Question

A wheel having moment of inertia $2\, kg - m ^{2}$ about its axis, rotates at $50 \,rpm$ about the same axis. The torque required to stop the wheel in one minute is

• A. $\frac{\pi}{10} Nm$
• B. $\frac{\pi}{18} Nm$
• C. $ - \frac{\pi}{12} Nm$
• D. $\frac{ 3 \pi}{8} Nm$

Answer 1

Answer: (B)

Given, moment of inertia of a wheel,
$I=2 \,Kg - m ^{2}$ and angular velocity of wheel,
$\omega=50\, rpm =\frac{50}{60} \times 2 \pi=\frac{5}{3} \pi rad s ^{-1}$
The torque required to stop the wheel,
$ \Rightarrow \tau =I \alpha=I\left(\frac{\omega}{t}\right) $
$\Rightarrow \tau=2 \times\left(\frac{5 / 3 \pi}{60}\right) [\because t=1 \min =60 sec ] $
$=\frac{\pi}{18} N - m $