A small planet is revolving around a very massive star in a circular orbit of Radius R with a period of revolution T. If the gravitational force between the planet and the star were proportional to `R^(-5//2)`, then T would be proportional to

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)`