Question

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