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

Answer 1

Answer: (A)

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