Question

The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then, [NEET 2017]

Easy

Solution

Acceleration due to gravity at height h above earth's surface,
$g_{h} = g (1 - \frac{2 h}{R}) (∵ h ≪ R)$
Acceleration due to g:t:avity at depth d below earth's surface,
$g_{d} = g (1 - \frac{d}{R})$
Given, h = 1km and g_d = g_h
or $g (1 - \frac{d}{R}) = g (1 - \frac{2 h}{R})$
$\Rightarrow d = 2 h or d = 2 km$

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