Question

A nucleus at rest splits 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

Answer: (A)

8:1

Answer 2

Given : $\frac{R_{1}}{R_{2}}=\frac{1}{2}$
According to the law of conservation of linear momentum, we have

m1V1 = m2V2
$\frac{v_{1}}{v_{2}}=\frac{m_{2}}{m_{1}}=\left(\frac{R_{2}}{R_{1}}\right)^{3}\left(\because m \propto A \propto R^{3}\right)$
i.e. $\frac{v_{1}}{v_{2}}=\left(\frac{2}{1}\right)^{3}=\frac{8}{1}$

Therefore, Option A) 8:1 is the correct answer.