If the angular momentum of a particle of mass $m$ rotating along a circular path of radius $r$ with uniform…

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
  1. $\frac{\mathrm{L}^{2}}{m r^{3}}$
  2. $\frac{\mathrm{L}^{2}}{m \mathrm{r}}$
  3. $\frac{\mathrm{L}}{\mathrm{mr}}$
  4. $\frac{\mathrm{L}^{2} m}{r}$

Solution

From the relation, angular momentum, $L=m v r \quad v=\frac{L}{m r}$
Centripetal force acting on the particle $F=\frac{m v^{2}}{r}=\frac{m\left(\frac{L}{m r}\right)^{2}}{r}=\frac{L^{2}}{m r^{3}}$

Asked in: JEE Mains - Rotational Motion - Test 4

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