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NCERT Solutions for Class 11th: Ch 1 Units and Measurements Physics Science

NCERT Solutions for Class 11th: Ch 1 Units and Measurements Physics SciencePage No: 35Exercises2.1. Fill in the blanks(a) The volume of a cube of side 1 cm is equal to.....m3(b) The surface area of a solid cylinder of radius 2.0 cmand height 10.0 cm is equal to... (mm)2(c) A vehicle moving with a speed of 18 km h–1covers....m in1 s(d) The relative density of lead is 11.3. Its density is ....g cm–3or . ...kg m–3.Answer(a) Length of edge = 1cm = 1/100 mVolume of the cube = side3Putting the value of side, we getVolume of the cube = (1/100 m)3The volume of a cube of side 1cm is equal to10-6m3(b) Given,Radius,r= 2.0 cm = 20 mm (convert cm to mm)Height,h= 10.0 cm =100 mmThe formula of total surface area of a cylinder S = 2πr(r+h)Putting the values in this formula, we getSurface area of a cylinder S= 2πr(r+h= 2 x 3.14 x 20 (20+100)= 15072 = 1.5 × 104mm2The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to1.5 × 104 mm2(c) Using the conversion,Given,Time, t = 1 secspeed = 18 km h-1= 18 km / hour1 km = 1000 m and 1hour = 3600 secSpeed = 18 × 1000 /3600 sec =5 m /secUse formulaSpeed = distance / timeCross multiply it, we getDistance = Speed × Time = 5 × 1 = 5 mA vehicle moving with a speed of 18 km h–1covers5m in 1 s.(d) Density of lead = Relativedensity of lead × Density of waterDensity of water = 1 g/cm3Putting the values, we getDensity of lead = 11.3 × 1 g/ cm3= 11.3 g cm-31 cm = (1/100 m) =10–2m31 g = 1/1000 kg = 10-3kgDensity of lead = 11.3 g cm-3= 11.3Putting the value of 1 cm and 1gram11.3 g/cm3= 11.3 × 10-3kg (10-2m)-3= 11.3 ×10–3× 106kg m-3=1.13 × 103kg m–3The relative density of lead is11.3. Its density is11.3g cm-3 g cm–3or1.13 × 103kg m–3.2.2. Fill in the blanks by suitable conversion of units:(a) 1 kg m2s–2= ....g cm2s–2(b) 1 m =..... ly(c) 3.0 m s–2=.... km h–2(d) G= 6.67 × 10–11N m2(kg)–2=.... (cm)3s–2g–1.Answer(a) 1 kg = 103g1 m2= 104cm21 kg m2s–2= 1 kg × 1 m2× 1 s–2=103g × 104cm2× 1 s–2= 107gcm2s–21 kg m2s–2=107 g cm2 s–2(b) Distance = Speed × TimeSpeed of light = 3 × 108m/sTime = 1 year = 365 days = 365 × 24 hours = 365 × 24 ×60 × 60 secPutting these values in above formula we get1 light year distance = (3 × 108m/s) × (365 × 24 × 60 × 60s) = 9.46 × 1015m9.46 × 1015m = 1 lySo that 1 m = 1/ 9.46 × 1015ly=1.06 × 10-16ly(c) 1 hour = 3600 sec so that 1sec = 1/3600 hour1 km = 1000 m so that 1 m = 1/1000 km3.0 m s–2= 3.0 (1/1000 km)( 1/3600 hour)-2= 3.0 × 10–3km × ((1/3600)-2h–2)= 3.0 × 10–3km × (3600)2h–2= 3.88 × 104km h–23.0 m s–2=3.88 × 104 km h–2(d) Given,G= 6.67 × 10–11N m2(kg)–2We know that1 N = 1 kg m s–21 kg = 103g1 m = 100 cm = 102cmPutting above values, we get6.67 × 10–11N m2kg–2= 6.67× 10–11× (1 kg m s–2) (1 m2) (1Kg–2)Solve and cancel out the units we get⇒ 6.67 × 10–11× (1 kg–1× 1 m3×1 s–2)Putting above values to convertKg to g and m to cm⇒ 6.67 × 10–11× (103g)-1× (102cm)3× (1 s–2)⇒ 6.67 × 10–11× 10-3g-1× 106cm3× (1 s–2)⇒ 6.67 × 10–8cm3s–2g–1G= 6.67 × 10–11 N m2 (kg)–2=6.67 × 10–8 (cm)3s–2 g–1.2.3. A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2s–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α–1β–2γ2in terms of the newunits.AnswerGiven that,1 Calorie=4.2 J = 4.2 Kg m2s-2               ...... (i)As new unit of mass = α Kg∴ 1 Kg = 1/α new unit of massSimilarly, 1 m = β-1new unit of length1 s = γ-1new unit of timePutting these values in (i), we get1 calorie = 4.2 (α-1new unit of mass) (β-1new unit of length)2 (γ-1new unit of time)-2= 4.2 α-1β-2γ2new unit of energy (Proved)2.4. Explain this statement clearly:“To call a dimensional quantity 'large' or 'small' is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary:(a) atoms are very small objects(b) a jet plane moves with great speed(c) the mass of Jupiter is verylarge(d) the air inside this room contains a large number of molecules(e) a proton is much more massive than an electron(f) the speed of sound is much smaller than the speed of light.AnswerThe given statement is true because a dimensionless quantity may be large or smallin comparision to some standard reference. For example, the coefficient of friction is dimensionless. The coefficient of sliding friction is greater than the coefficientof rolling friction, but less than static friction.(a) An atom is a very small object in comparison to a soccer ball.(b) A jet plane moves with a speed greater than that of a bicycle.(c) Mass of Jupiter is very large as compared to the mass of a cricket ball.(d) The air inside this room contains a large number of molecules as compared to that present in a geometry box.(e) A proton is more massive than an electron.