Nuclei - Result Question 13

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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)?

======= ####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)?

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/nuclei/nuclei—result-question-13.md (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:

  1. (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}} $