Physics - Rotation Question with Solution | TestHub

Using rotational kinematic equation, $\begin{array}{rl}& \omega ={\omega }_0-at\\ & \Rightarrow 0={\omega }_0-at\\ & \Rightarrow \alpha =\left(\frac{{\omega }_0}{t}\right)\end{array}$ We know torque is given by, $$F\cdot R=\text{ Torque }=I\alpha$$ and the moment of inertia is given by, $I=\frac{M{R}^2}{2}$ $$\therefore F=\frac{I\alpha }{R}=\left(\frac{M{R}^2}{2}\right)\cdot \left(\frac{1}{R}\right)\cdot \left(\frac{{\omega }_0}{t}\right)=\left(\frac{MR{\omega }_0}{2t}\right)$$ Given, $M=25\mathrm{kg},R=0.2\mathrm{m},{\omega }_0=\frac{240(2\pi )}{(60)\sec }$ and $t=20\sec$ $\begin{array}{rl}& \therefore F=\frac{(25\mathrm{kg})\times (0.2\mathrm{m})\times \left(8\pi {\sec }^{-1}\right)}{(2\times 20\sec )}\\ & \Rightarrow F=\pi N\end{array}$