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

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Solution

Q.
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 [2017]

1 $d = 1$ km

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

3 $d = 2$ km

4 $d = \frac{1}{2}$ km

Ans.
(3)

The acceleration due to gravity at a height $h$ is given as

$g_{h} = g (1 - \frac{2 h}{R_{e}})$

where $R_{e}$ is the radius of the Earth.

The acceleration due to gravity at a depth $d$ is given as

   $g_{d} = g (1 - \frac{d}{R_{e}})$

Given,   $g_{h} = g_{d}$

$∴ g (1 - \frac{2 h}{R_{e}}) = g (1 - \frac{d}{R_{e}})$

or    $d = 2 h = 2 \times 1 = 2 km$    $(∵ h = 1 km)$

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