Q. Imagine a light plant revolving around a very massive star in circular orbit of radius $r$ with a period of revolution $T$. If the gravitational force of attraction between the planet and the star is proportional to $r^{- 5/2}$. Then the correct relation is
A) $T^{2} \propto r^{5/2}$
B) $T^{2} \propto r^{7/2}$
C) $T^{\ } \propto r^{5/2}$
D) $T^{2} \propto r^{7/2}$
Explanation
(b) Since, gravitation provides centripetal force
$\frac{mv^{2}}{r} = \frac{k}{r^{5/2}}\ ie,\ v^{2} = \frac{k}{mr^{3/2}}$
So that $T = \frac{2\pi r}{v} = \sqrt{\frac{mr^{3/2}}{k}}\ ie,\ T^{2} = \frac{4\pi^{2}m}{k}r^{7/2}$
$\therefore T^{2} \propto r^{7/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.