Question

A hypothetical planet has density $\rho$, radius R, and surface gravitational acceleration $g$. If the radius of the planet were doubled, but the planetary density stayed the same, find the acceleration due to gravity at the planet's surface.

• A. $4g$
• B. $2g$
• C. $g$
• D. $g/2$

Answer 1

The correct option is B $2g$

We know that, $g=\frac{GM}{R^2}=\frac{G\frac{4}{3}\pi R^3\rho }{R^2}$$=\frac{4}{3}\pi G\rho R$
From the above equation we can deduce that, $g\propto R$, when $\rho$ is constant.

This means, when $R$ is doubled, acceleration due to gravity on the planet's surface should also be doubled.