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Question

# A chain of mass m and length L is over hanging from the edge of a smooth horizontal table such that 1nth of its length is lying on the table. The work done in pulling the chain completely on to the table is

A
mgL2n2
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B
mgL(n1)22n2
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C
mgL(n1)2n2
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D
mgLn2
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Solution

## The correct option is D mgL(n−1)22n2Mass of the chain lying below the table =M⎛⎜ ⎜ ⎜⎝L(1−1n)L⎞⎟ ⎟ ⎟⎠ =M(1−1n)The center of mass of the part of chain lying below the table is at a distance of 12×L(1−1n)Thus, work done to pull the chain up =M′gΔH =M(1−1n)×g×L2(1−1n) =MgL(n−1)22n2

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