Q. Two planets have the same average density but their radii are $R_{1}$ and $R_{2}$. If acceleration due to gravity on these planets be $g_{1}$ and $g_{2}$ respectively, then
A) $\frac{g_{1}}{g_{2}} = \frac{R_{1}}{R_{2}}$
B) $\frac{g_{1}}{g_{2}} = \frac{R_{2}}{R_{1}}$
C) $\frac{g_{1}}{g_{2}} = \frac{R_{1}^{2}}{R_{2}^{2}}$
D) $\frac{g_{1}}{g_{2}} = \frac{R_{1}^{3}}{R_{2}^{3}}$
Explanation
(a) $g = \frac{4}{3}\pi\rho GR$. If $\rho$ = constant then $\frac{g_{1}}{g_{2}} = \frac{R_{1}}{R_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.