The power $(\mathrm{P})$ is supplied to a rotating body having moment of inertia ' I ' and angular…

The power $(\mathrm{P})$ is supplied to a rotating body having moment of inertia ' I ' and angular acceleration ' $\alpha$ '. Its instantaneous angular velocity ' $\omega$ ' is
  1. $\quad \mathrm{P}(\mathrm{I} \alpha)^{-1}$
  2. $\quad \mathrm{P}^{-1}(\mathrm{I} \alpha)^{-1}$
  3. $\quad \mathrm{P} \alpha^{-1} \mathrm{I}$
  4. PI $\alpha$

Solution

$\begin{aligned} & \text { Power }=\frac{\text { Work done }}{\text { time }} \\ & P=\frac{\text { Torque } \times \text { angular displacement }}{\text { time }}=\tau \times \omega \\ & \ldots\left[\because \omega=\frac{\theta}{\mathrm{t}}\right] \\ & \therefore \quad P=I \alpha \omega \\ & \therefore \quad \omega=\frac{\mathrm{P}}{\mathrm{I} \alpha} \\ &=\mathrm{P}(\mathrm{I} \alpha)^{-1} \ldots(\because \tau=\mathrm{I} \alpha)\end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 1)

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