Rankers Physics

Nucleus: Practice Problem & Solution

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)? (1996)
$3^{1/2} : 1$
$1 : 3^{1/2}$
$2^{1/3} : 1$
$1 : 2^{1/3}$

Solution Explained:

To solve this problem, we apply the core principles of Nucleus. Understanding the underlying formula is key to arriving at the correct answer below:

By conservation of momentum, $m_1 v_1 = m_2 v_2$, meaning the mass ratio is $m_1 / m_2 = v_2 / v_1 = 1 / 2$. Since radius $R \propto m^{1/3}$, the ratio of their radii is $R_1 / R_2 = (1/2)^{1/3} = 1 : 2^{1/3}$.

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