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Q.
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:-
$m _1 v _1= m _2 v _2 \Rightarrow \frac{ m _1}{ m _2}=\frac{2}{3}$
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}} $
$\text { So, } x=2$
