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^(5//2)`
B. `R^(3//2)`
C. `R^(3)`
D. `R^(7//2)`

Answer

D

Explanation

The C.P. force is provided by the gravitational force
`(mv^(2))/(R )=(GMm)/(R^(5//2))therefore mR omega^(2)=(GMm)/(R^(5//2))`
`R omega^(2)prop R^(-5//2) " " therefore omega^(2)prop R^(-7//2)`
`therefore ((2pi)/(T))^(2)prop R^(-7//2)" " therefore (4pi^(2))/(T^(2))prop R^(-7//2)`
`therefore (4pi^(2))/(T^(2))prop (1)/(R^(+7//2))" " therefore T^(2)prop R^(7//2)`