1.

The time period `T` of the moon of planet mars (mass `M_(m)`) is related to its orbital radius `R` as (`G`=gravitational constant)A. `T^(2)=(4pi^(2)R^(3))/(GM_(m))`B. `T^(2)=(4pi^(2)GR^(3))/(M_(m))`C. `T^(2)=(4piR^(3)G)/(M_(m))`D. `T^(2)=4piM_(m)GR^(3)`

Answer» Correct Answer - A
(a) Time period, `T=(2pi R)/(sqrt((GM_(m))/( R)))=(2piR^(3//2))/(sqrt(GM_(m))`
where the symbols have their meanings as given in the question.
Squaring both sides, we get, `T^(2)=(4pi^(2)R^(3))/(GM_(m))`


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