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A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1: 2^{1 / 3}.Their respective speed have a ratio of n: 1.The value of n is ________

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Since the linear momentum of the system must be conserved,

the total momentum finally after disintegration remains the same as that in the beginning Hence using the principle of conservation of momentum we get,
\mathrm{m}_{1} \mathrm{v}_{1}=\mathrm{m}_{2} \mathrm{~V}_{2}

\frac{\mathrm{V}_{1}}{\mathrm{~V}_{2}}=\frac{\mathrm{m}_{2}}{\mathrm{~m}_{1}}=\frac{\mathrm{r}_{2}{ }^{3}}{\mathrm{r}_{1}^{3}}=\left(\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}\right)^{3}
\frac{\mathrm{V}_{1}}{\mathrm{~V}_{2}}=\left(\frac{2^{\frac{1}{3}}}{1}\right)^{3}=\frac{2}{1}
\mathrm{n}=2

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