A motor rotates a pulley of radius 25cm at 20 rpm. A rope around the pulley lifts a 50kg block. The power output of the motor is

The tension in the rope is equal to the weight since there is no acceleration. Thus
T = 500N.

$\mathrm{\tau }$ =TR =(500)(0.25) =125Nm

Angular velocity $\mathrm{\omega }=\frac{2\mathrm{\pi N}}{60}=\frac{2\mathrm{\pi }}{3}{\mathrm{rads}}^{-1}$

$\mathrm{P}=\mathrm{\tau \omega }=\left(125{\mathrm{Nm}}^{-1}\right)\left(\frac{2\mathrm{\pi }}{3}{\mathrm{rads}}^{-1}\right)\simeq 261\mathrm{W}$