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Question

A uniform chain of mass m and length l overhangs a table with its two third part on the table. Find the work to be done by a person to put the hanging part back on the table.

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Solution

Let 'dx' be the length of an element at distance x from the table.
Mass of the element, 'dm'=ml dx
Work done to putting back this mass element on the table is

dW=ml×x×g×dx

So, total work done to put 13 part back on the table

W=01/3ml gx dxW=ml g x221/3=mgl18 l=mgl18

The work to be done by a person to put the hanging part back on the table is mgl18.

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