Two balls possessing masses m and 2m are tied to two light strings of equal length l , as shown in the figure. The other ends of the strings are anchored at a common point O . Both strings are held in the same horizontal line before the system is released from rest. Given that the collision between the balls is elastic, determine the velocities of the balls just after the collision.

Step-by-step solution

Let the speed of each ball just before the collision be v₀ . Since both balls are released from the horizontal position and fall through a height l , their speeds are given by: v₀ = 2gl Let the right direction be positive. The initial velocity of the light ball (mass m ) is u₁ = v₀ and the initial velocity of the heavy ball (mass 2m ) is u₂ = -v₀ . Let v₁ and v₂ be the velocities of the light and heavy balls respectively just after the collision. By the principle of conservation of linear momentum: m u₁ + 2m u₂ = m