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

Explanation

Let m be the mass of each ball bearing. Before collision, total K.E of the sytem
`1/2mv^92)+0=1//2mv^(2)`
After collision, K.E of the system is
Case I, `E_(1)=1//2(2m)(v//2)^(2)= 1//4mv^(2)`
Case II, `E_(2) = 1//2mv^(2)`
Case III, `E_(3) = 1//2(3m)(v//3)^(2)=1//6mv^(2)`
Thus, case II is the only possibility since K.E is conserved in this case.