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The acceleration due to gravity g and mean density of earth $ρ$ are related by which of the following relations ? [G = gravitational constant and R = radius of earth].
$ρ = \frac{4 π g R^{2}}{3 G}$
$ρ = \frac{4 π g R^{3}}{3 G}$
$ρ = \frac{3 G}{4 π g R}$
$ρ = \frac{3 G}{4 π g R^{3}}$

A

ρ = \frac{4 π g R^{2}}{3 G}

B

ρ = \frac{4 π g R^{3}}{3 G}

C

ρ = \frac{3 G}{4 π g R^{3}}

D

ρ = \frac{3 G}{4 π g R}

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