Question

There is a planet name 'ALLEN' which has radius three times that of the earth and density two times that of the earth. The acceleration due to gravity on 'ALLEN' will be

• A. $\frac{1}{9}$ times that of earth's gravity.
• B. $\frac{2}{9}$ times that of earth's gravity.
• C. $6$ times that of earth's gravity.
• D. $3$ times that of earth's gravity.

Answer 1

The correct option is C $6$ times that of earth's gravity.

The acceleration due to gravity on earth's surface is given by, $g_e=\frac{G{M}_e}{R_e^2}=\frac{G\left(4/3\right)\pi R_e^3{\rho }_e}{R_e^2}=\frac{4}{3}G\pi R_e{\rho }_e$

(using density $\rho =M/V$)

Given, radius of Allen is $R_a=3R_e$ and density ${\rho }_a=2{\rho }_e$

The acceleration due to gravity on Allen is

$g_a=\frac{4}{3}G\pi R_a{\rho }_a=\frac{4}{3}G\pi \left(3R_e\right)\left(2{\rho }_e\right)=6g_e$