A heavy nucleus at rest breaks into two fragments which fly off with velocities

Question

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

Options:

A . 1 : 2

B . 1 : 4

C . 4 : 1

D . 2 : 1

Answer: Option A
:
A

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^{\frac{1}{3}} \Rightarrow \frac{r_{1}}{r_{2}} = {(\frac{A_{1}}{A_{2}})}^{\frac{1}{3}} = {(\frac{1}{8})}^{\frac{1}{3}} = \frac{1}{2}

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