Question

A nucleus ruptures into two nuclear parts which have heir 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)

Conserving momentum, $m_{1} v_{1}=m_{2} v_{2}$
$\frac{2}{1}=\frac{v_{1}}{v_{2}}=\frac{m_{2}}{m_{1}}$
$\Rightarrow \frac{m_{2}}{m_{1}}=\frac{2}{1}=\frac{\rho \cdot \frac{4}{3} \pi r_{2}^{3}}{\rho \cdot \frac{4}{3} \pi r_{1}^{3}}$
$\Rightarrow \frac{r_{2}}{r_{1}}=2^{\frac{1}{3}}$ or $r_{1}: r_{2}=1: 2^{\frac{1}{3}}$