Question

A nucleus at rest split into two nuclear parts having radii in the ratio 1:2. Their velocities are in the ratio

• A. 8:1
• B. 6:1
• C. 4:1
• D. 2:1

Answer 1

The correct option is A 8:1

Let $A_1$ and $A_2$ be the mass number of the two nuclear parts. The radii are given by

$R_1=R_0(A_1{)}^{1/3}\to (1)$

and $R_2=R_0(A{)}^{1/3}\to (2)$

Dividing equation $\left(1\right)$ and equation $\left(2\right)$

$\frac{R_1}{R_2}=(\frac{A_1}{A_2}{)}^{1/3}$ or $\frac{A_1}{A_2}=(\frac{R_1}{R_2}{)}^{3}As\frac{R_1}{R_2}=\frac{1}{2}$ [given$\frac{A_1}{A_2}=(\frac{1}{2}{)}^3=\frac{1}{8}]$

Hence ratio of masses $\frac{m_1}{m_2}=\frac{1}{8}$

According tolaw of conservation of momentum

Magnitude of $p_1=$ magnitude of $p_2$

$\Rightarrow m_1{v}_1=m_2{v}_2\Rightarrow \frac{v_1}{v_2}=\frac{m_2}{m_1}=\frac{8}{1}$