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The acceleration due to gravity g and mean density of the earth p are related by which of the following relations ? (where G is the gravitational constant and R is radius of the earth)

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$ρ = \frac{4 {πgR}^{3}}{3 G}$

$ρ = \frac{3 g}{4 {πGR}^{3}}$

$ρ = \frac{4 {πgR}^{2}}{3 G}$

$ρ = \frac{3 g}{4 πGR}$

answer is C.

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Detailed Solution

$\begin{array}{l} g = \frac{GM}{R^{2}} = \frac{G (4 / 3) {πR}^{3} ρ}{R^{2}} \\ or ρ = \frac{3 g}{4 πGR} \end{array}$

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