First slide

Acceleration due to gravity and its variation

Question

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 earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?

Moderate

A

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

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

$d = 2 h$
D

$d = h$

Solution

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

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