Q. A particle of mass $m$ is circulating on a circle of radius $r$ having angular momentum $L,$ then the centripetal force will be
A) $L^{2}/mr$
B) $L^{2}m/r$
C) $L^{2}/mr^{3}$
D) $L^{2}/mr^{2}$
Explanation
(c) Angular momentum $L = r \times p = r \times m \times v$
$v = \frac{L}{mr}\ \ \ \ \ldots.(i)$
$Now,\ as\ centripetal\ force,\ F_{c} = \frac{{mv}^{2}}{r}\ \ldots.(ii)$
Substituting the value of $v$ from Eq. (i) in Eq. (ii), we get
$F_{c} = \frac{m}{r}\left\lbrack \frac{L}{mr} \right\rbrack^{2} = \frac{L^{2}}{{mr}^{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.