A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to $2: 1$. What wil

Question

A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to $2: 1$. What will be the ratio of their nuclear size (nuclear radius)?\

Professor PC Thomas Classes · Answer

(d): Velocity ratio $\left(v_{1}: v_{2}ight)=2: 1$ 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 $\frac{r_{1}}{r_{2}}=\left(\frac{v_{2}}{v_{1}}ight)^{1 / 3}=\left(\frac{1}{2}ight)^{1 / 3}=\frac{1}{2^{1 / 3}}$\ or $r_{1}: r_{2}=1: 2^{1 / 3}$\