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)

Question

Dr. Abubacker · Accepted Answer

(b) The value of $g$ at the height $h$ from the surface of earth
$g^{'} = g\left( 1 - \frac{2h}{R} \right)$
The value of $g$ at depth $x$ below the surface of earth
$g' = g\left( 1 - \frac{x}{R} \right)$
These two are given equal, hence $\left( 1 - \frac{2h}{R} \right) = \left( 1 - \frac{x}{R} \right)$
On solving, we get $x = 2h$

Q. 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)

Explanation

Reviewed by Dr. Abubacker

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