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Question

A body of mass 'm' is raised from the surface of the earth to a height 'nR' (R- radius of earth). Magnitude of the change in the gravitational potential energy of the body is (g-acceleration due to gravity on the surface of earth)

A
(nn+1)mgR
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B
(n1n)mgR
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C
mgRn
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D
mgR(n1)
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Solution

The correct option is A (nn+1)mgR
At surface gravitaional potential energy U1=GMmR
At height nR,U2=GMmR+nR
|U2U1|=(GMmR+nR)(GMmR)=GMmRGMmR+nRGMmR[11n+1](nn+1)GMmR(nn+1)mgR

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