Question

A circular disc of radius $R$ is free to rotate about an axis passing through its centre. An external tangential force $F$ is applied on the disc along its edge. If the angular velocity of disc is increased from $0$ to $\omega$ in a time $t$ then the work done by $F$ during same time t is :

• A. $RF\omega t$
• B. $2RF\omega t$
• C. $\frac{RF\omega t}{2}$
• D. $RF(\omega t{)}^2$

Answer 1

The correct option is C $\frac{RF\omega t}{2}$

Torque $\tau =\overrightarrow{R}\times \overrightarrow{F}=FR$
Work done $=\int \tau .d\theta =\int \tau \omega dt$
As $\omega$ increases from $0$ to $\omega$ in time $t$ (so we are going to do the calculations based on $\text{average angular acceleration}$)
$Totalworkdone={\int }_0^{\omega }\tau \alpha tdt=\frac{FR\times \frac{\omega }{t}\times t^2}{2}=\frac{RF\omega t}{2}$