Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity on the surface of the earth is given by

$g=\frac{GM}{R^2}$

The mass of the earth $M$ can be written in terms of its mean density $\rho$ and volume $V$ as

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

Substituting the value of $M$ in the expression for $g$

$g=\frac{G}{R^2}\left(\frac{4}{3}\pi R^3\rho \right)$

$g=\frac{4}{3}\pi RG\rho$

Rearranging the above equation for density $\rho$

$\rho =\frac{3g}{4\pi RG}$

Answer: $\frac{3\mathrm{g}}{4\pi \mathrm{RG}}$