A body of mass' $\mathrm{m}$ ' and radius of gyration ' $\mathrm{K}$ ' has an angular momentum ' $L$ '. Then…

A body of mass' $\mathrm{m}$ ' and radius of gyration ' $\mathrm{K}$ ' has an angular momentum ' $L$ '. Then its angular velocity is
  1. $\frac{\mathrm{L}}{\mathrm{mK}^2}$
  2. $\frac{\mathrm{mK}^2}{\mathrm{~L}}$
  3. $\frac{\mathrm{K}^2}{\mathrm{~mL}}$
  4. $\mathrm{mK}^2 \mathrm{~L}$

Solution

$\begin{aligned} & \mathrm{I}=\mathrm{mK}^2 \text { and } \mathrm{L}=\mathrm{I} \omega=\mathrm{mK}^2 \omega \\ & \therefore \omega=\frac{\mathrm{L}}{\mathrm{mK}^2}\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 1)

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