Question

Two identical ball bearings in contact with each other and resting on a frictionless table are hit head - on by another ball bearing of the same mass moving initially with a speed v as shown in figure.If the collision is elastic, which of the following is a possible result after collision?

Answer 1

Correctoption: Option (B). Hint: In an elastic collision, the initial kinetic energy of the system must be equal to the final kinetic energy of the system. Explanation: Let m the mass of all the bearing and v bethe velocity of the moving bearing.Initial Kinetic energy of the system, Ki = 12mv^2 CaseA: Inthis case, both the initially resting bearings move with a velocity v2 and Final kinetic energy of the system becomes, Kf = 0 + 12(2m)(v2)^2 = 14mv^2 CaseB:In this case, the third bearing moves with a velocity v after collision,total kinetic energy of the system will be, Kf = 0 + 12mv^2 = 12mv^2 CaseC:In this case, all the bearing moves with a velocity v3 , so thetotal kinetic energy of the system becomes, Kf = 12(3m)(v3)^2 = 3mv^218 = 16mv^2 CaseD:In this case, total kinetic energy of the system is given by, Kf = 12mv^2 + 12m(v2)^2 + 12m(v3)^2 = 12mv^2 + 18mv^2 + 118mv^2 = 4972mv^2 Since, it’s an elastic collision, the initialkinetic energy of the system must be equal to the final kinetic energy of thesystem. Therefore, case (B) is only the possible result of the collision Thus,option (B) is correct.