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

The gravitational force provided necessary centripetal force `(mV^(2))/r=K/(r^(5//2))rArrV^(2)=K/(mr^(3//2))`
But `T=(2pir)/V=2pirsqrt((mr^(3//2))/K), :. T^(2)alphar^(7//2)`