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Question

A uniform chain of mass M and length L is held on a horizontal frictionless table with 1nth of its length hanging over the edge of the table. The work done is pulling the chain up on the table is


A

MgLn

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B

MgL2n

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C

MgLn2

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D

MgL2n2

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Solution

The correct option is D

MgL2n2


The mass per unit length of the chain m=ML. The mass of the hanging portion of the chain is m=Mn. This mass can be assumed to be concentrated at the centre of the hanging portion of the chain which is a distance of x=L2n from the edge of the table. Therefore, the work done in pulling the hanging portion of the chain on to the table top is W=mgx=Mn×g×L2n=MgL2n2.


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