If the change in the value of g at a height h | vedclass

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(B) The value of acceleration due to gravity at a height $h$ above the surface of the earth is given by $g_h = g \left( 1 - \frac{2h}{R} \right)$.The

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$x = 2h$

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(B) The value of acceleration due to gravity at a height $h$ above the surface of the earth is given by $g_h = g \left( 1 - \frac{2h}{R} \right)$.The change in the value of $g$ at height $h$ is $\Delta g_h = g - g_h = g \left( \frac{2h}{R} \right)$.The value of acceleration due to gravity at a depth $x$ below the surface of the earth is given by $g_x = g \left( 1 - \frac{x}{R} \right)$.The change in the value of $g$ at depth $x$ is $\Delta g_x = g - g_x = g \left( \frac{x}{R} \right)$.According to the problem,the change in the value of $g$ is the same at height $h$ and depth $x$,so $\Delta g_h = \Delta g_x$.Therefore,$g \left( \frac{2h}{R} \right) = g \left( \frac{x}{R} \right)$.On solving this equation,we get $x = 2h$.

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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