Thank you for reporting, we will resolve it shortly
Q.
A nucleus at rest breaks into two nuclear parts which have their velocities ratio equal to $2 : 1.$ What will be the ratio of their radii of the nuclei?
Atoms
Solution:
Velocity ratio $\left(v_{1}: v_{2}\right)=2: 1$.
Mass $(m) \propto$ Volume $\propto r^{3}$.
According to law of conservation of momentum, $m_{1} v_{1}=m_{2} v_{2}$
Therefore $\frac{v_{1}}{v_{2}}=\frac{m_{2}}{m_{1}}=\frac{r_{2}^{3}}{r_{1}^{3}}$
or $\frac{r_{1}}{r_{2}}=\left(\frac{v_{2}}{v_{1}}\right)^{1 / 3}=\left(\frac{1}{2}\right)^{1 / 3}=\frac{1}{2^{1 / 3}}$
or $r_{1}: r_{2}=1: 2^{1 / 3}$.