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. `T^2` is proportional to `R^2`
B. `T^2` is proportional to `R^(7//2)`
C. `T^2` is proportional to `R^(3//2)`
D. `T^2` is proportional to `R^(3.75)`

Answer

B

Explanation

`(mv^2)/R prop R^(-5//2) , therefore V prop R^(-3//4)` Now, `T=(2pR)/v` or `T^2 prop (R/v)^2 , T^2 prop (R/(R^(-3//4))^2` or `T^2 prop R^(7//2)`