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Question

A chain is held on a frictionless table with one third of its length hanging over the edge. The total length of the chain is l and the mass is m. The work required to pull the hanging part back to the table is


A
2mgl
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B
mgl5
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C
mgl9
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D
mgl18
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Solution

The correct option is D $$\dfrac { mgl }{ 18 } $$
Length of hanging chaing is $$l/3$$ , and mass of hanging chain is $$M=m/3$$  .

The center of mass of hanging chain is at $$h=\dfrac{l/3}{2}=\dfrac{l}{6}$$ from the table top.

So work done ,$$W=Mgh=\dfrac{mgl}{3\times 6}=\dfrac{mgl}{18}$$

Physics

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