The time period `T` of the moon of planet mars (mass `M_(m)`) is related to its orbital radius `R` as (`G`=gravitational constant)

Options

A. `T^2 = (4pi^2R^3)/(GM_m)`
B. `T^2 = (4pi^2 GR^3)/(M_m)`
C. `T^2 = (2pi R^3 G)/(M_m)`
D. `T^2 = 4pi M_m GR^3`

Answer

A

Explanation

Time period, `T = (2pi R)/(sqrt( (GM_m)/( R) ) ) = (2pi R^(3//2))/(sqrt(GM_m))`
where the symbols have their meaning as given in the question.
Squaring both sides, we get `T^2 = (4pi^2 R^3)/(GM_m)`