If the change in the value of 'g' at a height h above the surface of the earth is the same as at a depth x below it, then (both x and h being much smaller than the radius of the earth)

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The change in the value of g at a height h above the surface of earth is the same as at a depth d below the earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?

The correct option is C d=2hwe know gh=g(1−2hR)gd=g(1−dR)But gh=gd∴g(1−2hR)=g(1−dR)1−2hR=1−dRor d=2h

The change in the value of $g$ at a height $h$ above the surface of earth is the same as at a depth $d$ below the earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct?

The correct option is C $d = 2 h$
we know $g_{h} = g (1 - \frac{2 h}{R})$
$g_{d} = g (1 - \frac{d}{R})$
But $g_{h} = g_{d}$
$∴ g (1 - \frac{2 h}{R}) = g (1 - \frac{d}{R})$
$1 - \frac{2 h}{R} = 1 - \frac{d}{R}$
or $d = 2 h$