Two balls having masses m and 2m are affixed to two light strings of identical length l . The upper ends of the strings are fixed at point O . The system is released from rest while the strings are aligned in the same horizontal line. Following the perfectly elastic collision between the balls at the lowest point, determine the maximum height reached by each ball after the collision.

Step-by-step solution

Let the velocities of the light ball of mass m and the heavy ball of mass 2m just before the collision be u₁ and u₂ respectively. Since both are released from a horizontal position, they fall through a height l . u₁ = 2gl u₂ = - 2gl For a perfectly elastic collision, the velocities after the collision are given by: v₁ = m₁ - m₂ m₁ + m₂ u₁ + 2m₂ m₁ + m₂ u₂ v₂ = 2m₁ m₁ + m₂ u₁ + m₂ - m₁ m₁ + m₂ u₂ Substituting m₁ = m and m₂ = 2m : v₁ = m - 2m 3m ( 2gl ) + 4m 3m (- 2gl ) = - 5 3 2gl v₂ = 2m 3m ( 2gl ) + 2m - m 3m (- 2