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

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

For the mass of each ball bearing m, the total kinetic energy of the system before collision:

$= \frac{1}{2}{\mathrm{mV}}^2 + \frac{1}{2}\left(2\mathrm{m}\right)0^2$
$= \frac{1}{2}{\mathrm{mV}}^2$

Case (i)

The total kinetic energy of the system after the collision:

$= \frac{1}{2}\mathrm{m} \times {\left(0\right)}^2+ \frac{1}{2}\left(2\mathrm{m}\right){\left(\frac{\mathrm{V}}{2}\right)}^2$
$= \frac{1}{4}{\mathrm{mV}}^2$

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

Case (ii)

The total kinetic energy of the system after a collision:

$= \frac{1}{2}\left(2\mathrm{m}\right) \times {\left(0\right)}^2 + \frac{1}{2}{\mathrm{mV}}^2$
$= \frac{1}{2}{\mathrm{mV}}^2$

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

Case (iii)

The total kinetic energy of the system after a collision:

$= \frac{1}{2}\left(3\mathrm{m}\right){\left(\frac{\mathrm{V}}{3}\right)}^2$
$= \frac{1}{6}{\mathrm{mV}}^2$

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