Physical World

Class 11 NCERT Physics

NCERT

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”?

Solution :

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

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.

Solution :

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 , energy depends on the speed of the body.

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

Solution :

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 in terms of some basic laws. So as 'Politics is the art of possible' similarly 'Science is the art of the soluble'.

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.

Solution :

Some important factors in our view which have hindered the advancement of science in India are:$\\$ $\bullet$ Proper funds are not arranged for the development of research work and laboratories.$\\$ The labs and scientific instruments are very old and outdated.$\\$ $\bullet$ Most of the people in India are uneducated and highly traditional. They don't understand the importance of Science.$\\$ $\bullet$ There is no proper employment opportunity for the science educated person in India.$\\$ $\bullet$ There are no proper facilities for science education in schools and colleges in India.

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?

Solution :

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 to measure 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.

6   The shells of crabs found around a particular coastal location in Japan seem mostly to resemble the legendary face of a Samurai. Given below are two explanations of this observed fact. Which of these strikes you as a scientific explanation?$\\$

Solution :

Explanation (b) is correct is a scientific explanation of the observed fact

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 ?

Solution :

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 about industrial revolution in England and Western Europe.

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.

Solution :

Some of the key contemporary areas of science and technology which may transform the society radically are:$\\$ $\bullet$ Development of super-fast computers$\\$ $\bullet$ Internet and tremendous advancement in information technology$\\$ $\bullet$ Development in Biotechnology$\\$ $\bullet$ Development of super-conducting materials at room temperature$\\$ $\bullet$ Development of robots.

9   Write in about $1000$ words a fiction piece based on your speculation on the science and technology of the twenty-second century.

Solution :

Imagine you alongwith your friends are in a spaceship which is moving towards Mars. The body of the spaceship is made of a specially designed matter which becomes more harder as its temperature increases. The spaceship is using nuclear fuel and there are three nuclear power plants in a spaceship. Two of them work alternatively and the third is for emergency. The speed of the spaceship is very high and all of you are very happy. The energy produced in power plants is converted into electric energy which runs the motors of the spaceship. You alongwith your friends reach safely on Mars, collects data, takes photographs and then returns to the Earth. On the return journey, the spaceship collides with an object in the space due to which two power plants stop to work. Now, only one power plant is working and due to overheating its efficiency is decreasing continuously. You and your friends try to reduce the temperature of the power plant by flowing air in the plant and try to repair the fuse of the other power plants. Finally, fuse of one other plant is repaired and start to work before the first plant crosses the danger limit of an excess of temperature. Finally, you and your friends return safely to Earth

10   Attempt to formulate your ‘moral’ views on the practice of science. Imagine yourself stumbling upon a discovery, which has great academic interest but is certain to have nothing but dangerous consequences for the human society. How, if at all, will you resolve your dilemma?

Solution :

In our view a type of discovery which is of great academic interest but harmful for human society should not be made public because Science is for the society, society is not for science.

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).$\\$ (b) Television for eradication of illiteracy and for mass communication of news and ideas.$\\$ (c) Prenatal sex determination$\\$ (d) Computers for increase in work efficiency$\\$ (e) Putting artificial satellites into orbits around the Earth$\\$ (f) Development of nuclear weapons$\\$ (g) Development of new and powerful techniques of chemical and biological warfare.$\\$ (h) Purification of water for drinking$\\$ (i) Plastic surgery$\\$ (j) Cloning

Solution :

(k)Good$\\$ (l)Good$\\$ (m)Bad$\\$ (n)Good$\\$ (o)Good$\\$ (p)Bad$\\$ (q)Bad$\\$ (r)Good$\\$ (s)Good$\\$ $\\$ (t)Good

12   India has had a long and unbroken tradition of great scholarship - in mathematics, astronomy, linguistics, logic and ethics. 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 of science to develop strategies to counter these attitudes?

Solution :

Poverty and illiteracy are the two major factors which make people superstitious in India. So to remove the superstitious and obscurantist attitude we have to first overcome these factors. Everybody should be educated, so that one can have scientific attitude. 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.

13   Though the law gives women equal status in India, many people hold unscientific views on a woman’s innate nature, capacity and intelligence, and in practice give them a secondary status and role. Demolish this view using scientific arguments, and by quoting examples of great women in science and other spheres; and persuade yourself and others that, given equal opportunity, women are on par with men.

Solution :

Some people in our society have the 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 abilities in Science and other fields. Madam Curie, Mother Teresa, Indira Gandhi, Marget Thatcher, Rani Laxmi Bai, Florence Nightingale are some examples. So in this era women are definitely not behind man in any field.$\\$

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. Criticize this statement. Look out for some equations and results in this book which strike you as beautiful.

Solution :

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 = mc$^2$ (Energy of light)$\\$ E = hv (Energy of a photon)$\\$ KE = 1/ 2 mv $^2$ (Kinetic energy of a moving particle)$\\$ PE = mgh (Potential energy of 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 equations in Physics coming from different experiments.

