Question 126 of 280

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$2\mu FR/3$B$\mu FR/3$C$\mu FR/6$D$\mu FR/2$

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Answer: (A) $2\mu FR/3$

Net torque $=\sum Torqueonring$

$\int d\tau =\int _{0}^{R}\mu \times \left(\dfrac{F}{\pi {R}^{2}}\times 2\pi xdx\right)x$
$\tau =\dfrac{2\mu }{3}FR$