A small mass m is moved slowly from the surface of earth to height R above the earth. The work done in doing this is

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

for h < < R

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mgh for all values of h

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

for h =R

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\frac{1}{2} m g R

for h =R

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Solution

The correct option is D $\frac{1}{2} m g R$ for h =R
When, h = R
Work done $= - \frac{G M m}{R + R} - [- \frac{G M m}{R}]$
$= \frac{G M m}{2 R} = \frac{1}{2} m g R$

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A small mass m is moved slowly from the surface of earth to height R above the earth. The work done in doing this is

The correct option is D 12mgR for h =RWhen, h = R Work done =−GMmR+R−[−GMmR] =GMm2R=12mgR

The correct option is D $\frac{1}{2} m g R$ for h =R
When, h = R
Work done $= - \frac{G M m}{R + R} - [- \frac{G M m}{R}]$
$= \frac{G M m}{2 R} = \frac{1}{2} m g R$