Question

A nucleus ruptures into two nuclear parts which have their velocity ratio equal to 2 : 1. The ratio of their respective nuclear sizes (nuclear radii )is :

• A. 1 : 2
• B. $1:\sqrt{2}$
• C. $1:2^{1/3}$
• D. 1 : 8

Answer 1

Answer: (C)

$1:2^{1/3}$

By conservation of linear momentum, $\frac{m_1}{m_2}=\frac{v_2}{v_1}$
Assuming the shape of the nucleus spherical,
$\Rightarrow \frac{\rho \times \frac{4}{3}\pi r_1^3}{\rho \times \frac{4}{3}\pi r_2^3}=\frac{1}{2}\Rightarrow \frac{r_1}{r_2}=\frac{1}{2^{1/3}}$