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  4. A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 8: 1. The ratio of radii of the fragments is

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Q. A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $8 : 1.$ The ratio of radii of the fragments is

Solution:

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By conservation of momentum $m_{1} \,v_{1}=m_{2} \,v_{2}$
$\Rightarrow \frac{v_{1}}{v_{2}}=\frac{8}{1}=\frac{m_{2}}{m_{1}}\,\,\,...(i)$
Also from $r \propto A^{1 / 3} $
$\Rightarrow \frac{r_{1}}{r_{2}}=\left(\frac{A_{1}}{A_{2}}\right)^{1 / 3}=\left(\frac{1}{8}\right)^{1 / 3}=\frac{1}{2}$.