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

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

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$x=2h$

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(B) The acceleration due to gravity at a height $h$ above the surface is given by $g_h = g(1 - \frac{2h}{R_e})$.The change in the value of $g$ at height $h$ is $\Delta g_h = g - g_h = g(\frac{2h}{R_e})$.The acceleration due to gravity at a depth $x$ below the surface is given by $g_x = g(1 - \frac{x}{R_e})$.The change in the value of $g$ at depth $x$ is $\Delta g_x = g - g_x = g(\frac{x}{R_e})$.According to the problem,the change in $g$ is the same in both cases:$\Delta g_h = \Delta g_x$$g(\frac{2h}{R_e}) = g(\frac{x}{R_e})$$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 (where $x$ and $h$ are much smaller than the radius of the earth $R_e$):

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