Question

To mop-clean a floor, a cleaning machine presses a circular mop of radius $R$ vertically down with a total force $F$ and rotates it with a constant angular speed about its axis. If the force $F$ is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is $\mu$, the torque, applied by the machine on the mop is :

• A. $\frac{2}{3} \mu FR$
• B. $ \mu FR /3$
• C. $ \mu FR / 2$
• D. $ \mu FR / 6$

Answer 1

The Correct Option is A

Consider a strip of radius x & thickness dx, Torque due to friction on this strip. \(\int d\tau =\int^{R}_{0} \frac{x\mu F.2\pi x dx }{\pi R^{2}}\) 

\(\tau = \frac{ 2\mu F}{R^{2}} . \frac{R^{3}}{3}\) 

\(\tau = \frac{2 \mu FR}{ 3}\)

\(\text{Therefore, the correct option is (A): }\frac{2}{3} \mu FR\)