Physics - Modern Physics Question with Solution | TestHub

Let heavy nucleus breaks into two nuclei of mass $m_1$ and $m_2$ and move away with velocities $V_1$ and $V_2$ respectively. According to question, $\frac{V_1}{V_2}=\frac{8}{27}$ $m_1{V}_1=m_2{V}_2$ (Law of momentum conservation) $$\begin{array}{rl}& \Rightarrow \frac{m_1}{m_2}=\frac{V_2}{V_1}=\frac{27}{8}\\ & \frac{\rho \times \frac{4}{3}\pi R_1^3}{\rho \times \frac{4}{3}\pi R_2^3}\left(\because \text{ density }\rho =\frac{\text{ mass }}{\text{ volume }}\right)\end{array}$$ $$\begin{array}{rl}& \Rightarrow \left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)={\left(\frac{27}{8}\right)}^{\frac{1}{3}}={\left(\frac{3}{2}\right)}^{3\times \frac{1}{3}}\\ & \therefore \frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}=\frac{3}{2}\end{array}$$