A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1 : 4^{1 / 3} .$ Their respective speed have a ratio of n :1. The value of n is _____

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answer is 4.

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Detailed Solution

$m ∝ V = \frac{4}{3} π r^{3}$

$m ∝ r^{3}$

$\begin{array}{l} \frac{m_{1}}{m_{2}} = {(\frac{r_{1}}{r_{2}})}^{3} = {(\frac{1}{4^{\frac{1}{3}}})}^{3} \\ = \frac{1}{4} \\ ∴ \frac{V_{1}}{V_{2}} = \frac{m_{2}}{m_{1}} = \frac{4}{1} \end{array}$

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