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 :

Options

A. `TpropR^(3//2)` for any n
B. `TpropR^(n//2+1)`
C. `TpropR^((n+1)//2)`
D. `TpropR^(n//2)`

Answer

C

Explanation

`momega^(2)R="Force "prop(1)/(R^(n))` (Force = `(mv^(2))/(R )`)
implies `omega^(2)prop(1)/(R^(n+1))impliesomegaprop(1)/(R(n+1)/(2))`
Time period `T=(2pi)/(omega)`
Time period, `TpropR^((n+1)/(2))`