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A nucleus at rest splits into two nuclear parts having radii in the ratio \( 1: 2 \). Their velocities are
in the ratio
Options:
in the ratio
Solution:
1481 Upvotes
Verified Answer
The correct answer is:
8:1
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 \( 8: 1 \).
\[
\begin{aligned}
m_{1} v_{1} &=m_{2} v_{2} \\
\Rightarrow \frac{v_{1}}{v_{2}} &=\frac{m_{2}}{m_{1}}
\end{aligned}
\]
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 \( 8: 1 \).
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