# A bucket filled with water weighing 50kg is raised from a well of depth 100m.if the linear density of the rope is 1kg per metre.then the work done is?

Sep 22, 2017

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 ($g$).

$W = m g h$

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.

$W = 50 \cdot 9.8 \cdot 100 + 100 \cdot 9.8 \cdot 50 \text{ } N m$