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  4. Work done in taking a body of mass m to a height nR above surface of earth will be: ( R = radius of earth )

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Q. Work done in taking a body of mass $m$ to a height $nR$ above surface of earth will be : $( R =$ radius of earth $)$

Solution:

$W =\frac{ GmM }{ R }-\frac{ GmM }{ nR + R }$
$=\frac{ GMm }{ R }\left[1-\frac{1}{ n }\right]=\frac{ GMm }{ R }\left[\frac{ n }{ n +1}\right]$
$= mgR \left(\frac{ n }{ n +1}\right)$