Question

If $R$ is the radius of a planet, $g$ is the acceleration due to gravity and $G$ is the gravitational constant then find the density of the planet.

• A. $\frac{3g}{4G\pi R}$
• B. $\frac{3g}{8G\pi R}$
• C. $\frac{2g}{4G\pi R}$
• D. $\frac{6g}{4G\pi R}$

Answer 1

The correct option is A $\frac{3g}{4G\pi R}$

Acceleration due to gravity is given by, $g=\frac{GM}{R^2}$..........$\left(1\right)$

where G is the gravitational constant, M is the mass of the planet, R is the radius of the planet.

Now $\text{Mass}=\text{Volume}\times \text{density of planet}$

M $=\frac{4}{3}\pi R^3\times \rho$ , where $\rho$ is the Density of the planet

Equation $\left(1\right)$ becomes

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