(f) Speed of sound is less thanthe speed of light.2.5. A new unit of length is chosen such that the speed of light in vacuum is unity. Whatis the distance between the Sun and the Earth in terms ofthe new unit if light takes 8 min and 20 s to cover this distance?AnswerDistance between the Sun andthe Earth = Speed of light x Time taken by light to cover the distanceGiven that in the new unit, speed of light = 1 unitTime taken, t = 8 min 20 s =500 s∴Distance between the Sun and the Earth = 1 x 500 = 500 units2.6. Which of the following is the most precise device for measuring length:(a) a vernier callipers with 20divisions on the sliding scale(b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale(c) an optical instrument that can measure length to within awavelength of light?Answer(a) Least count of this verniercallipers = 1SD - 1 VD  = 1 SD - 19/20 SD = 1/20 SD=1.20 mm = 1/200 cm = 0.005 cm(b) Least count of screw gauge= Pitch/Number of divisions =1/1000 = 0.001 cm.(c) Wavelength of light, λ ≈ 10-5cm = 0.00001 cmHence, it can be inferred thatan optical instrument is the most suitable device to measure length.2.7. A student measures the thickness of a human hair by looking at it through a microscope of magnification 100.He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair?AnswerMagnification of the microscope= 100Average width of the hair in the field of view of the microscope = 3.5 mm∴Actual thickness of the hair is 3.5/100 = 0.035 mm.2.8. Answer the following:(a) You are given a thread anda metre scale. How will you estimate the diameter of the thread?AnswerWrap the thread on a uniform smooth rod in such a way that the coils thus formed are very close to each other. Measure the length of the thread using a metre scale. The diameter ofthe thread is given by the relation,Diameter = Length of thread/Number of turns(b) A screw gauge has a pitch of 1.0 mm and 200 divisions onthe circular scale. Do you think it is possible to increasethe accuracy of the screw gauge arbitrarily by increasingthe number of divisions on thecircular scale?AnswerIt is not possible to increase the accuracy of a screw gauge by increasing the number of divisions of the circular scale. Increasing the number divisionsof the circular scale will increase its accuracy to a certain extent only.(c) The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?AnswerA set of 100 measurements is more reliable than a set of 5 measurements because random errors involved in the former are very less as compared to the latter.2.9. The photograph of a house occupies an area of 1.75 cm2ona 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 m2. What is thelinear magnification of the projector-screen arrangement?AnswerArea of the house on the slide= 1.75 cm2Area of the image of the houseformed on the screen = 1.55 m2 = 1.55 × 104 cm22.10. State the number of significant figures in the following:(a) 0.007 m2► 1(b) 2.64 x 1024kg► 3(c) 0.2370 g cm-3► 4(d) 6.320 J► 4(e) 6.032 N m-2► 4(f) 0.0006032 m2► 4Page No: 362.11. The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area andvolume of the sheet to correct significant figures.AnswerGiven that,length,l= 4.234 mbreadth,b =1.005 mthickness,t= 2.01 cm = 2.01 × 10-2mArea of the sheet = 2 (l×0 +b×t +t×l) = 2 (4.234 × 1.005 + 1.005 × 0.0201 + 0.0201 × 4.234)= 2(4.3604739) = 8.7209478 m2As area can contain a maximum of three significant digits, therefore, rounding off, we getArea = 8.72 m2Also, volume =l×b×tV= 4.234 × 1.005 × 0.0201 = 0.0855289 = 0.0855 m3      (Significant Figures = 3)2.12. The mass of a box measured by a grocer's balanceis 2.300 kg. Two gold pieces ofmasses 20.15 g and 20.17 g are added to the box. What is (a) the total mass of the box, (b) the difference in the masses of the pieces to correct significant figures?AnswerMass of grocer's box = 2.300 kgMass of gold piece I = 20.15g =0.02015 kgMass of gold piece II = 20.17 g= 0.02017 kg(a) Total mass of the box = 2.3 + 0.02015 + 0.02017 = 2.34032 kgIn addition, the final result should retain as many decimal places as there are in the number with the least decimalplaces. Hence, the total mass of the box is 2.3 kg.(b) Difference in masses = 20.17 - 20.15 = 0.02 gIn subtraction, the final resultshould retain as many decimal places as there are in the number with the least decimalplaces.2.13. A physical quantity P is related to four observables a, b, c and d as follows:The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P? If the value of P calculated using the above relation turns out to be 3.763,to what value should you roundoff the result?AnswerPercentage error in P = 13 %Value of P is given as 3.763.By rounding off the given value to the first decimal place, we get P = 3.8.2.14. A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion:(a= maximum displacement of the particle,v= speed of the particle.T= time-period of motion). Rule out the wrong formulas on dimensional grounds.AnswerThe displacement y has the dimension of length, therefore, the formula for it should also have the dimension of length. Trigonometric functions are dimensionless and their arguments are also dimensionless. Based on these considerations now check each formula dimensionally.The formulas in (ii) and (iii) are dimensionally wrong.

