Q. The time period $T$ of the moon of planet Mars ($mass\ M_{m}$) is related to its orbital radius $R(G$ = Gravitational constant) as
A) $T^{2} = \frac{4\pi^{2}R^{3}}{GM_{m}}$
B) $T^{2} = \frac{4\pi^{2}{GR}^{3}}{M_{m}}$
C) $T^{2} = \frac{2\pi R^{3}G}{M_{m}}$
D) $T^{2} = 4\pi M_{m}GR^{3}$
Explanation
(a) Time period, $T = \frac{2\pi R}{\sqrt{\frac{GM_{m}}{R}}} = \frac{2\pi R^{3/2}}{\sqrt{GM_{m}}}$
Where the symbols have their meaning as given in the question
Squaring both sides, we get
$T^{2} = \frac{4\pi^{2}R^{3}}{GM_{m}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.