Q. A nucleus reptures into two nuclear parts which have their velocity ratio equal to 2:1. What will be the ratio of their nuclear size?
A) $2^{1/3}:1$
B) $1:2^{1/3}$
C) $3^{1/2}:1$
D) $1:3^{1/2}$
Explanation
(b) From conservation law of momentum
$\frac{v_{1}}{v_{2}} = \frac{2}{1} = \frac{m_{2}}{m_{1}} = \frac{\frac{4}{3}\pi r_{2}^{3}\rho}{\frac{4}{3}\pi r_{1}^{3}\rho} = \left( \frac{r_{2}}{r_{1}} \right)^{3}$
$\Rightarrow \ \frac{r_{2}}{r_{1}} = (2)^{1/3}:1$
Or $r_{1}:r_{2} = 1:(2)^{1/3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.