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. If the collision is elastic, which of the following figure is a possible result after collision?

Answer 1

Case (ii)

It can be observed that the total momentum before and after a collision in each case is constant.
For an elastic collision, the total kinetic energy of a system remains conserved before and after a collision.
For a mass of each ball bearing m, we can write:
Total kinetic energy of the system before collision:

Case (i)
Total kinetic energy of the system after collision:

Hence, the kinetic energy of the system is not conserved in case (i).

Case (ii)
Total kinetic energy of the system after collision:

Hence, the kinetic energy of the system is conserved in case (ii).

Case (iii)
Total kinetic energy of the system after the collision:

Hence, the kinetic energy of the system is not conserved in case (iii).