A disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc, so…

A disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity ' $\omega$ ' in time $t$ ?
  1. $\frac{\mathrm{MR} \omega}{4 \mathrm{t}}$
  2. $\frac{\mathrm{MR} \omega}{2 \mathrm{t}}$
  3. $\frac{\mathrm{MR} \omega}{\mathrm{t}}$
  4. $M R \omega t$

Solution

Torque: $\tau=\mathrm{I} \alpha=\frac{\mathrm{MR}^2}{2} \times \frac{\omega}{\mathrm{t}}$ $\begin{array}{ll} \therefore & \tau=\frac{\mathrm{MR}^2 \omega}{2 \mathrm{t}} \\ & \text { But } \tau=\mathrm{R} \times \mathrm{F} \\ \therefore \quad & \mathrm{F}=\frac{\tau}{\mathrm{R}}=\frac{\mathrm{MR} \omega}{2 \mathrm{t}} \end{array}$

Asked in: MHT CET 2023 (11 May Shift 1)

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