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  4. A man is holding a chain of mass m and length l such that the lower end of the chain just touches a table. Now the man places half the length of the chain very slowly on the table while keeping the other half vertical. The work done by the man in this process is

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Q. A man is holding a chain of mass $m$ and length $l$ such that the lower end of the chain just touches a table. Now the man places half the length of the chain very slowly on the table while keeping the other half vertical. The work done by the man in this process is

NTA AbhyasNTA Abhyas 2020Work, Energy and Power

Solution:

The work done by man is negative of magnitude of decrease in potential energy of chain.


Solution

$\Delta U=mg \, \frac{L}{2} \, - \, \frac{m}{2}g \, \frac{L}{4}=3 \, mg \, \frac{L}{8}$
$\therefore W=- \, \frac{3 m g l}{8}$