Question

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. $T^2=\frac{4\pi^2R^3}{GM_m}$
• B. $T^2=\frac{4\pi^2GR^3}{M_m}$
• C. $T^2=\frac{2\pi R^3G}{M_m}$
• D. $T^2=4\pi M_mGR^3$

Answer 1

Answer: (A)

Time period $T=\frac{2\pi r}{v_o}$
$T=\frac{2\pi R}{\sqrt{GM_m}}$ $\left(\therefore v_o=\sqrt{\frac{GM}{R}}\right)$
$T^2=\frac{4\pi^2R^3}{GM_m}$