Question

# The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of the earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?

A
d=3h2
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B
d=h2
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C
d=h
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D
d=2h
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Solution

## The correct option is D d=2hVariation of g with altitude h is given by gh=g[1−2hR] (∵h<<R) Also, variation of g with depth d is given as gd=g[1−dR] (∵d<<R) Equating gh and gd, we get d=2h Hence, option (d) is correct. Why this question? Tip: The result gd=g(1−dR) is valid for any value of d, small or large.

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