Question

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3:2$. The ratio of their nuclear sizes will be ${\left(\frac{x}{3}\right)}^{\frac{1}{3}}$. The value of ' $x$ ' is:-

Answer 1

Answer: 2

$m_1{v}_1=m_2{v}_2\Rightarrow \frac{m_1}{m_2}=\frac{2}{3}$
Since, Nuclear mass density is constant
$\frac{m_1}{\frac{4}{3}\pi r_1^3}=\frac{m_2}{\frac{4}{3}\pi r_2^3}$
${\left(\frac{r_1}{r_2}\right)}^3=\frac{m_1}{m_2}$
$\frac{r_1}{r_2}={\left(\frac{2}{3}\right)}^{\frac{1}{3}}$
$\text{ So, }x=2$