Choose the correct statement.

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(D) The acceleration due to gravity at an altitude $h$ is given by $g_h = \frac{GM}{(R+h)^2}$.Since $g_h$ is inversely proportional to the square of t

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Acceleration due to gravity decreases with increasing depth assuming earth to be a sphere of uniform density.

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(D) The acceleration due to gravity at an altitude $h$ is given by $g_h = \frac{GM}{(R+h)^2}$.Since $g_h$ is inversely proportional to the square of the distance from the center,$g_h$ decreases as altitude $h$ increases.Acceleration due to gravity at the surface is $g = \frac{GM}{R^2}$,which clearly depends on the mass of the Earth $M$.$A$ geostationary satellite must have a time period of exactly $24 \ h$ to remain stationary relative to the Earth's surface.The acceleration due to gravity at a depth $d$ is given by $g_d = g(1 - \frac{d}{R}) = g(\frac{R-d}{R})$.As depth $d$ increases,the term $(\frac{R-d}{R})$ decreases,so $g_d$ decreases with increasing depth.Therefore,option $D$ is the correct statement.

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