A body moves in a circular orbit of radius R under the action of a central force. Potential due to the central force is given by V(r) = kr (k is a positive constant). Period of revolution of the body is proportional to-

Options

A. `R^(1//2)`
B. `R^(-1//2)`
C. `R^(-3//2)`
D. `R^(-5//2)`

Answer

A

Explanation

`V (r) kr`
`U (r) = mkr" "omega^(2) = (k)/(r)`
`F = -(dU)/(dr) = -m" "omega = sqrt((k)/(r))`
`T = (2pi sqrt(r))/(sqrt(k))`