Question

A uniform chain of length Land mass M is lying on a smooth table and 1/3 of its lengths hanging down over the edge of the table. If his the acceleration due to gravity , the work done to pull the hanging part on the table is :-

Answer 1

unit length of rope is M/L

given L/3 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/3

Potential energy = mgh

here dE= integral of ( Mx/L*g*dx)

       E = integral of ( M/L*g*x.dx) limits from 0 to L/3

   P.E = MgL/18

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Answer 2

Refer to the above attachment to see the solution.