Q. A particle of mass $m$ is rotating in a plane in circular path of radius $r$. Its angular momentum is $L$. The central force acting on the particle is
A) $L^{2}/mr$
B) $L^{2}m/r$
C) $L^{2}/m^{2}r^{2}$
D) $L^{2}/mr^{3}$
Explanation
(d) Centripetal force $F = \frac{mv^{2}}{r} = \frac{m}{r}\frac{L^{2}}{m^{2}r^{2}} = \frac{L^{2}}{mr^{3}}$
$\left\lbrack As\ L = mvr\ \therefore v = \frac{L}{mr} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.