Imagine a light planet revoling around a very massiv star in a circular orbit of radius R with a period of revolution T. if the gravitatinal force of attraction between the planet and the star is proportional to `R-(5//2)`

Options

A. `T^2 is proportional to R^(-5//2)`
B. `T^2 is proportonal to R^(7//2)`
C. `T^2 is proportional to R^(3//2)`
D. `T^2 is proportional to R^(3//2)`

Answer

B

Explanation

(b) The centripetal force is provided by `mRomega^2 = GMmR(-5//2)`
`rArr (mR xx 4pi^2)/(T^2) = (GMm)/(R^(5//2) rArr T^2 prop R^(7//2)`