A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be . The value of is ______. [2023]

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Solution

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 ${(\frac{x}{3})}^{1 / 3}$ . The value of $' x'$ is ______. [2023]

Ans.
(2)

$\frac{v_{1}}{v_{2}} = \frac{3}{2}$

$m_{1} v_{1} = m_{2} v_{2} \Rightarrow \frac{m_{1}}{m_{2}} = \frac{2}{3}$

$Since nuclear mass density is constant$

$\frac{m_{1}}{\frac{4}{3} π r_{1}^{3}} = \frac{m_{2}}{\frac{4}{3} π r_{2}^{3}}$

${(\frac{r_{1}}{r_{2}})}^{3} = \frac{m_{1}}{m_{2}}$

$\frac{r_{1}}{r_{2}} = {(\frac{2}{3})}^{\frac{1}{3}} So, x = 2$

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