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NCERT Solutions for Class 11th: Ch 1 Physical World Physics Science

NCERT Solutions for Class 11th: 

Ch 1 Physical World Physics Science

Page No: 13

Exercises1.

1. Some of the most profound statements on the nature of science have come from Albert Einstein, one of the greatest scientists of all time. What do
you think did Einstein mean when he said : “The most incomprehensible thing about the world is that it is comprehensible”?

Answer :-The Physical world around us is full of different complex natural phenomena so the world is in-comprehensible. But with the help of study andobservations it has been foundthat all these phenomena are based on some basic physical laws and so it is comprehensible.

1.2. "“Every great physical theory starts as a heresy and ends as a dogma"”. Give some examples from the history of science of the validity of this incisive remark.

Answer:- The statement above is true. Validity of this incisive remark can be validated from the example of moment of inertia. It states that the moment of inertia of a body depends on its energy.

 But according to Einstein's mass-energy relation (E = mc2), energy depends on the speed of the body.

1.3. "“Politics is the art of thepossible"”. Similarly, “"Science is the art of the soluble"”. Explain this beautiful aphorism on the nature and practice of science.

Answer:- It is well known that to win over votes, politicians would make anything and everything possible even when they are least sure of the same. and in Science the various natural phenomena can be explained interms of some basic laws. So as 'Politics is the art of possible' similarly 'Science is the art of the soluble'.

1.4. Though India now has a large base in science and technology, which is fast expanding, it is still a long way from realizing its potential of becoming a world leader in science. Name some important factors, which in your view have hindered the advancement of science in India.

Answer:- Some important factors in our view which have hindered the advancement of science in India are:

→ Proper funds are not arranged for the development of research work and laboratories. 

The labs and scientific instruments are veryold and outdated.

→ Most of the people in India are uneducated and highly traditional.

 They don't understand the importance of Science.

→ There is no proper employment opportunity for thescience educated person in India.

→ There are no proper facilities for science educationin schools and colleges in India.

1.5. No physicist has ever"“seen"” an electron. Yet, all physicists believe in the existence of electrons. An intelligent but superstitious man advances this analogy to argue that ‘ghosts’ exist even though no one has '‘seen'’ one. How will you refute his argument?

Answer:- No physicist has ever seen an atom but there are practical evidences which prove the presence of electron. Their size is so small, even powerful microscopes find it difficult tomeasure their sizes. But still its effects could be tested On the other end there is no phenomena which can be explained on the basis of existence of ghosts.Our senses of sight and hearing are very limited to observe the existence of both.

So there is no comparison between the two given cases.

1.6. The shells of crabs found around a particular coastal location in Japan seem mostly to resemble the legendary faceof a Samurai. Given below aretwo explanations of this observed fact. Which of these strikes you as a scientific explanation ?

