A particle of mass `m` is moving in a plane along a circular path of radius `r`. Its angular momentum about the axis of rotation is `L`. The centripetal force acting on the particle is.

Options

A. `(L^(2))/(mr)`
B. `(L^(2))/(mr^(2))`
C. `(L^(2))/(mr^(3))`
D. `(L^(2)m)/(r^(3))`

Answer

C

Explanation

For the revolving mass, angular momentum,
`L=Iomega" "therefore L=mr^(2)xx(v)/(r)="mvr"`
`therefore v=(L)/(mr)`
`therefore " C.P. force "=(mv^(2))/(r) =(mL^(2))/(m^(2)r^(2))xx(1)/(r)=(L^(2))/(mr^(3))`