One-fourth chain of mass M and length L is hanging down from a table. The work done to pull the hanging part of the chain on to the table is

Concept:

• Work is said to be done by a force when the body is displaced actually through some distance in the direction of the applied force.
• Since the body is being displaced in the direction of F, therefore work done by the force in displacing the body through a distance s is given by:

\(W = \vec F \cdot \vec s\)

Or, W = Fs cos θ

Calculation:

Total mass m & length L = mg

Weight of the hanging part (L/4) = 1/4 mg

This weight acts at the centre of gravity of the hanging part, which is at a distance of = L/8 from the table

We know that,

Work done = Force × Distance

 \(Work \ done = {mg \over4} \times {l \over8} = {MgL \over 32}\)