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 by the machine on the mop is : a) `muFR//3` b) `muFR//6` c) `muFR//2` d) `(2)/(3)muFR`

Options

A. `2/3 mu FR`
B. `mu F R//3`
C. `mu F R/2`
D. `mu F R //6`

Answer

A

Explanation

`dT = (df) .x`
` = ( mu N) x = mu (F)/(piR^2) . 2pi xdx . = (2mu F)/( R^2) x^2 dx`
` T = (2mu F)/( 3R^2) R^3 = (2mu FR)/(3)`