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13.Nuclei
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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 :
A
$1$
B
$2$
C
$3$
D
$4$
(JEE MAIN-2023)
Solution
$\frac{ v _1}{ v _2}=\frac{3}{2}$
$m _1 v _1= m _2 v _2 \Rightarrow \frac{ m _1}{ m _2}=\frac{2}{3}$
Since, Nuclear mass density is constant
$\frac{ m _1}{\frac{4}{3} \pi r _1^3}=\frac{ m _2}{\frac{4}{3} \pi r _2^3}$
$\left(\frac{ r _1}{ r _2}\right)^3=\frac{ m _1}{ m _2}$
$\frac{ r _1}{ r _2}=\left(\frac{2}{3}\right)^{\frac{1}{3}}$
$\text { So, } x =2$
Standard 12
Physics
