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Question

If the change in value of acceleration due to gravity at a height h above the surface of the earth is same as at a depth x below it, then (Assume, x and h being much smaller than the radius of the Earth)

A
x=h
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B
x=2h
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C
x=h2
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D
x=h2
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Solution

The correct option is B x=2h
The acceleration of due to gravity at a depth d below the surface of the Earth is given by gd=g(1dR)...(1) The acceleration due to gravity at a height h above the surface of the Earth is given by gh=g(12hR)...(2)
According to the question,
ghg=gxg

Substituting the values,

g(12hR)g=g(1xR)g

g(2hRe)=g(xRe)

x=2h

Hence, option (b) is the correct answer.
The acceleration of due to gravity at a depth d below the surface of the earth is given by gd=g(1dR)Why this question?
The result gd=(1dR) is valid for any value of d, small or large.

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