Imagine a light planet revolving around a very massive star in a circular orbit of radius r with a period of revolution T. On what power of r will the square of time period will depend if the gravitational force of attraction between the planet and the star is proportional to `r^(-5//2)`.

Explanation

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