If an ivory ball of mass 2m moving with a velocity 'v' strikes head on to a close row of three identical ivory balls each of mass m as shown in the figure. Then after the collisions which may be assumed as elastic, which of the following would occur?

Moderate

A

The balls numbered 2 and 3 will move with velocity v, the others staying at rest.
B

The balls numbered 2 will move with velocity v, the others staying at rest.
C

The ball numbered 3 moves with velocity 4v/3 and the striking ball moves with velocity v/3
D

The balls numbered 1, 2 and 3 move with velocity v/3 and the striking ball stops dead

Solution

In option (1), final momentum of the system = mv + mv = 2mv. Initial momentum of the system = 2m x v = 2mv
Initial energy of the system $\large =\frac 12.2m.v^2=mv^2$
Final energy of the system $\large =\frac 12mv^2+\frac 12mv^2=mv^2$
Therefore Linear momentum and energy, both are conserved.

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