Question:
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:
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:
Updated On: Jan 31, 2026
- (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
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The Correct Option is A
Approach Solution - 1
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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Approach Solution -2
Step 1: Recall the relevant formulas
For a planet of mass \( m \) orbiting the Sun of mass \( M \) at a distance \( a \):
- Kinetic energy of planet, \( K = \dfrac{GMm}{2a} \)
- Gravitational potential energy of the Sun–planet system, \( U = -\dfrac{GMm}{a} \)
- Total mechanical energy of planet, \( E = K + U = -\dfrac{GMm}{2a} \)
- Escape energy per unit mass from surface of planet, \( \varepsilon = \dfrac{GM}{r} \)
Step 2: Match each quantity correctly
| List-I | List-II |
|---|---|
| (A) Kinetic energy of planet | \( +\dfrac{GMm}{2a} \) |
| (B) Gravitational potential energy of Sun–planet system | \( -\dfrac{GMm}{a} \) |
| (C) Total mechanical energy of planet | \( -\dfrac{GMm}{2a} \) |
| (D) Escape energy at the surface of planet for unit mass object | \( +\dfrac{GM}{r} \) |
Step 3: Final correspondence
\[ (A) - II, \quad (B) - I, \quad (C) - IV, \quad (D) - III \]
Final answer
(A) – II, (B) – I, (C) – IV, (D) – III
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