To $$mop-clean$$ a floor, a cleaning machine 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 a mop and if coefficient of friction between the mop and the floor is μ . The torque, applied by the machine on the mop is

Question

To $$mop-clean$$ a floor, a cleaning machine 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  a mop and if coefficient of friction between the mop and the floor is μ . The torque, applied by the machine on the mop is

Infinity Learn · Accepted Answer

Force on the small area element F$$π$$$$R2(dA)$$ Frictional torque on then elements area $$dT=$$μ$$(F$$$$π$$$$R2)dAr=r$$μ$$(F$$$$π$$$$R2)2$$$$π$$rdrOn integrating $$T=$$μF$$π$$$$R22$$$$π$$$$R33=2$$μ$$FR3$$

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