A chain of mass M is placed on a smooth table with 1/3 of its length L hanging over the edge. the work done in pulling the chain back to the surface of the table.a) MgL/3b)MgL/6c)MgL/9d)MgL/18

The mass of the chain is M and 1/3 of it is habging down i.e. L/3 length of chain is hanging down. The work done in pulling the hanging part of chain up is =M*g*h

h=L/3

W=MgL/3

option (a) is correct

mass of 1/3rd section of chain will be  M/3

now consider the center of mass of hanging part will be at center of hanging part...

workdone in pulling hanging part  above the table is equal to workdone in pulling center of mass of hanging part  to the table...

displacement of center of mass (h)= l/6

workdone = (dm)gh

              =Mgl/18

Approved