Question

A uniform chain is held on a frictionless table with half of its length hanging over the edge. If the chain has a mass $m$ and length $L$, how much work is required to pull the hanging part back onto the table? (Given acceleration due to gravity $=g$)

• A. $\frac{mgL}{4}$
• B. $\frac{mgL}{2}$
• C. $\frac{mgL}{8}$
• D. $\frac{mgL}{16}$

Answer 1

The correct option is C $\frac{mgL}{8}$

Here we need to pull only the hanging part, that is $L/2$ and as a chain is a uniform so hanging part has weight $mg/2$

In the first situation, the part is hanging and its center of mass is $L/4$ from the table.

And in the second situation that part is pulled on the table.

So here $mg/2$ weight is pulled by a height of $L/4$.

$\therefore$ Work done = $\frac{mg}{2}\times \frac{L}{4}=\frac{mgL}{8}$