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Question

A chain is held on a frictionless table with (1n)th of its length hanging over the edge. If the chain has length L and mass M, how much work is required to pull the hanging part back on the table?

A
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B
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C
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D
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Solution

The correct option is A The chain is pulled very slowly. Let λ is the mass per unit length of the chain. Consider a differential element of the chain of length dy at a depth y from the surface of the table. The force acting on the element due to gravity is equal to λdyg. So the work done in pulling this element of the chain on the table is dW = F(y) mass of this element is dm=λy dW=λgydy=MLgydyW=MgL∫L/n0ydy=MgL2n2

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