If R is the radius of the earth and g is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be: [2023]

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Solution

Q.
If R is the radius of the earth and g is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be: [2023]

1 $\frac{π R G}{12 g}$

2 $\frac{3 π R}{4 g G}$

3 $\frac{3 g}{4 π R G}$

4 $\frac{4 π G}{3 g R}$

Ans.
(3)

The relation between acceleration due to gravity and radius of earth is $g = \frac{G M}{R^{2}}$

We know $M = ρ V$

Then, $g = \frac{4}{3} π G R ρ or ρ = \frac{3 g}{4 π G R}$

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