Three identical balls each of mass m = 0.5 kg are connected with each other as shown in Fig. and rest over a smooth horizontal table. At moment t = 0, ball B is imparted a horizontal velocity v0 = 9ms–1. Calculate velocity of A w.r.t ground just before it collides with ball C.
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This system involves three connected balls on a frictionless table. When ball B is given initial velocity v₀, the connecting strings become taut, transferring momentum. Since all balls are identical and the system is symmetric, the center of mass moves with constant velocity. Just before collision, balls A and C approach each other symmetrically relative to the center of mass.
The center of mass velocity is: due to conservation of momentum (total mass 3m).
Relative to cm, balls A and C have equal and opposite velocities. Just before collision, A's velocity relative to ground is the vector sum of cm velocity and its relative velocity. For the impending collision along the line, A's speed becomes: .
Final answer: