A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?

To find the work performed in pulling a chain of uniform density onto a table, let us consider a chain 2 meters long, the total mass being 4 kilograms. When put on the table, it overhangs the edge by 60 centimeters. The work performed to raise this overhanging part against the force of gravity can be evaluated using the formula for gravitational potential energy.

Initially, the hanging portion of the chain has a mass that corresponds to its length. Since the entire chain weighs 4 kilograms, the mass of the hanging segment, which is 60 centimeters, is proportionately lighter. As the chain is pulled onto the table, the work required to lift this hanging part involves raising it to a height that gradually reduces to zero.

Since this is the average height of the hanging segment, it is the height to which each mass was lifted to get the work done. The work done against gravity is calculated by multiplying the mass, gravitational force, and height. Using these considerations, the total work done in pulling the whole chain onto the table is found to be about 3.6 joules, which is the energy expended in overcoming the force of gravity in repositioning the chain.

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