Question

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

• A. 4:1
• B. 8:1
• C. 2:1
• D. 6:1

Answer 1

The correct option is(D) 8:1

According to the question, both fragments are generated from the same nucleus so their density will be equal.

We know,

$Mass=Volume\times Density$

Since densities are equal so the mass of the fragments are in the ratio of the volume

We know,

Volume is directly proportional to the radius so we can write

$\frac{V_1}{V_2}=\frac{m_1}{m_2}=\frac{{r_1}^3}{{r_2}^3}$

Or, $\frac{m_1}{m_2}=1^3:2^3=1:8$

We know, By the conservation of momentum

$m_1{v}_1=m_2{v}_2$

From the above equation we can write that the ratio of the velocities is 8 : 1