If g is acceleration due to gravity on earth's surface, gain in potential energy of an object of

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7.Gravitation

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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

$\frac{1}{2}mgR$

$2 mgR$

$mgR$

$\frac{1}{4}mgR$

(IIT-1983)

Solution

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

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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

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