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

Options

A. MgL
B. `MgL//3`
C. `MgL//9`
D. `MgL//18`

Answer

D

Explanation

The hanging part of the chain which is to be pulled can be considered as a point mass situated at the centre of the hanging part. The equivalent diagram is drawn. The work done in bringing the mass up will be equal to the change in potential energy of the mass.
W = Change in potential energy
`= M/3 xx g xx L/6 = (Mg L)/(18)`