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Question

# A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is [IIT 1985]

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 D If point mass m is pulled through a height h then work done W = mgh Similarly for a chain we can consider its centre of mass at the middle point of the hanging part i.e. at a height of L/(2n) from the lower end and mass of the hanging part of chain =Mn So work done to raise the centre of mass of the chain on the table is given by W=Mn×g×L2n [As W = mgh] or W=MgL2n2 As 13 part of the chain is hanging from the edge of the table. So by substituting n = 3 in standard expression W=MgL2n2=MgL2(3)2=MgL18

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