Match list-I with list-II:List-I List-II (A) Kinetic energy of planet \(- \frac{GMm}{a}\) (B) Gravitational Potential energy of Sun-planet system \(- \frac{GMm}{2a}\) (C) Total mechanical energy of planet \(\frac{GM}{r}\) (D) Escape energy at the surface of planet for unit mass object \(- \frac{GMm}{2a}\)
(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:
| List-I | List-II |
|---|---|
| (A) Kinetic energy of planet | \(- \frac{GMm}{a}\) |
| (B) Gravitational Potential energy of Sun-planet system | \(- \frac{GMm}{2a}\) |
| (C) Total mechanical energy of planet | \(\frac{GM}{r}\) |
| (D) Escape energy at the surface of planet for unit mass object | \(- \frac{GMm}{2a}\) |
- (A) – II, (B) – I, (C) – IV, (D) – III
- (A) – III, (B) – IV, (C) – I, (D) – II
- (A) – I, (B) – IV, (C) – II, (D) – III
- (A) – I, (B) – II, (C) – III, (D) – IV
The Correct Option is A
Solution and Explanation
The kinetic energy (KE) of a planet is given by:
\[ \text{KE} = \frac{1}{2} mv^2 = \frac{GMm}{2a} \]
The gravitational potential energy (PE) of the Sun-planet system is:
\[ \text{PE} = -\frac{GMm}{a} \]
The total mechanical energy (TE) of the planet is:
\[ \text{TE} = \text{KE} + \text{PE} = -\frac{GMm}{2a} \]
Escape energy at the surface of the planet for a unit mass object is given by:
\[ \text{Escape Energy} = \frac{Gm}{r} \]
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