A light planet is revolving around a very massive star in a circular orbit of radius R with a period of revolution T, if the gravitational force of attraction between the two varies as `R^(-5//2)`, then `T^(2)` is proportional to :

Options

A. `R^(3)`
B. `R^((7)/(2))`
C. `R^((3)/(2))`
D. `R^((5)/(2))`

Answer

B

Explanation

Here `(mv^(2))/(R )=(GMm)/(R^(5//2)) rArr v^(2)=(GM)/(R^(3//2))`
Now `T=(2pi R)/(v) therefore T^(2)=(4pi^(2)R^(2))/(v^(2))`
`T^(2)=(4pi^(2)R^(2)xxR^(3//2))/(GM) rArr T^(2)prop R^(7//2)`
Thus correct choice is (b).