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

Answer: (A)

$\frac{2}{3} \mu FR$

Answer 2

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

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

$\tau = \frac{2 \mu FR}{ 3}$

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