Question

If the angular momentum of a particle of mass $m$ is rotating along a circular path of radius $r$ with uniform speed. Its angular momentum about the axis of rotation 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

The correct option is A $\frac{L^2}{m{r}^3}$

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)]

$F=\frac{m{L}^2}{r\cdot m^2\cdot r^2}$

$F=\frac{L^2}{m{r}^3}$