Q. Two planets have radii $r_{1}$ and $r_{2}$ and densities $d_{1}$ and $d_{2}$ respectively. Then the ratio of acceleration due to gravity on them will be
A) $r_{1}d_{1}:r_{2}d_{2}$
B) $r_{1}d_{2}:r_{2}d_{1}$
C) $r_{1}^{2}d_{1}:r_{2}^{2}d_{2}$
D) $r_{1}:r_{2}$
Explanation
(a) The relation between density $(d)$ and acceleration due to gravity $(g)$ is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d = \frac{3g}{4\pi R_{e}G}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{d_{1}}{d_{2}} = \frac{g_{1}}{r_{1}} \times \frac{r_{2}}{g_{2}}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{g_{1}}{g_{2}} = \frac{d_{1}r_{1}}{d_{2}r_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.