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If the change in the value of g at the height above the surface of the earth is the same as at a depth x below it, then (both x and h being much smaller than the radius of the earth)

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x = h

x = 2h

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

$x = h^{2}$

answer is B.

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Detailed Solution

$g_{h} = g_{x}$

$\begin{array}{l} \Rightarrow g (1 - \frac{2 h}{R}) = (1 - \frac{x}{R}) \\ \Rightarrow 1 - \frac{2 h}{R} = 1 - \frac{x}{R} \\ \Rightarrow x = 2 h \end{array}$

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