15   Though the statement quoted above may be disputed, most physicists do have a feeling that the great laws of physics are at once simple and beautiful. Some of the notable physicists, besides Dirac, who have articulated this feeling, are : Einstein, Bohr, Heisenberg, Chandrasekhar and Feynman. You are urged to make special efforts to get access to the general books and writings by these and other great masters of physics. (See the Bibliography at the end of this book.) Their writings are truly inspiring !

Solution :

It is absolutely true that great laws of physics are simple and beautiful. Few examples are given below.$\\$ (i) Einstein's mass-energy equivalence relation E = mc$^ 2$ is simple and beautiful.$\\$ (ii) According to Max Planck's quantum, the energy of a photon is E = hv, is also a simple and beautiful equation.$\\$ (iii) De-Broglie wavelength associated with a particle of mass m is given by $\lambda $=h/mv . It is also a simple and beautiful equation.

16   Textbooks on science may give you a wrong impression that studying science is dry and all too serious and that scientists are absent-minded introverts who never laugh or grin. This image of science and scientists is patently false. Scientists, like any other group of humans, have their share of humorists, and many have led their lives with a great sense of fun and adventure, even as they seriously pursued their scientific work. Two great physicists of this genre are Gamow and Feynman. You will enjoy reading their books listed in the Bibliography.

Solution :

It is true that scientists like any other group of humans have their share of humorists. Two great physicists of this genre are Gamow and Feynman. Few other scientists whose name can be added in this list are CV Raman, Einstein, Bohr, former Indian president. APJ Abdul Kalam etc.

17   Explain this common observation clearly : If you look out of the window of a fast moving train, the nearby trees, houses etc. seem to move rapidly in a direction opposite to the train’s motion, but the distant objects (hill tops, the Moon, the stars etc.) seem to be stationary. (In fact, since you are aware that you are moving, these distant objects seem to move with you).

Solution :

Line of sight is defined as an imaginary line joining an object and an observer’s eye. When we observe nearby stationary objects such as trees, houses, etc. while sitting in a moving train, they appear to move rapidly in the opposite direction because the line of sight changes very rapidly. On the other hand, distant objects such as trees, stars, etc. appear stationary because of the large distance. As a result, the line of sight does not change its direction rapidly.

18   The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth ‘s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit $\approx 3*10^{11}m$ However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of meters?

Solution :

Diameter of Earth’s orbit $3*10^{11}m$$\\$ Radius of Earth’s orbit, r = 1.5 $*10^{11}m$$\\$ Let the distance parallax angle be 1" =$4.847 * 10 ^- 6$ rad$\\$ Let the distance of the star be D$\\$ Parsec is defined as the distance at which the average radius of the Earth’s orbit subtends an angle of 1”$\\$ $\therefore $ we have$ \theta =\dfrac{r}{D}\\ D=\dfrac{r}{\theta}=\dfrac{1.5*10^{11}}{4.847*10^{-6}}\\ =0.309*10^{-6} \approx 3.09*10^{16}m\\ $ $\\$ Hence,1 parse$ \approx 3.09*10^{16}m$

19   The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri ) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?

Solution :

Distance of the star from the solar system = 4.29 ly$\\$ 1 light year is the distance travelled by light in one year.$\\$ 1 light year = Speed of light × 1 year$\\$ $= 3 * 10^ 8 * 365 * 24 * 60 * 60 = 94608 * 10 ^{11} m$$\\$ $=4.29 ly = 405868.32 *10^{ 11} m$$\\$ 1 pare sec = $3.08 *10 ^{16} m$$\\$ $\therefore 4.29 ly =\dfrac{405868.32 *10^{ 11} m} {3.08 *10 ^{16} m} =1.32 /$ sec$\\$ Using the relation,$\\$ $\theta =\dfrac{d}{D}$ $\\$ Where, Diameter of Earth’s orbit, d = $3 * 10^{ 11 }m$ $\\$ Distance of the star from the Earth, D =$ 405868.32 * 10^{ 11} m$ $\\$ $\therefore \theta=\dfrac{3 * 10^{ 11 }m}{405868.32 * 10^{ 11} m}=7.39*10^{-6} $ rad $\\$ 1 sec=4.85*10^-6 rad$\\$

20   Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed

Solution :

It is indeed very true that precise measurements of physical quantities are essential for the development of science. For example, ultra-shot laser pulses ultra-shot laser pulses ( time interval $\sim 10 ^{- 15} s )$ are used to measure time intervals in several physical and chemical processes. X-ray spectroscopy is used to determine the inter-atomic separation or inter-planer spacing. The development of mass spectrometer makes it possible to measure the mass of atoms precisely.

