Gravitational potential of the body of mass m at a height h from surface of earth of radius R is (Take $g =$ acceleration due to gravity at earth's surface)

- g (R + h)

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- g (R - h)

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g (R + h)

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g (R - h)

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Solution

The correct option is B $- g (R - h)$
If a point mass m is placed at a height h from surface of earth, the potential energy is
$U_{h} = - \frac{G M m}{(R + h)} = \frac{- g R^{2} m}{R (1 + \frac{h}{R})} = \frac{- g R^{2} m}{R} {(1 + \frac{h}{R})}^{- 1}$
$(∵ g = \frac{G M}{R^{2}})$

$U_{h} = \frac{- g R^{2} m (R - h)}{R^{2}}$ $= - g m (R - h)$

$\Rightarrow V = \frac{U_{h}}{m} = \frac{- g m (R - h)}{m} = - g (R - h)$

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