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)
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)
$x = h$
$x = 2h$
$x = \frac{h}{2}$
$x = {h^2}$
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)
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 $x = 2h$
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