Question

Two planets have radii $r_1$ and $r_2$ and densities $d_1$ and $d_2$ respectively. Then the ratio of accelerations due to gravity on them is

• A. $r_1d_1 : r_2d_2$
• B. $r_1d_2 : r_2d_1$
• C. $r_1^2d_1 : r_2^2d-2$
• D. $r_1d^2_1 : r_2d_2^2$

Answer 1

Answer: (A)

Acceleration due to gravity
$g=\frac{GM}{r^2}$
or $g=\frac{G}{r^2}\times\frac{4}{3}\pi r^3d=\frac{4}{3}\pi rdG$
= $\frac{g_1}{g_2}=\frac{d_1r_1}{d_2r_2}$