Mechanical efficiency η = useful work/total work ... Because the pulley is not a smooth ideal pulley, there must be friction between the pulley and the rope.

The useful work here is to raise the water and bucket as high as H, so the useful work is (g water +g bucket) H.

Because it is a moving pulley, the object rises H .. and then the rope F goes for 2 hours (the law of moving pulley). Total work =f*2h.

So the mechanical efficiency η = (gram water+gram barrel) h/

f*2h

The weight of the bucket may be given in the exam ... don't worry.