Question

If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth is?

• A. $\frac{4\pi G}{3gR}$
• B. $\frac{3\pi R}{4gG}$
• C. $\frac{3g}{4\pi RG}$
• D. $\frac{\pi R}{12G}$

Answer 1

The correct option is C $\frac{3g}{4\pi RG}$

Expression of g is: $g=\frac{G{M}_E}{R^2}$ that given the mass of earth $\left(M_E\right)$ as :-

$M_E=\frac{g{R}^2}{G}$, R: Radius of earth.

Assuming Earth to be spherical, It would have volume (v) $=\frac{4}{3}\pi R^3$

So mean density of Earth :-

$d=\frac{M_E}{V}=\frac{g{R}^2}{G}\times \frac{3}{4\pi R^3}=\frac{3g}{4\pi RG}$ (Ans)