If g is the acceleration due to gravity on

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If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth $R$, is

A

$\frac{1}{2}mgR$

B

$2 mgR$

C

$mgR$

D

$\frac{1}{4}mgR$

If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth $R$, is

Gain in potential energy $\Delta U = \frac{{mgh}}{{1 + \frac{h}{R}}}$
If $h = R$ then $\Delta U = \frac{{mgR}}{{1 + \frac{R}{R}}} = \frac{1}{2}mgR$