra Board Class 11 Physics Important Questions Chapter 1 Units and Measurements 38