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>> $If g is the acceleration due to gravity$

Question

If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

A

$\frac{1}{2} m g R$

B

$2 m g R$

C

$\frac{1}{4} m g R$

D

$m g R$

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Updated on : 2022-09-05

Solution

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Correct option is A)

Gain in potential energy
$= (- \frac{G M m}{2 R}) - (- \frac{G M m}{R})$
$= \frac{G M m}{R} - \frac{G M m}{2 R}$
$= \frac{G M m}{2 R}$
$= \frac{m g R ^{2}}{2 R} A s, G M = g R^{2}$
$= \frac{1}{2} m g R$

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