Question

A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to 2:1. What will be the ratio of their nuclear size (nuclear radius)?

Options

• 2^1/3 : 1

• 1 : 2^1/3

• 3^1/2 : 1

• 1 : 3^1/2

Answer 1

1 : 2^1/3

Explanation:

Using law of conservation of momentum:

\[m_1v_1=m_2v_2\]

Now, \[v_1v_2=m_1m_2\]

Since, \[m=\frac{4}{3}\pi r^3\times\rho\]

It shows that m ∝ r³

Now, \[m_2/m_1=r_2^3/r_1^3\]

Hence, \[v_1/v_2=r_2^3/r_1^3\]

So, \[r_2/r_1=(1/2)^{1/3}\]