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
B
mgl5
C
mgl9
D
mgl18

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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