A uniform rope of length L and mass M hangs over a horizontal table with two third part on the table.The coefficient of friction between the table and the rope is u. Calculate the work done by the friction during the period the rope slips copletely off the table?

Length hanging = L/3 

therefore, force applying mass = M/3

force applied = Mg/3   (weight of the hanging portion)

work done during slipping = force * displacement
                                           = (Mg/3)*(2L/3)
                                           = 2MgL/9

work done by friction = work done * u (coefficient of friction)
                                   =  2/9 u MgL