Q. Two balls of masses 2g and 6g are moving with KE in the ratio of 3:1. What is the ratio of their liner momenta?
A) 1 : 1
B) 2 : 1
C) 1 : 2
D) None of these
Explanation
(a) $K = \frac{1}{2}mv^{2} = \frac{1}{2} \times \frac{m(mv^{2})}{2} = \frac{(mv)^{2}}{m} = \frac{(mv)^{2}}{2m}$ or $K = \frac{p^{2}}{2m}$
$\therefore\ \frac{K_{1}}{K_{2}} = \frac{p_{1}^{2}}{2m_{1}} \times \frac{2m_{2}}{p_{2}^{2}}$ or $\frac{3}{1} = \frac{p_{1}}{p_{2}} \times \frac{6}{2}$
$\therefore p_{1}:\ p_{2} = 1:1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.