Two identical spheres, each of mass m are suspended by vertical strings such that they are in contact with their centres at the same level. A third identical sphere strikes the other two spheres simultaneously with a velocity u such that the centres of the spheres at the instant of impact form an equilateral triangle in a vertical plane. If the collision is perfectly elastic, then the combined impulse due to the stri

Step-by-step solution

Let us assume that after the collision, the velocity of the incoming ball changes from u to u ' and the other two balls move in the opposite directions with the same speed v , then - 2 N ∆ t cos 30 ° =   m u ' - m u ⇒ - N ∆ t 3 = m u ' - m u For the ball attached to the string, N ∆ t sin 30 ° = m v ⇒ N ∆ t = 2 m v Eliminating N ∆ t , we obtain - 2 3 m v = m u ' - m u Using the coefficient of restitution equation we get 1 = v cos 60 ° - u