Imagine a light planet 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 planet and the star is proportional to `R^(-5//2)`, then `T^2` is proportional to

Options

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

Answer

B

Explanation

For motion of planet in a circular orbit,
Centripetal force = Gravitational force
or `mRomega^2 = (GmM)/R^(5//2)` or `R^(7//2)omega^2=GM`
`R^(7//2)=(GM)/omega^2 =(GM)/(2pi//T)^2 =(T^2xxGM)/(4pi^2)` or `T^2 prop R^(7//2)`