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15.12)  For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same (a) frequency, (b) phase, (c) amplitude? Explain your answers. (ii) What is the amplitude of a point 0.375 m away from one end?

(i) (a) All the points vibrate with the same frequency of 60 Hz. (b) They all have the same phase as it depends upon time. (c) At different points, the amplitude is different and is equal to A(x) given by   (ii)

14.22 Show that for a particle in linear SHM the average kinetic energy over a period of
oscillation equals the average potential energy over the same period.

Let the equation of oscillation be given by  Velocity would be given as  Kinetic energy at an instant is given by Time Period  is given by The Average Kinetic Energy would be given as follows The potential energy at an instant T is given by  The Average Potential Energy would be given by We can see Kav = Uav

Q 4. 22  $\hat i$ and $\hat j$ are unit vectors along x- and y- axis respectively. What is the magnitude and direction of the vectors $\hat i + \hat j$, and $\hat i - \hat j$−? What are the components of a vector$A=2\hat i +3 \hat j$ along the directions of $\hat i + \hat j$ and $\hat i - \hat j$? [You may use graphical method]

Let A be a vector such that:-                  Then the magnitude of vector A is given by   :             Now let us assume that the angle made between vector A and x-axis is . Then we have:-                                                                                   Similarly, let B be a vector such that:-        The magnitude of vector B is     :                        Let  be the angle...

2.30 (f)    Explain, giving reasons, which of the following sets of quantum numbers are not possible.

$n=3,l=1\: \: \: \: \: m_{l}=0,m_{s}=+1/2$

Given quantum numbers : It is possible and it is 3p orbital.

2.30 (e)   Explain, giving reasons, which of the following sets of quantum numbers are not possible.

$n=3,l=3\: \: \: \: \: m_{1}=-3,m_{s}=+1/2$

Given quantum numbers : It is NOT possible because when , .

2.30 (d)   Explain, giving reasons, which of the following sets of quantum numbers are not possible.

$n=2,l=1\: \: \: \: \: m_{1}=0,m_{s}=-1/2$

Given quantum numbers : It is possible and it is 2p orbital.

2.30 (c)    Explain, giving reasons, which of the following sets of quantum numbers are not possible.

$n=1,l=1\: \: \: \: \: m_{1}=0,m_{s}=+1/2$

Given quantum numbers : It is NOT possible because when .

2.30  (b)   Explain, giving reasons, which of the following sets of quantum numbers are not possible.

$n=1,l=0\: \: \: \: \: m_{1}=0,m_{s}=-1/2$

Given quantum numbers : It is possible and it is 1s orbital.

2.30  (a)  Explain, giving reasons, which of the following sets of quantum numbers are not possible.

$n=0,l=0\: \: \: \: \: m_{1}=0,m_{s}=+1/2$

Given quantum numbers : NOT possible, because n cannot be equal to zero.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(j) Cloning

Cloning of organs is good but by cloning technique, the clone of human can also be made which will create social disturbance and fraud in the society.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(i) Plastic surgery

Plastic surgery is good for the people who are victims of acid attack or fire burn. However, it also has side-effects.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(h) Purification of water for drinking

Purification of water for drinking is very important for some of the regions as the people living there are having many water-related diseases. Also, the pure water is limited so we need to develop many techniques for purification of the water.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(g) Development of new and powerful techniques of chemical and biological warfare).

Development of new and powerful techniques of chemical and biological warfare is not good for society as it only has a bad effect in maintaining peace in the world. Further, they may also be used by terrorists which is harmful to safety for the citizens.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(f ) Development of nuclear weapons

Nuclear weapons are the most dangerous weapons in the current world as they may wipe off not only a country but they also have long term effects. Thus nuclear elements should only be used for the generation of electricity.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(e) Putting artificial satellites into orbits around the Earth

The artificial satellite are good as they make the life of people more easier by providing modern days must facilities like internet connectivity, mobile network or GPS.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(d) Computers for increase in work efficiency

The computer can definitely decrease the human effort and increase efficiency so they are good the progress in society. But it must be noticed that excessive use of a computer may lead to unemployment in the world.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(c) Prenatal sex determination

Prenatal sex determination cannot be good for society as the thinking of modern people is to give birth only to a male child. So this will create imbalance by creating gender inequality.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(b) Television for eradication of illiteracy and for mass communication of news and ideas.

Television for the eradication of illiteracy and for mass communication of news and ideas will be good as in the modern few are left behind so we need to make them literate in one form or the other for a better society.

Q1.11    Science, like any knowledge, can be put to good or bad use, depending on the user. Given below is an application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised :

(a) Mass vaccination against smallpox to curb and finally eradicate this disease from the population. (This has already been successfully done in India).

The mass vaccination is very good for the society as the world has witnessed so many deaths due to the small pox virus.

Q1.16    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.

Scientists as other human have hobbies and are humorists. For e.g, Albert Einstein had the hobby of playing the violin. So apart from doing their serious work on physics they also have fun in their lifestyle. Thus the image of science and scientists is patently false which states that science is tough and boring. You may read a few of the books which supports the above statement and tell you...
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