Let ' $g_{h}$ ' and ' $g_{d}$ ' be the acceleration due to gravity at height ' $h$ ' above the earth's surface and at depth ' $d$ ' below the earth's surface respectively. IF $g_{h} = g_{d}$ then the relation between ' $h$ ' and ' $d$ ' is

d = h

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d = \frac{h}{2}

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d = \frac{h}{4}

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d = 2 h

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Solution

The correct option is D $d = 2 h$
Acceleration due to gravity at height $h$ above the earth surface $g_{h} = g (1 - \frac{2 h}{R})$
where $R$ is the radius of earth.
Acceleration due to gravity at depth $d$ below the earth surface $g_{d} = g (1 - \frac{d}{R})$
But $g_{h} = g_{d}$ implies $g (1 - \frac{2 h}{R}) =$ $g (1 - \frac{d}{R})$
$⟹$ $d = 2 h$

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Let 'gh' and 'gd' be the acceleration due to gravity at height 'h' above the earth's surface and at depth 'd' below the earth's surface respectively. IF gh=gd then the relation between 'h' and 'd' is

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Let ' $g_{h}$ ' and ' $g_{d}$ ' be the acceleration due to gravity at height ' $h$ ' above the earth's surface and at depth ' $d$ ' below the earth's surface respectively. IF $g_{h} = g_{d}$ then the relation between ' $h$ ' and ' $d$ ' is