Two identical ball-bearings in contact with each other and resting on

1.	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 (Fig.) is a possible result after collision?
Answer» The system consists of three identical ball-bearings marked as 1,2 and 3. Let m be the mass of each ball-bearing. Total kinetic energy of the system before collision = 1/2 mv² + 0 + 0 = 1/2 mv² Case (i) K.E. of the system after collision = 0 + 1/2 (2m)(v/2)² = 1/4 mv² Case (ii) K.E. of the system after collision = 0 + 1/2 mv² = 1/2 mv² Case (iii) K.E. of the system after collision = 1/2 (3m)(v/3)² = 1/6 mv² As in an elastic collision, the kinetic energy of the system remains unchanged case (ii) is the only possible result of the collision.

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 (Fig.) is a possible result after collision?

Answer»

The system consists of three identical ball-bearings marked as 1,2 and 3. Let m be the mass of each ball-bearing.

Total kinetic energy of the system before collision

= 1/2 mv² + 0 + 0 = 1/2 mv²

Case (i) K.E. of the system after collision

= 0 + 1/2 (2m)(v/2)² = 1/4 mv²

Case (ii) K.E. of the system after collision

= 0 + 1/2 mv² = 1/2 mv²

Case (iii) K.E. of the system after collision

= 1/2 (3m)(v/3)² = 1/6 mv²

As in an elastic collision, the kinetic energy of the system remains unchanged case (ii) is the only possible result of the collision.