A particle of mass ' $\mathrm{m}$ ' is rotating along a circular path of radius ' $r$ ' having angular…

A particle of mass ' $\mathrm{m}$ ' is rotating along a circular path of radius ' $r$ ' having angular momentum ' $L$ '. The centripetal force acting on the particle is given by
  1. $\frac{\mathrm{L}^2}{\mathrm{mr}}$
  2. $\frac{\mathrm{L}^2}{\mathrm{mr}^2}$
  3. $\frac{\mathrm{mL}^2}{\mathrm{r}}$
  4. $\frac{\mathrm{L}^2}{\mathrm{mr}^3}$

Solution

$\begin{array}{ll} & \text { Centripetal force }=m \omega^2 r \\ \therefore \quad & \omega=\frac{L}{I}=\frac{L}{m r^2} \quad \ldots(\because L=I \omega) \\ \therefore \quad & F=m\left(\frac{L}{m r^2}\right)^2 \quad r=\frac{m^2 r}{m^2 r^4}=\frac{L^2}{m r^3}\end{array}$

Asked in: MHT CET 2023 (10 May Shift 1)

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