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 system is `=(1)/(2)mv^(2)+0=(1)/(2)mv^(2)`
After collision. K.E. of the system is
Case I, `E_(1)=(1)/(2)(2m)(v//2)^(2)=(1)/(4)mv^(2)`
Case II, `E_(2)=(1)/(2)mv^(2)`
Case III, `E_(3)=(1)/(2)(3m)(v//3)^(2)=(1)/(6)mv^(2)`
We observe that K.E. is conserved only in case II.
Hence case II is the only possibility.