A uniform chain of mass m and length l is lying on the table such that its one-fifth part is hanging from the edge of the table. What minimum work is required to lift this part of the chain on the table?

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Solution

unit length of rope is M/L

given L/5 part of rope is hanging
we have to solve using integration methods, lets say 'x' part of rope is consided with an element 'dx' which is pulled up with limits from 0 to L/5

Potential energy = mgh

here dE= integral of ( Mx/Lgdx)

E = integral of ( M/Lgx.dx) limits from 0 to L/5

P.E = MgL/50

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