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The time period T of the moon of planet ...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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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