Question

A particle of mass 'm'is circulating on a circle of radius 'r' having angular momentum 'l' about center.then centripetal force will be

Answer 1

Answer:

$F=\frac{l^{2} }{mr^{3} }$

Explanation:

A particle of mass 'm' moving with a tangential velocity 'v' in a circular orbit of radius 'r' is

$F=\frac{mv^{2} }{r}$ ----(1)

and the angular momentum is

l = mvr ----(2)

Rewrite equation (1) as

$F=\frac{mv^{2} }{r}=\frac{m^{2} v^{2}r^{2}  }{mr^{3} }$ ----(3)

Substitute value of angular momentum from equation (2) to equation (3),

$F=\frac{l^{2} }{mr^{3} }$