Question

A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as on the surface of earth. Its radius in terms of radius of earth R will be:

• A. R/4
• B. R/2
• C. R/3
• D. R/8

Answer 1

The correct option is B

R/2

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

$\therefore \frac{g_p}{g_e}=\left(\frac{P_p}{P_e}\right)\left(\frac{R_p}{R_e}\right)\Rightarrow 1=\left(2\right)\frac{R_p}{R_e}$

$\Rightarrow \frac{R_p}{R_e}=\frac{1}{2}$ $\Rightarrow R_p=\frac{R}{2}$