# Q16  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 (Fig. 6.14) is a possible result after collision?

The initial kinetic energy of the system is given by :

$=\ \frac{1}{2}mv^2\ -\ \frac{1}{2}2m(0)$

or                                                   $=\ \frac{1}{2}mv^2$

Case (i):-      The final kinetic energy is :

$=\ \frac{1}{2}m.0\ -\ \frac{1}{2}2m(\frac{v}{2})^2\ =\ \frac{1}{4}mv^2$

Thus the kinetic energy is not conserved in this case.

Case (ii):-      The final kinetic energy is :

$=\ \frac{1}{2}2m.0\ -\ \frac{1}{2}mv^2\ =\ \frac{1}{2}mv^2$

Thus kinetic energy is conserved in this case.

Case (iii):-    The final kinetic energy is:-

$=\ \frac{1}{2}\times 3m\times \left ( \frac{v}{3} \right )^2$

or                                                       $=\ \frac{1}{2}m v^2$

Thus the kinetic energy is not conserved in this case.

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