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1. Is it possible for one object to gain mechanical energy from another without touching it? Explain. Answer: Yes. It is possible for one object to gain mechanical energy from another without touching it. Consider following few examples. a) GRAVITATION: Recall Newton’s law of gravitation. The force of attraction between the two bodies is given by mm F G 12 2 r Hence when any object is released from some height, it automatically gains the kinetic energy because of Earth’s gravitational force acting on it and it approaches the ground. In this case, initially, there is obviously no contact between the object and the earth. In this case, the object is in the gravitational field of the Earth and hence it has gravitational potential energy due to earth’s gravitational field. When released, this gravitational potential energy gets converted into kinetic energy. b) ELECTROSTATICS: Recall Coulomb’s law in Electrostatics, of the force between the two electric charges. The force of attraction between the two charges is given by qq F K 12 2 r where K is a constant of proportionality. Now, if the charges are placed in vacuum, the equation becomes 1 q 1q 2 where the symbols have their usual meanings. F 4 0 r 2 Consider two charged particles charges of 1 coulomb. Both the charges are +ve. If the charges are held at some finite distance, these charges will repel each other. But if released, both the charges will move away from each other, because of repulsive force. In this case, each charge is in electric field of another one. Hence Each charge has some finite potential energy because of presence of the other. This potential energy gets converted into kinetic energy, and the charges depart. c) Magnetism: On the parallel ground, think of what would happen in case, if a north or south pole of one magnet is brought near N/S pole of another magnet. Without touching, the magnets will experience the force of Repulsion/Attraction depending on the poles facing each other. 2. A ball is thrown straight upward on the Moon. Is the maximum height it reaches less than, equal to, or greater than the maximum height reached by a ball thrown upward on the Earth with the same initial speed (no air resistance in both cases)? Explain. Answer: Consider the third kinematical equation, v2 = u2 + 2as --- (1) where u – initial velocity, v –velocity after traveling distance s. a – acceleration. For vertically upward motion, the gravitational acceleration (g) acts as a retardation and therefore is to be taken as –ve. Then equation (1) gives v2 = u2 – 2gh --- (2) When the ball attains maximum height i.e. Hmax, its velocity v = 0. Then eqn (2) gives, 0= u2 – 2gHmax i.e. u2 =2gHmax The maximum height attained ON EARTH H max u2 2g ------ (4) On MOON: th 1 The gravitational acceleration of the moon (say gm) is that of the Earth. 6 g i.e. g m 6 u2 The maximum height attained ON MOON h max 6 2g h max 6H max for the same initial speed. i.e. i.e. The maximum height attained on the Moon will be 6 times that on the Earth for the same initial speed, i.e. greater than that attained on the earth. ------------