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  • A nucleus disintegrates into two smaller parts, which have their velocities in the ratio . The ratio of their nuclea

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3: 2. The ratio of their nuclear sizes will be \left(\frac{x}{3}\right)^{\frac{1}{3}}. The value of  ' $x$ ' is:-

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

 

\begin{aligned} & \frac{\mathrm{v}_1}{\mathrm{v}_2}=\frac{3}{2} \\ & \mathrm{~m}_1 \mathrm{v}_1=\mathrm{m}_2 \mathrm{v}_2 \\ & \Rightarrow \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\frac{2}{3} \end{aligned}

Since, Nuclear mass density is constant 

\begin{aligned} & \frac{\mathrm{m}_1}{\frac{4}{3} \pi_1^3}=\frac{\mathrm{m}_2}{\frac{4}{3} \pi_2^3} \\ & \left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^3=\frac{\mathrm{m}_1}{\mathrm{~m}_2} \\ & \frac{\mathrm{r}_1}{\mathrm{r}_2}=\left(\frac{2}{3}\right)^{\frac{1}{3}} \\ & \text { So, } x=2 \end{aligned}

Posted by

Pankaj Sanodiya

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