Question

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. 5.14) is a possible result after collision ?

Answer 1

**Case (ii) **

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

or 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:

= $\frac{1 }{ 2 }$ mV2 + $\frac{1 }{ 2 }$ (2m)0

= $\frac{1 }{ 2 }$ mV2

**Case (i) **

Total kinetic energy of the system after collision:

= $\frac{1 }{ 2 }$ m × 0 + $\frac{1 }{ 2 }$ (2m) ($\frac{v }{ 2 }$)2

= $\frac{1 }{ 4 }$ mV2

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

Case (iii)

Total kinetic energy of the system after collision:

= $\frac{1 }{ 2 }$ (3m) $(\frac{v }{ 3 })$ 2

$=\frac{ 1 }{ 2} mV^2$

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