Q. A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 8:1. The ratio of radii of the fragments is
A) 1 : 2
B) 1 : 4
C) 4 : 1
D) 2 : 1
Explanation
(a) By conservation of momentum $m_{1}v_{1} = m_{2}v_{2}$
$\Rightarrow \frac{v_{1}}{v_{2}} = \frac{8}{1} = \frac{m_{2}}{m_{1}}$ …(i)
Also from $r \propto A^{1/3} \Rightarrow \frac{r_{1}}{r_{2}} = \left( \frac{A_{1}}{A_{2}} \right)^{1/3} = \left( \frac{1}{8} \right)^{1/3} = \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.