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Question

Two identical balls marked 2 and 3, in contact with each other and at rest on a horizontal frictionless table, are hit head-on by another identical ball marked 1 moving initially with a speed 'v' as shown in the figure. If the collision is elastic, what is observed?

  1. Balls 1 and 2 comes to rest and ball 3 rolls out with speed v.
  2. Ball A comes to rest and balls 2 and 3 roll out with speed each.
  3. Balls 1, 2 and 3 roll out with speed each.
  4. Balls, 1, 2 and 3 come to rest.


Solution

The correct option is A Balls 1 and 2 comes to rest and ball 3 rolls out with speed v.
The system consists of three identical balls marked 1, 2, and 3. Let m be the mass of each ball.
Before the collision,
KE of the system = KE of 1 + KE of 2 + KE of 3 = 12mv2+0+0=12mv2
Case (a) After the collision,
KE of the system = KE of 1 + KE of 2 + KE of 3
=0+12m(v2)2+12m(v2)2=14mv2
Case (b)
KE of the system = KE of 1 + KE of 2 + KE of 3
=0+0+12mv2=12mv2
Case (c)
KE of the system = KE of 1 + KE of 2 + KE of 3
=12m(v3)2+12m(v3)2+12m(v3)2
=16mv2
Case (d)
KE of the system = 0
Now, in an elastic collision, the kinetic energy of the system remains unchanged. Hence choice (b) is the only possible result of the collision.

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