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A body moves in a circular orbit of radi...

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-

A

`R^((1)/2)`

B

`R^(-(1)/2)`

C

`R^(-(3)/2)`

D

`R^(-(5)/2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Potential V(r) = k r
Electric field `(E) = (-dV)/(dr)`
`implies E=-k`
`implies` Force (F) `=qE=-kq` [As force is constant]
Now, `kq=(mv^2)/R`
`implies v^2 prop R`
Time period `(T) = (2piR)/v=(2piR)/(sqrtR)`
`implies T prop R^(1/2)`
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