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A particle is moving with a uniform spee...

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the `n^(th)` power of R. If the period of rotation of the particle is T, then :

A

`TpropR^(((n+1)/(2)))`

B

`TpropR^((n)/(2))`

C

`TpropR^((3)/(2))` For any n

D

`TpropR^((n)/(2)+1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Since, `Fprop(1)/(R^(n))implies(k)/(R^(n))=(mv^(2))/(R)impliesvpropR^(((1-n)/(2)))`
`T=(2piR)/(v)impliesTpropR^(((n+1)/(2)))`
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