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A man places a chain (of mass m and length l) on a table slowly. Initially, the lower end of the chain just touches the table. The man brings down the chain by length l/2. Work done by the man in this process is

a
-mg12
b
-mgl4
c
-3mgl8
d
-mgl8

detailed solution

Correct option is D

The work done by the man is negative of the magnitude of decrease in potential energy of the chainwork done in lifting chain =mgl2n2 m  is mass of chain, g acceleration due to gravity,  l is length of chain, n is fraction of chain that is hanging here, work done =mgl2 1n21 -1n22 =mgl2 -mgl8 =3mgl8  but with a negative sign , as work is done by man against gravity

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