Question

A bucket of water 50kg is raised from a depth of 100m to the ground by a rope the mass of the rope is 1kg per meter what is work done

Answer 1

That's a pretty hefty rope. But since you are bringing up 110 pounds of water, it might be reasonable. If the weight of the bucket is nominal, you're bring up about 15 gallons of water. So it's a good idea to use the really big rope. Though, honestly, that rope should lift about 2 tons.

Now that I've confused you about the units. Work done (W) in this situation can be calculated knowing the mass lifted (m), how far it was lifted (h), and the strength of gravity (g).

W=mgh

There are two parts. The bucket and water are lifted 100 meters.
The center of mass of the rope is lifted 50 meters. The mass of the rope will be 100 kg.

W=50⋅9.8⋅100+100⋅9.8⋅50 Nm