If R=radius of the earth and g =acceleration due to gravity on the surface of the earth, the acceleration due to gravity at a distance (r<R) from the centre of the earth is proportional to
A
r
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B
r2
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C
r−2
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D
r−1
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Solution
The correct option is Ar F(d)=GM′m/r2 M′=Mr3/R3 F(d)=GMmr/R3 r=R−d g(d)=GM(R−d)/R3 g(d)=g[(R−d)/R] g(d)=g(1−dR) Therefore, the gravitational field varies proportional to r.