Introduction:
To solve this problem, we need to determine the amount of work required to pull the hanging portion of the chain back onto the table. This can be done by considering the gravitational potential energy of the hanging chain and the work done against gravity to lift it back up.

Given:
- Length of the chain (L)
- Mass of the chain (M)
- One-third of the chain hangs over the edge

Calculating the mass of the hanging portion:
Since one-third of the chain hangs over the edge, the length of the hanging portion can be calculated as L/3. To determine the mass of this portion, we can use the formula:

Mass = (length / total length) * total mass

Given that the length of the hanging portion is L/3 and the total length of the chain is L, the mass of the hanging portion (m) can be calculated as:

m = (L/3 / L) * M
m = M/3

Calculating the work done against gravity:
The work done against gravity can be calculated using the formula:

Work = force * distance

The force exerted by gravity on the hanging portion of the chain can be calculated as:

Force = mass * acceleration due to gravity

Since we are working in a frictionless environment, there are no other forces acting on the chain. Therefore, the force exerted by gravity is the only force to consider.

The distance over which the force is applied is equal to the length of the hanging portion of the chain, which is L/3.

Thus, the work done against gravity (W) can be calculated as:

W = Force * Distance
W = (m * g) * (L/3)
W = (M/3 * g) * (L/3)

Conclusion:
The amount of work required to pull the hanging portion of the chain back onto the table is (M/3 * g) * (L/3), where M is the mass of the chain, g is the acceleration due to gravity, and L is the length of the chain.

A chain of uniform mass m and length l is lying on a table with l/n part hanging. find workdone to pull the hanging part on the table.