If R is radius of earth and g is acceleration due to gravity on earth's surface. Then mean densi

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7.Gravitation

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If $R$ is the radius of earth and $g$ is the acceleration due to gravity on the earth's surface. Then mean density of earth is ..........

A

$\frac{4 \pi G}{3 g R}$

B

$\frac{3 \pi R}{4 g G}$

C

$\frac{3 g}{4 \pi R G}$

D

$\frac{\pi R g}{12 G}$

Solution

(c)

Acceleration due to gravity at earth's surface is given by,

$g=\frac{G M}{R^2}$

$M=\frac{4}{3} \pi R^3 \rho$

$M \rightarrow$ Mass of earth

$\rho \rightarrow$ Density of earth

$R \rightarrow$ Radius of earth

$\Rightarrow g=\frac{G}{R^2} \times \frac{4}{3} \pi R^3 \rho$

$\Rightarrow \rho=\frac{3 g}{4 \pi G R}$

Standard 11

Physics

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