Question

Two identical ball bearings in contact with each other and resting on a frictionless table are hit headon 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)

Let $m$ be the mass of each ball
Total $KE$ of the system before collision $=\frac{1}{2} mv ^{2}$
Total $KE$ of the system after collision is
Case (i) $E _{1}=\frac{1}{2}(2 m )\left(\frac{ v }{2}\right)^{2}=\frac{1}{4} mv ^{2}$
Case (ii) $E _{2}=\frac{1}{2} mv ^{2}$
Case (iii) $E _{3}=\frac{1}{2}(3 m )\left(\frac{ v }{2}\right)^{3}=\frac{1}{6} mv ^{2}$
$\therefore $ case (ii) is only possible since $KE$ of the system is conserved