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. $\frac{L^2}{m{r}^2}$
• C. $\frac{L}{m{r}^3}$
• D. $\frac{L}{m^2{r}^3}$

Answer 1

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

Angular momentum is given by
$L=mvr$, where $v$ is the uniform speed of the particle.
Therefore, we have
$v=\frac{L}{mr}$
Also, centripetal force is given by $F_c=\frac{m{v}^2}{r}\Rightarrow F_c=\frac{m\left(\frac{L^2}{m^2{r}^2}\right)}{r}$
$\Rightarrow F_c=\frac{L^2}{m{r}^3}$