Question

A uniform chain is held on a frictionless table with one third of its length hanging over the edge.if the chain has a length L and mass M, how much work is required to pull the Hanging part back on the table.

Answer 1

One way to think of this is to consider the weight hanging off the table as being a point load at the center of mass. The center of mass is 1/2 of the length that is hanging over the edge, or L/6. The work to lift this force times distance, where

Mass of hanging part=M/3

force = Mg/3, and the distance it needs to be raised is L/6,
hence,
work done = F×distance
Work=Mg/3 ×L/6
W=MgL/18


OR
Shortcut

There is a short cut to calaulate work
It is mgL/(2 ×n^2 )
If 1/n th part is hanging

MgL/ (2×3^2)

MgL/ 2×9
MgL/18
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