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Q.

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, work required to pull the hanging part on to the table is 

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a

MgL3

b

MgL

c

MgL18

d

MgL9

answer is D.

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Detailed Solution

The weight of hanging part L3 of chain is 13Mg. This weight acts at centre of gravity of the hanging part, which is at a distance of L6 from the table .
As work done = force×distance
W=Mg3×L6=MgL18

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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, work required to pull the hanging part on to the table is