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  4. 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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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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Solution:

Mass of hanging portion is $M / 3$ (one-third) and centre of mass $c$, is at a distance $h=\frac{L}{6}$ below the table top.
Therefore, the required work done is,
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$W=m g h=\left(\frac{M}{3}\right)(g)\left(\frac{L}{6}\right)=\frac{M g L}{18}$