A nucleus breaks into two parts whose velocities are in the ratio 2 : 1. The ratio of their radius is

1 : 2^{\frac{2}{3}}

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2^{\frac{2}{3}} : 1

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1 : 2^{\frac{1}{3}}

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2^{\frac{1}{2}} : 1

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Solution

The correct option is C $1 : 2^{\frac{1}{3}}$
As per conservation of momentum
$m_{1} v_{1} + m_{2} v_{2} = 0$ so $\frac{m_{1}}{m_{2}} = \frac{v_{2}}{v_{1}}$
ratio of radii, $\frac{R_{1}}{R_{2}} = {(\frac{A_{1}}{A_{2}})}^{\frac{1}{3}} = {(\frac{m_{1}}{m_{2}})}^{\frac{1}{3}} = {(\frac{1}{2})}^{\frac{1}{3}}$
so, $R_{1} : R_{2} = 1 : 2^{\frac{1}{3}}$

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