Question

Two planets have radii in the ratio $1:2$ and densities in the ratio $1:3$. The value of the ratio between acceleration due to gravity on the first planet to that of the second planet is:

• A. $6$
• B. $3$
• C. $1/4$
• D. $1/6$

Answer 1

The correct option is D. $1/6$.

We know that,

$g=\frac{G{M}_p}{r^2}$

where

$M_p=Density\times Volume=Density\times \frac{4\pi r^3}{3}$

$g=\frac{G\times density\times 4\pi r^3}{3r^2}$

Thus g$\propto r$ and g$\propto Density$

So,$\frac{g_1}{g_2}=\frac{1\times 1}{2\times 3}=\frac{1}{6}$