Question

A disc of mass $Mkg$ and radius $R$ metre is rotating at an angular speed of $\omega rad/s$ when the motor is switched off. Neglecting the friction at the axle, the force that must be applied tangentially to the wheel to bring it to rest in time $t$ is

• A. $\frac{MR\omega }{2t}$
• B. $\frac{MR\omega }{t}$
• C. $\frac{2MR\omega }{t}$
• D. $\frac{M{R}^2\omega }{2t}$

Answer 1

The correct option is A $\frac{MR\omega }{2t}$

Let force be $F$ and radius be $R$
$\therefore Torque=I\alpha$
$FR=\frac{M{R}^2}{2}\alpha (I=\frac{M{R}^2}{2}fordisc)$
$\alpha =\frac{2F}{MR}$
This $\alpha$ retards $\omega$ to $0$
$\therefore \frac{2F}{MR}=\frac{\omega }{t}\leftarrow (acceleration=\frac{\Delta V}{t})$
$\Rightarrow F=\frac{MR\omega }{2t}$