question_answer

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, calculate work required to pull the hanging part on the chain.

Answer:

                Weight of length L of the chain \[=Mg\] Weight of length \[\frac{L}{3}\] of the chain\[=\frac{1}{3}Mg\] As the centre of gravity of the hanging part lies at its midpoint i.e. at a distance equal to \[\text{L}/\text{6}\]below the edge of the table, so the work required to pull the hanging part on the table is \[W\text{ }=\]Force \[\times \] distance \[=\frac{1}{3}Mg\times \frac{L}{6}=\frac{MgL}{18}.\]