Match List-I with List-II, Gravitational Potential, Potential Energy and Escape Velocity

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Q.
Match List-I with List-II [2024]

List - I List - II

A Kinetic energy of planet (I) $- G M m / a$

B Gravitation Potential energy of sun planet system (II) $G M m / 2 a$

C Total mechanical energy of planet (III) $G M m / r$

D Escape energy at the surface of planet for unit mass object (IV) $- G M m / 2 a$

1 (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

2 (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

3 (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

4 (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Ans.
(2)

Potential energy = $- \frac{G M m}{a}$

Total energy = $- \frac{G M m}{2 a}$

kinetic energy = $\frac{G M m}{r}$

Escape energy = $\frac{G M m}{r}$

Solution

1 (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

2 (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

3 (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

4 (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Ans.
(2)

Potential energy = $- \frac{G M m}{a}$

Total energy = $- \frac{G M m}{2 a}$

kinetic energy = $\frac{G M m}{r}$

Escape energy = $\frac{G M m}{r}$

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	List - I		List - II
A	Kinetic energy of planet	(I)	$- G M m / a$
B	Gravitation Potential energy of sun planet system	(II)	$G M m / 2 a$
C	Total mechanical energy of planet	(III)	$G M m / r$
D	Escape energy at the surface of planet for unit mass object	(IV)	$- G M m / 2 a$

Solution

Q. Match List-I with List-II [2024] List - I List - II A Kinetic energy of planet (I) -GMm/a B Gravitation Potential energy of sun planet system (II) GMm/2a C Total mechanical energy of planet (III) GMm/r D Escape energy at the surface of planet for unit mass object (IV) -GMm/2a

1 (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

2 (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

3 (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

4 (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Ans. (2) Potential energy = -GMma Total energy = -GMm2a kinetic energy = GMmr Escape energy = GMmr

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Ans.
(2)

Potential energy = $- \frac{G M m}{a}$

Total energy = $- \frac{G M m}{2 a}$

kinetic energy = $\frac{G M m}{r}$

Escape energy = $\frac{G M m}{r}$