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  4. A body of mass m rises to height h=R / 5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is

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Q. A body of mass $m$ rises to height $h=R / 5$ from the earth's surface, where $R$ is earth's radius. If $g$ is acceleration due to gravity at earth's surface, the increase in potential energy is

Solution:

$U _{ f }= u _{ i }=\frac{- GmM }{\left( R +\frac{ R }{5}\right)}+\frac{ GmM }{ R }$
$=\frac{-5 GmM }{6 R }+\frac{ GmM }{ R }$
$=\frac{ GmM }{6 R }=\frac{ mgR }{6}$