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