If the angular momentum of a particle of mass m rotating along a circular path of radius r with uniform speed is L, the centripetal force acting on the particle is

Options

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

Answer

A

Explanation

Angular momentum
`L = I omega `
where `I = mr ^(2) and omega = (v)/(r)`
`L = mr ^(2) xx (v)/(r)`
`L = mvr " "...(i)`
Centripetal force
`F = ( mv ^(2))/( r)`
`F = (m)/(r).((L)/(mr)) ^(2) ` [From Eq. (i)]
`F = (mL ^(2))/( r.m ^(2). r ^(2))`
`F = (L ^(2))/( mr ^(3))`