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Q.

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

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a

$d = \frac{h}{2}$

b

$d = \frac{3 h}{2}$

c

$d = h$

d

$d = 2 h$

answer is C.

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Detailed Solution

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At height g above the surface of the earth, therefore
$g^{'} = g (1 - \frac{2 h}{R}) \Rightarrow Δ g_{1} = \frac{2 h}{R} g$
At depth d below the surface of the earth
$\begin{array}{l} g^{'} = g (1 - \frac{d}{R}) \Rightarrow {Δg}_{2} = \frac{d}{R} g \end{array}$

According to question

${Δg}_{1} = {Δg}_{2} \Rightarrow d = 2 h$

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