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Match List-I with List-II. List-I (A) Kinetic energy of planet (B) Gravitation Potential energy of Sun-planet system. (C) Total mechanical energy of planet (D) Escape energy at the surface of planet for unit mass object List-II (I) GMm/a (II) GMm/2a (III) Gm/r (IV) -GMm/2a (Where a = radius of planet orbit, r = radius of planet, M = mass of Sun, m = mass of planet) Choose the correct answer from the options given below:

1. (A) – II, (B) – I, (C) – IV, (D) – III
2. (A) – III, (B) – IV, (C) – I, (D) – II
3. (A) – I, (B) – IV, (C) – II, (D) – III
4. (A) – I, (B) – II, (C) – III, (D) – IV

Correct answer: (A) – II, (B) – I, (C) – IV, (D) – III

Solution

The correct matches are based on the definitions of the energies involved: Kinetic energy of a planet in orbit is given by GMm/2a (option II), the gravitational potential energy of the Sun-planet system is -GMm/a (option I), the total mechanical energy combines both kinetic and potential energies resulting in -GMm/2a (option IV), and the escape energy for a unit mass object is GM/r (option III).

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