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 proportioinal 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 propR^(-5//2), :. vpropR(-3//4)`
Now `T=(2piR)/v` or `T^(2)prop(R/v)^(2)`
`T^(2) prop(R/R^(-3/4))^(2)` or `T^(2)propR^(7//2)`