A body of mass $m$ is placed on the surface of earth. Find the work required to lift this body by a height $h = \frac{R_{e}}{1000}$

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$\frac{G M_{e} m}{1000 R_{e}}$

$\frac{G M_{e} m}{100 R_{e}}$

$\frac{G M_{e} m}{10 R_{e}}$

$\frac{G M_{e} m}{R_{e}}$

answer is A.

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Detailed Solution

$h = \frac{R_{e}}{1000},$ as $h ≪ R_{e},$ so
we can apply $W_{e x t} = m g h; W_{e x t} = (m) (\frac{G M_{e}}{{R_{e}}^{2}}) (\frac{R_{e}}{1000}) = \frac{G M_{e} m}{1000 R_{e}}$

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