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 proportational to `R^(-5//2)`, then
(a) `T^(2)` is proportional to `R^(2)`
(b) `T^(2)` is proportional to `R^(7//2)`
(c) `T^(2)` is proportional to `R^(3//3)`
(d) `T^(2)` is proportional to `R^(3.75)`.

Options

A. `R^(3)`
B. `R^(7//2)`
C. `R^(3//2)`
D. `R^(3.75)`

Answer

B

Explanation

`mRomega^(2)=F_(gr)impliesmRomega^(2)=(k)/(R^(5//2))`
`impliesomega^(2)=(k)/(mR^(7//2))`
`implies omega prop (1)/(R^(7//4))`
`impliesT prop R^(7//4)`
`impliesT^(2) prop R^(7//2)`