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)`.

Answer

A, B, C, D

Explanation

`(mv^(2))/(R) prop R^(-5//2)`
`:. upsilon prop R^(-3//4)`
Now, `T = (2piR)/(upsilon)` or `T^(2) prop ((R)/(upsilon))^(2)`
or `T^(2) prop ((R)/(R^(-3//4)))^(2)` or `T^(2) prop R ^((7)/(2))`

The correct answer is (b).