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Question

The gravitational potential energy of a body at a distance 'r' from the centre of the earth is 'U'. Its weight at a distance 'R' from the centre of the earth is

A
UrR
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B
UrR2
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C
Ur2R2
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D
None of these
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Solution

The correct option is A UrRGravitational potential energy ,U=GMmr.For calculating the weight at distance 2r from centre of earth , we need to get m×g.But here acceleration due to gravity , g is not equal to 9.8m/s−2.Calculation of g can be done using the formula :-g=GMr2Therefore, the value of g at a distance of R=GMR2Thus , weight of the body at a distance R from the body =mg=GMmR=UrRHenece option A is correct

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