Question

A uniform rope lies on a table with some portion hanging. the rope begins to slide when the length of hanging part 25% of entire length. the coefficien of friction between rope and table is

Answer 1

k=1/3

Since l×25/100 ×mg=k*(l-25/100)mg
Solving this k will come as 1/3 or 0.333...

Answer 2

L is length of the rope, then l2 is length of hanging rope = (1/3)l, mass of the hanging rope is M2=  (1/3)l x m,  then is length of rope on table  l1=  l-1/3)l = (2/3)l, the mass of the rope on table M1= (2/3)l x m.

Find  the coefficient of friction between rope and table , assume μ as coefficient,  apply motion equation, weight of the rope  on table = weight of the rope or μ (2/3)l x mg = (1/3)l x mg, μ= ½ or 0.5.