KCET · Physics · Dual Nature of Matter

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 4:1
C 6:1
D \( 2: 1 \)

Verified Solution

Answer & Solution

Correct Answer

(A) 8:1

Step-by-step Solution

Detailed explanation

Given, nucleus at rest splits into two nuclear parts, then
\[
\begin{aligned}
m_{1} v_{1} &=m_{2} v_{2} \\
\Rightarrow \frac{v_{1}}{v_{2}} &=\frac{m_{2}}{m_{1}}
\end{aligned}
\]
We know that \( A \propto R^{2} \)
Also, \( A \propto m \)
\[
\begin{array}{l}
\Rightarrow m \propto R^{3} \\
\Rightarrow \frac{v_{1}}{v_{2}}=\frac{R_{2}{ }^{3}}{R_{1}{ }^{3}}
\end{array}
\]
Now, given ratio of radii is \( 1: 2 \).
Therefore, the velocities are in the ratio \( 8: 1 \).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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

Step-by-step Solution

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