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Question

A person pulls a bucket of water from a well of depth h. If the mass of uniform rope is m and that of the bucket full of water is M, then work done by the person is:
  1. (M+m2)gh
  2. (M2+m)gh
  3. 12(M+m)gh
  4. (M+m)gh

A
12(M+m)gh
B
(M+m2)gh
C
(M+m)gh
D
(M2+m)gh
Solution
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Work done by the person is the change in potential energy of the bucket and the rope.
Given, the rope has a uniform mass m. So the center of mass for the rope is at half of the length of the rope.
So, it will be at a distance h/2 from the bottom.
Work done = Change in PE of bucket+Change in PE of rope
W=Mgh+mgh2=(M+m2)gh
Option A.

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