A particle of mass m rotating in a plane circular path of radius r has angular momentum L. The centripetal force acting on its is :

Options

A. `(L^(2))/(mr)`
B. `(L^(2)m)/(r^(2))`
C. `(L^(2))/(mr^(3))`
D. `[(L)/(mr)]^(1//2)`

Answer

C

Explanation

Centripetal force, `F_(C)=(mv^(2))/(r)` and angular momentum `L=mvr`
`F_(C)=(m^(2)v^(2))/(mr)" "(because mv=(L)/(r))`
`therefore F_(C)=(L^(2))/(mr^(2).r)=(L^(2))/(mr^(3))`