Change in potential energy when a body of mass m is raised to height n R from earth's surface is

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7.Gravitation

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The change in potential energy when a body of mass $m$ is raised to height $n R$ from the earth's surface is ( $R$ is radius of earth)

A

$m g R\left(\frac{n}{n-1}\right)$

B

$n m g R$

C

$m g R\left(\frac{n}{n+1}\right)$

D

$m g R\left(\frac{n^2}{n^2+1}\right)$

Solution

(c)

Potential energy at the surface $=-\frac{G M m}{R}$

Potential energy at height, $n R=-\frac{G M m}{(n+1) R}$

Change in potential energy $=-\frac{G M m}{(n+1) R}+\frac{G M m}{R}$

$=\frac{G M m}{R}\left(\frac{-1+n+1}{n+1}\right)$

$=\left(\frac{n}{n+1}\right)\left(\frac{G M}{R^2}\right) m \times R$

$=m g R\left(\frac{n}{n+1}\right)$

Standard 11

Physics

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