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Variation of G Due to Height and Depth

At which heig...

Question

At which height above earth's surface value of $^{'} g^{'}$ is same as in a mine $100 k m$ deep.

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Solution

The variation of $g$ with height is $g = g (1 - \frac{2 h}{r})$

The variation of $g$ with depth is $g = g (1 - \frac{d}{r})$

Equating the above two equation we get the height as

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

$= 50 k m$

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