Q.

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is

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a

32mgR

b

m g R

c

2mgR

d

12mgR

answer is D.

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Detailed Solution

Work done =Change in potential energy                     =Uf-Ui=-GMm(R+h)--GMmRwhere  M is the mass of earth and R  is the radius of earth.∴ W=GMm1R-1(R+h)  Now, h=R ∴W=GMm1R-12R=GMm2R ⇒ W=mgR2                                                 ∵ g=GMR2
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The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is