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)

Consider a strip of radius x & thickness dx, Torque due to friction on this strip.
$\int d\tau ={\int }_0^R\frac{x\mu F.2\pi xdx}{\pi R^2}$
$\tau =\frac{2\mu F}{R^2}.\frac{R^3}{3}$
$\tau =\frac{2\mu FR}{3}$