A nucleus ruptures into two nuclear parts which have their velocity ratio equal to 2 : 1 . What will

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13.Nuclei

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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

$1:{3^{1/2}}$

(AIPMT-1996) (AIEEE-2004)

Solution

Conserving momentum, $m_1 v_1=m_2 v_2$

$\frac{2}{1}=\frac{v_1}{v_2}=\frac{m_2}{m_1}$

$\Rightarrow \frac{m_2}{m_1}=\frac{2}{1}=\frac{\rho \cdot \frac{4}{3} \pi r_2^3}{\rho \cdot \frac{4}{3} \pi r_1^3}$

$\Rightarrow \frac{r_2}{r_1}=2^{\frac{1}{3}}$

$r_1: r_2=1: 2^{\frac{1}{3}}$

Standard 12

Physics

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