Question

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 $\text{8 s}$ to bring it to rest finally. The value of torque $\left(\text{in} N m\right)$ is $\left(\text{Given} I = \frac{24}{\pi } kg m^{2}\right)$

• A. $48$
• B. $72$
• C. $96$
• D. $120$

Answer 1

Answer: (B)

In given question torque is constant
So $\tau=\frac{L_{2} - L_{1}}{t_{2} - t_{1}}$ $...\left(i\right)$
$L$ is angular momentum here
Given $t_{2}-t_{1}=8s,L_{1}=Iω_{1}andL_{2}=0$
$\omega _{1}=2\pi n,heren=720rpm$
So
$n=\frac{720}{60}rps=12rps$ $\left(rps = \text{rotations per second}\right)$
So from eq $\left(i\right) \tau=\frac{0 - \left(\frac{24}{\pi }\right) \left(2 \pi \left(12\right)\right)}{8}$
$\tau=-72\,Nm$
So $\tau=72\,Nm$ (Opposing Torque)