Q. If $g \propto \frac{1}{R^{3}}$ (instead of $\frac{1}{R^{2}}$ ), then the relation between time period of a satellite near earth’s surface and radius $R$ will be
A) $T^{2} \propto R^{3}$
B) $T \propto R^{2}$
C) $T^{2} \propto R$
D) $T \propto T$
Explanation
(b) Gravitational force provides the required centripetal force
$m\omega^{2}R = \frac{GMm}{R^{3}} \Rightarrow \frac{4\pi^{2}}{T^{2}} = \frac{GM}{R^{4}} \Rightarrow T \propto R^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.