A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0 . 5 , the maximum length of the chain hanging from the table is _____ m .

Step-by-step solution

Let, λ = mass per unit length of the chain and length of mass hanging through the table is x . Normal force applied by the table on the chain will be, N = l - x λ g . Tension developed in the chain will balance the gravitational force acting in the downward direction, T = λ x g . Maximum limiting force possible for the part of the table, f m a x = μ N = μ l - x λ g For equilibrium, f m a x = T , ⇒ μ l - x λ g = λ x g ⇒ 1 2 × 6 - x = x   ⇒ x =