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Question

A body of mass m is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

A
3mgR
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B
13mgR
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C
2mgR
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D
23mgR
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Solution

The correct option is D 23mgR
From work-energy theorem, work done = change in potential energy.
Work done = 3RRGmMx2dx=2GmM3R=2mgR3.

Please note that the gravitational force will necessarily vary over this height because it is comparable with earth's radius.

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