Question

Two planets of radii $R_1$ and $R_2$ have the same density. The ratio of the acceleration due to gravity on these planets is

• A. $\frac{R_1}{R_2}$
• B. $\frac{R_2}{R_1}$
• C. $\left(\frac{R_2}{R_1}\right)^2$
• D. $\left(\frac{R_1}{R_2}\right)^2$

Answer 1

The Correct Option is A

We know acceleration due to gravity of a planet is given by,
$g = \frac{GM}{R^{2}} = \frac{G\rho \frac{4}{3} \pi R^{3}}{R^{2}}$

or, $g = \frac{4}{3}\pi\rho GR $ or , $g \propto R$
$\therefore\:\:\: \frac{g_{1}}{g_{2}} = \frac{R_{1}}{R_{2}}$