SATHEE: Gravitation Question 294

Gravitation Question 294

Question: Assuming the radius of the earth as R, the change in gravitational potential energy of a body of mass m, when it is taken from the earth’s surface to a height 3R above its surface, is

Options:

A) $[3 m g R]$

B) $[\frac{3}{4} m g R]$

C) $[1 m g R]$

D) $[\frac{3}{2} m g R]$

Show Answer

Answer:

Correct Answer: B

Solution:

Gravitational potential energy (GPE) on the surface of earth,

$[E_{1} = - \frac{G M m}{R}]$ GPE at $[3 R, E_{2} = - \frac{G M m}{(R + 3 R)} = - \frac{G M m}{4 R}]$

$[∴]$ Change in GPE $[= E_{2} - E_{1} = - \frac{G M m}{4 R} + \frac{G M m}{R} = \frac{3 G M m}{4 R}]$

$[= \frac{3 g R^{2} m}{4 R} (∵ g = \frac{G M}{R^{2}}) = \frac{3}{4} m g,, R]$

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Gravitation Question 294

Question: Assuming the radius of the earth as R, the change in gravitational potential energy of a body of mass m, when it is taken from the earth’s surface to a height 3R above its surface, is

Options:

Answer:

Solution:

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