Q. If different planets have the same density but different radii, then the acceleration due to gravity on the surface of the planet is related to the radius $(R)$ of the planet as
A) $g \propto R^{2}$
B) $g \propto R^{\ }$
C) $g \propto \frac{1}{R^{2}}$
D) $g \propto \frac{1}{R^{\ }}$
Explanation
(b) $g = \frac{GM}{R^{2}} = \frac{G}{R^{2}}\frac{4}{3}\pi R^{3}\rho = \frac{4}{3}\pi G\rho R\ ie,\ g = R$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.