A uniform chain of length $l$ and mass $m$ is placed on a smooth table with one-fourth of its length hanging over the edge. The work that has to be done to pull the whole chain back onto the table is

\frac{1}{4} m g l

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\frac{1}{6} m g l

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\frac{1}{72} m g l

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\frac{1}{36} m g l

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Solution

The correct option is B $\frac{1}{36} m g l$
Weight of chain to be lifted $= \frac{m g}{4}$
Height through which centre of gravity is raised $= \frac{l}{8}$
Work done $= \frac{m g}{4} \times \frac{l}{8} = \frac{m g l}{32}$ .

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A uniform chain of length l and mass m is placed on a smooth table with one-fourth of its length hanging over the edge. The work that has to be done to pull the whole chain back onto the table is

The correct option is B 136mglWeight of chain to be lifted =mg4Height through which centre of gravity is raised =l8Work done =mg4×l8=mgl32.

A uniform chain of length $l$ and mass $m$ is placed on a smooth table with one-fourth of its length hanging over the edge. The work that has to be done to pull the whole chain back onto the table is

The correct option is B $\frac{1}{36} m g l$
Weight of chain to be lifted $= \frac{m g}{4}$
Height through which centre of gravity is raised $= \frac{l}{8}$
Work done $= \frac{m g}{4} \times \frac{l}{8} = \frac{m g l}{32}$ .