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Variation of G Due to Height and Depth

Question

If $g$ is same at a height $h$ and at a depth $d$ , then
$R = 2 d$
$h = d$
none
$d = 2 h$

A

h = d

B

none

C

d = 2 h

D

R = 2 d

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Solution

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We know, $g_{h} = g (1 - \frac{2 h}{R})$ and $g_{d} = (1 - \frac{d}{R})$
When $g_{d} = g_{h}$ then,
$(1 - \frac{2 h}{R}) = 1 - \frac{d}{R}$
$∴ (\frac{- 2 h}{R}) = - \frac{d}{R}$
$d = 2 h$

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