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

Answer 1

The correct option is B $\frac{2}{3}\mu FR$

Diagram
Consider a strip of radius 𝑥 and its thickness is $dx$
The torque due to friction on the strip.
$\int dx={\int }_0^R\frac{\mu Fx}{\pi R^2}\times 2\pi xdx$
$\tau =\frac{2\mu FR}{3}$