Question

A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table
(a) 20% (b) 25% (c) 35% (d) 15%

Answer 1

F = p g x    where x is length of chain hanging over table and p is mass per unit of length of chain

F = u g p (L - x)    frictional force of chain lying on table

then  u (L - x) = x      for frictional force to equal gravitational force

u L - u x = x    and u L = x (1 + u)

x / L = u / (1 + u) = .25 / 1.25 = .2 or 20 %