Question

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

• A. $\frac{L^2}{mr^3}$
• B. $\frac{L^2}{mr}$
• C. $\frac{L}{mr^2}$
• D. $\frac{L^2m}{r}$
• E. $\frac{Lm}{r^2}$

Answer 1

Answer: (A)

Angular momentum
$L=I \omega$
where$I=m r^{2}$ and $ \omega=\frac{V}{r} $
$L=m r^{2} \times \frac{V}{r} $
$L=m v r\,\,\,...(i)$
Centripetal force
$F=\frac{m v^{2}}{r}$
$F=\frac{m}{r} \cdot\left(\frac{L}{m r}\right)^{2} \,\,\,[$ From Eq. (i)]
$F=\frac{m L^{2}}{r \cdot m^{2} \cdot r^{2}}$
$F=\frac{L^{2}}{m r^{3}}$