21   Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity)$\\$ the total mass of rain-bearing clouds over India during the Monsoon$\\$ the mass of an elephant$\\$ the wind speed during a storm$\\$ the number of strands of hair on your head$\\$ the number of air molecules in your classroom.

Solution :

During monsoons, a metrologist records about 215 cm of rainfall in India i.e., the height of$\\$ water column h = 215 cm = 2.15 m$\\$ Area of country, $A = 3.3 * 10 ^{12} m ^2$$\\$ Hence, volume of rain water, V = A * h =7.09 * $^{12} m ^3$$\\$ Density of water $\Phi= 1 *10 ^3 kg \ m ^ 3$$\\$ Hence, mass of rain water $\Phi * V = 7.09 * 10^{ 15} kg$$\\$ Hence, the total mass of rain-bearing clouds over India is approximately $7.09 * 10^{ 15} kg$$\\$ Consider a ship of known base area floating in the sea. Measure its depth in sea (say d 1 )$\\$ Volume of water displaced by the ship, $V_ b = Ad _1$$\\$ Now, move an elephant on the ship and measure the depth of the ship d 2 in this case$\\$ Volume of water displaced by the ship with the elephant on board V be = Ad 2$\\$ Volume of water displaced by the elephant Ad 2 - Ad 1$\\$ Density of water = D$\\$ Mass of elephant = AD ( d 2 - d 1 )$\\$ Wind speed during a storm can be measured by an anemometer. As wind blows, it rotates.$\\$ The rotation made by the anemometer in one second gives the value of wind speed Area of the head surface carrying hair = A$\\$ With the help of a screw gauge, the diameter and hence, the radius of a hair can be determined. Let it be r.$\\$ Area of one hair =$\pi r^ 2$$\\$

$\approx=$Total surface area/Area of one hari $\pi =\dfrac{A}{r^2}$ $\\$ Let the volume of the room be V One mole of air at NTP occupies 22.4 l i.e., 22.4, 22.4$ * 10 ^ 3 m ^3$ volume. $\\$Number of molecules in one mole = 6.023* $10^{ 23}$$\\$ Number of molecules in room of volume V$\\$ =$\dfrac{6.023*10^{23}}{22.4*10^{-3}}*V=134.915*10^{26}V\\ =1.35*10^{28}V$

22   The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding 10 7 K and its outer surface at a temperature of about 6000 K At these high temperatures no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be, in the range of densities of solids and liquids or gases? Check if your guess is correct from the following data: mass of the Sun = $2.0 * 10^ {30} kg$, radius of the Sun $= 7.0 * 10^ 8 m$

Solution :

Mass of the Sun, M= $2.0 * 10^ {30} kg$,$\\$ Radius of the Sun, R $= 7.0 * 10^ 8 m$$\\$ Volume of the Sun, V=$\dfrac{4}{3}\pi R^3\\ =\dfrac{4}{3}*\dfrac{22}{7}*(7.0*10^8)^3\\ =\dfrac{88}{21}*343*10^{24}=1437.3*10^{24}m^3$ $\\$ Density of the Sun =$\dfrac{Mass}{Volume}=\dfrac{2.0*10^{30}}{1437.3*10^{24}} \sim 1.4*10^3 kg/m^5$ $\\$ The density of the Sun is in the density range of solids and liquids. This high density is attributed to the intense gravitational attraction of the inner layers on the outer layer of the Sun.

23   When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72" of arc. Calculate the diameter of Jupiter

Solution :

Distance of Jupiter from the Earth $D = 824.7 * 10^ 6 km = 824.7 * 10^ 9 m$ $\\$ Angular diameter$35.72" = 35.72 * 4.874 * 10 ^ 6$ rad$\\$ Diameter of Jupiter = d$\\$ Using the relation,$\\$ $\theta =\dfrac{d}{D}\\ d=\theta D=824.7*10^9*35.72*4.872*10^{-6}\\ =143520.67*10^3=1.435*10^5 km$

24   A man walking briskly in rain with speed v must slant his umbrella forward making an angle $\theta$ with the vertical. A student derives the following relation between $\theta$ and v tan $\theta= v $and checks that the relation has a correct limit: as v =0, $\theta$= 0, as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Do you think this relation can be correct? If not, guess the correct relation.

Solution :

Incorrect; on dimensional ground The relation is tan $\theta= v$ $\\$ Dimension of R.H.S = $M^ 0 L^1T^{-1}$$\\$ Dimension of L.H.S = $M ^0 L^ 0 T ^0$$\\$ (The trigonometric function is considered to be a dimensionless quantity)$\\$ Dimension of R.H.S is not equal to the dimension of L.H.S. Hence, the given relation is not correct dimensionally.$\\$ To make the given relation correct, the R.H.S should also be dimensionless. One way to achieve this is by dividing the R.H.S by the speed of rainfall v’ Therefore, the relation reduces to$\\$ $\tan \theta=\dfrac{v}{v'}$ This relation is dimensionally correct.