question_answer

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 the floor is\[\mu ,\]the torque, applied the machine on the mop is:

A) \[\mu FR\text{/3}\]

B) \[\mu FR\text{/6}\]

C) \[\mu FR\text{/2}\]

D) \[\frac{2}{3}\mu FR\]

Correct Answer: D

Solution :

\[d\tau =(m\,dN)x\]

\[=\mu \left( \frac{F}{\pi {{R}^{2}}}\times 2\pi \times dx \right)x\]

\[\tau =\int\limits_{0}^{R}{d\tau }.\]