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 $=\frac{1}{2}m{v}^2$
Total $KE$ of the system after collision is
Case (i) $E_1=\frac{1}{2}(2m){\left(\frac{v}{2}\right)}^2=\frac{1}{4}m{v}^2$
Case (ii) $E_2=\frac{1}{2}m{v}^2$
Case (iii) $E_3=\frac{1}{2}(3m){\left(\frac{v}{2}\right)}^3=\frac{1}{6}m{v}^2$
$\therefore$ case (ii) is only possible since $KE$ of the system is conserved