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. `r^(3)`
B. `r^(2)`
C. `r^(2.5)`
D. `r^(3.5)`

Answer

D

Explanation

`(mv^(2))/r=(GMm)/R^(5//2) [:.Fprop1/r^(5//2)]`
or `romega^(2)=(GM)/r^(5//2)`
or `r(4pi^(2))/(T^(2))=(GM)/r^(5//2)`
or `T^(2)propr^(5//2)` or `T^(2)propr^(3.5)`