Question

The radius of a planet A is twice that of planet B. The average density of the material of planet A is thrice that of planet B. The ratio between the values of acceleration due to gravity on the surface of planet A and that on the surface of planet B is :

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $\frac{4}{3}$
• D. 6

Answer 1

The correct option is D 6

Acceleration due to gravity at planet's surface $g=\frac{GM}{R^2}$

Mass of the planet $M=\rho V=\rho \frac{4}{3}\pi R^3$

$⟹$ $g=\frac{4}{3}\pi G\rho R$

OR $\frac{g_A}{g_B}=\frac{{\rho }_A{R}_A}{{\rho }_B{R}_B}$

Given : ${\rho }_A=3{\rho }_B$ and $R_A=2R_B$

$\therefore$ $\frac{g_A}{g_B}=\frac{3{\rho }_B\left(2R_B\right)}{{\rho }_B{R}_B}=6$