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 as shown in figure.

If the collision is elastic, which of the following is a possible result after collision?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Answer 2

Let m be mass of each ball bearing.

Total kinetic energy of the system before collision,

$= \frac{1}{2}mv^{2} + 0 = \frac{1}{2}mv^{2}$

In (1), Kinetic energy of the system after collision,

$K_{1} = \frac{1}{2}(2m)\left( \frac{v}{2} \right)^{2} = \frac{1}{4}mv^{2}$

In (2), kinetic energy of the system after collision.

$K_{2} = \frac{1}{2}(m)(v)^{2} = \frac{1}{2}mv^{2}$

In (3), kinetic energy of the system after collision

$k_{3} = \frac{1}{2}(3m)\left( \frac{v}{3} \right)^{2} = \frac{1}{6}mv^{2}$

In (4), kinetic energy of the system after collision,

$k_{4} = \frac{1}{2}mv^{2} + \frac{1}{2}m\left( \frac{v}{2} \right)^{2} + \frac{1}{2}m\left( \frac{v}{3} \right)^{2} = \frac{49}{72}mv^{2}$

We see that kinetic energy is conserved only in (2)

Hence, (2) is the only possibility.