Nuclei - Result Question 13
13. 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)?
(a) $2^{1 / 3}: 1$
(b) $1: 2^{1 / 3}$
(c) $3^{1 / 2}: 1$
(d) $1: 3^{1 / 2}$
[1996]
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Answer:
Correct Answer: 13. (b)
Solution:
- (b) Applying law of conservation of momentum,
$m_1 v_1=m_2 v_2$
$\frac{v_1}{v_2}=\frac{m_2}{m_1}$
As $m=\frac{4}{3} \pi r^{3} \rho \Rightarrow m \propto r^{3}$
Hence, $\frac{m_2}{m_1}=\frac{r_2^{3}}{r_1^{3}}$
$ \therefore \frac{v_1}{v_2}=\frac{r_2^{3}}{r_1^{3}} \Rightarrow \frac{r_2}{r_1}=(\frac{1}{2})^{\frac{1}{3}} $
