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(B) Initial angular velocity $\omega_1 = 720 \, rpm = \frac{720 	imes 2\pi}{60} \, rad/s = 24\pi \, rad/s$.Final angular velocity $\omega_2 = 0 \, ra

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$72$

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(B) Initial angular velocity $\omega_1 = 720 \, rpm = \frac{720 	imes 2\pi}{60} \, rad/s = 24\pi \, rad/s$.Final angular velocity $\omega_2 = 0 \, rad/s$.Time taken $t = 8 \, s$.Using the equation of rotational motion $\omega_2 = \omega_1 - \alpha t$,where $\alpha$ is the angular retardation:$0 = 24\pi - \alpha(8) \implies \alpha = \frac{24\pi}{8} = 3\pi \, rad/s^2$.The magnitude of torque $	au$ is given by $	au = I\alpha$.Given $I = \frac{24}{\pi} \, kg \cdot m^2$,we have:$	au = \left(\frac{24}{\pi}ight) 	imes (3\pi) = 72 \, N \cdot m$.

$A$ wheel is rotating about an axis through its centre at $720 \, rpm$. It is acted on by a constant torque opposing its motion for $8 \, s$ to bring it to rest finally. The value of torque (in $N \cdot m$) is (Given $I = \frac{24}{\pi} \, kg \cdot m^2$)

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