Question

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of $8:27$. The ratio of the radii of the nuclei (assumed to be spherical ) is:

• A. $8:27$
• B. $2:3$
• C. $3:2$
• D. $4:9$

Answer 1

Answer: (C)

$3:2$

$\frac{V_1}{V_2}=\frac{8}{27}$

$m_1{V}_1=m_2{V}_2$

$\frac{m_1}{m_2}=\frac{V_2}{V_1}=\frac{27}{8}$

$\frac{\rho \times \frac{4}{3}\pi R_1^3}{\rho \times \frac{4}{3}\pi R_2^3}$

$\left(\frac{R_1}{R_2}\right)={\left(\frac{27}{8}\right)}^{\frac{1}{3}}$

$={\left(\frac{3}{2}\right)}^{3\times \frac{1}{3}}$

$\frac{R_1}{R_2}=\frac{3}{2}$