(a) A tragic sea accident several centuries ago drowned a young Samurai. As a tribute to his bravery, nature through its inscrutable ways immortalized his face by imprinting it on the crab shells in that area.

(b) After the sea tragedy, fishermen in that area, in a gesture of honor to their dead hero, let free any crab shell caught by them which accidentally had a shape resembling the face of a Samurai. 

Consequently, the particular shape of the crab shell survived longer and therefore in course of time the shape was genetically propagated. This is an exampleof evolution by artificial selection.

[Note : This interesting illustration taken from Carl Sagan’s ‘The Cosmos’ highlights the fact that often strange and inexplicable facts which on the first sight appear ‘supernatural’ actually turn out to have simple scientific explanations. Try to think out other examples of this kind].

Answer:- Explanation (b) is correct is ascientific explanation of the observed fact.Page No: 14

1.7. The industrial revolution in England and Western Europe more than two centuries ago was triggered by some key scientific and technological advances. What were these advances ?

Answer:- More than two centuries ago, England and Western Europe invented steam engine, electricity, theory of gravitation and the explosives. Steam engines helped them in the field of hat and thermodynamics, theory of gravitation in field of motion and making guns and cannons. These progresses brought aboutindustrial revolution in England and Western Europe.

1.8. It is often said that the world is witnessing now a second industrial revolution, which will transform the society as radically as did the first. List some key contemporary areas of science and technology, which are responsible for this revolution.

Answer:- Some of the key contemporary areas of science and technologywhich may transform the society radically are:

→ Development of super fast computers

→ Internet and tremendous advancement in information technology

→ Development in Biotechnology

→ Development of super-conducting materials at room temperature.

→ Dvelopment of robots.

1.10. Attempt to formulate your‘moral’ views on the practice ofscience. Imagine yourself stumbling upon a discovery, which has great academic interest but is certain to havenothing but dangerous consequences for the human society. How, if at all, will youresolve your dilemma?

Answer:- In our view a type of discoverywhich is of great academic interest but harmful for human society should not be made public because Science isfor the society, society is not for science.

1.11. Science, like any knowledge,can be put to good or bad use, depending on the user.

Given below are some of the applications of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorized :

(a) Mass vaccination against small pox to curb and finally eradicate this disease from the
population.

(This has already been successfully done in India).

► Good
(b) Television for eradication of illiteracy and for mass communication of news and ideas.
► Good
(c) Prenatal sex determination
► Bad
(d) Computers for increase in work efficiency
► Good
(e) Putting artificial satellites into orbits around the Earth
► Good
(f ) Development of nuclear weapons
► Bad(g) Development of new and powerful techniques of chemical and biological warfare).
► Bad(h) Purification of water for drinking
► Good
(i) Plastic surgery
► Good
(j ) Cloning
► Good
(You can use your own prespective for answering above questions)

1.12. India has had a long and unbroken tradition of great scholarship

 — in mathematics, astronomy, linguistics, logic andethics. 

Yet, in parallel with this, several superstitious and obscurantist attitudes and practices flourished in our society and unfortunately continue even today

 — among many educated people too. How will you use your knowledge ofscience to develop strategies tocounter these attitudes ?

Answer:-Poverty and illiteracy are the two major factors which make people superstitious in India. Soto remove the superstitious andobscurantist attitude we have to first overcome these factors.Everybody should be educated, so that one can have scientificattitude. Knowledge of science can be put to use to prove people's superstitious wrong by showing them the scientific logic behind everything happening in our world.

1.13

Answer:- Some people in our society havethe view that women do not have the innate nature, capacity and intelligence.To demolish this view there are many examples of women who have proven their abilitiesin Science and other fields.Madam Curie, Mother Teresa, Indira Gandhi, Marget Thatcher, Rani Laxmi Bai, Florence Nightingale are some examples. So in this era womenare definitely not behind man in any field.

1.14. “It is more important to have beauty in the equations of physics than to have them agree with experiments”. The great British physicist P. A. M.Dirac held this view. Criticizethis statement. Look out for some equations and results in this book which strike you as beautiful.

Answer:- An equation which agrees with experiment must also be simple and hence beautiful. We have some simple and beautiful equations in Physics such as
→ E = mc2 (Energy of light)
→ E = hv (Energy of a photon)
→ KE = 1/2mv2(Kinetic energyof a moving particle)
→ PE = mgh (Potential energyof a body at rest)
→ W = F.d (Work done)

All have the same dimensions. 

One experiment shows dependency of energy on speed, the other shows dependency on frequency & displacement.That's the beauty of equationsin Physics coming from different experiments.

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