### Q.16:- 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 figure is a possible result after collision?

**Answer:-**It can be observed that the total momentum before and after collision in each case is constant.

For an elastic collision, the total kinetic energy of a system remains conserved before and after collision.

For mass of each ball bearing *m*, we can write:

Total kinetic energy of the system before collision:

= (1/2)*mV*^{2} + (1/2)(2*m*) × 0^{2}

= (1/2)*mV*^{2}

^{
}__Case____ (i) __

Total kinetic energy of the system after collision:

= (1/2) *m* × 0 + (1/2) (2*m*) (*V*/2)^{2}

= (1/4)*mV*^{2}

Hence, the kinetic energy of the system is not conserved in case (i).

__Case____ (ii)__

Total kinetic energy of the system after collision:

= (1/2)(2*m*) × 0 + (1/2)*mV*^{2}

= (1/2) *mV*^{2}

Hence, the kinetic energy of the system is conserved in case (ii).

__Case____ (iii)__

Total kinetic energy of the system after collision:

= (1/2)(3*m*)(*V*/3)^{2}

= (1/6)*mV*^{2}

Hence, the kinetic energy of the system is not conserved in case (iii).

Hence, Case II is the only possibility.