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)`.

Explanation

`F prop r^(-5//2) implies F=kr^(-5//2)`
`(mv^(2))/r=kr^(-5//2) implies v^(2)=k/mr^(-3//2)`
`v prop r^(-3//4)`
`T=(2pir)/vimplies T prop1/(r^(3//4))`
`T propr^(3//4) implies T^(2) propr^(7//2)`