Question

A nucleus of rest splits into two nuclear parts having radii in the ratio $1:2$. Their velocities are in the ratio

• A. $1:8$
• B. $1:4$
• C. $4:1$
• D. $8:1$

Answer 1

Answer: (D)

If $A_1$ and $A_2$ are the mass number of two parts.
The radius of nucleus is given by
$R=R_0(A{)}^{1/3}$
So, $R_1=R_0{\left(A_1\right)}^{1/3}$ and $R_2=R_0{\left(A_2\right)}^{1/3}$
$\Rightarrow \frac{R_1}{R_2}={\left(\frac{A_1}{A_2}\right)}^{1/3}$
$\Rightarrow \frac{A_1}{A_2}={\left(\frac{R_1}{R_2}\right)}^3={\left(\frac{1}{2}\right)}^3=\frac{1}{8}$
$\therefore \text{ Ratio of masses, }\frac{m_1}{m_2}=\frac{A_1}{A_2}=\frac{1}{8}$
From conservation of momentum,
$\Rightarrow m_1{v}_1=m_2{v}_2$
$\Rightarrow \frac{v_1}{v_2}=\frac{m_2}{m_1}=\frac{8}{1}\text{ or }8:1$