Question

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

Answer 1

The correct option is A 1 : 2



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 $r\propto A^{\frac{1}{3}}\Rightarrow \frac{r_1}{r_2}={\left(\frac{A_1}{A_2}\right)}^{\frac{1}{3}}={\left(\frac{1}{8}\right)}^{\frac{1}{3}}=\frac{1}{2}$