Question

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2:1$ . The ratio of their nuclear size will be

• A. $2^{\frac{1}{3}}:1$
• B. $1:3^{\frac{1}{2}}$
• C. $3^{\frac{1}{2}}:1$
• D. $1:2^{\frac{1}{3}}$

Answer 1

Answer: (D)

According to the law of conservation of momentum, we get
$m_1{v}_1=m_2{v}_2$
Or $\left(\frac{m_1}{m_2}\right)=\left(\frac{v_2}{v_1}\right)$
But $m=\frac{4}{3}\pi r^3\rho orm\propto r^3$
$\Rightarrow \frac{m_1}{m_2}=\frac{r_1^2}{r_2^3}$
$\therefore \frac{r_1^3}{r_2^3}=\frac{v_2}{v_1}=\frac{1}{2}$
$\Rightarrow \frac{r_1}{r_2}={\left(\frac{1}{2}\right)}^{\frac{1}{3}}$
$\therefore r_1:r_2=1:{\left(2\right)}^{\frac{1}{3}}$