A) \[{{2}^{\frac{1}{3}}}:1\]
B) \[1:{{3}^{\frac{1}{2}}}\]
C) \[{{3}^{\frac{1}{3}}}:1\]
D) \[1:{{2}^{\frac{1}{3}}}\]
Correct Answer: D
Solution :
According to the law of conservation of momentum \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{{{v}_{2}}}{{{v}_{1}}}=\frac{1}{2}\] Since, masses are directly proportional to volume as densities are roughly same, so it follows that: \[\frac{{{m}_{1}}}{{{m}_{2}}}\propto \frac{r_{1}^{3}}{r_{2}^{3}}\]or \[\frac{{{r}_{1}}}{{{r}_{2}}}\propto {{\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)}^{\frac{1}{3}}}\] \[\therefore \]ratio of nuclear sizes\[=\frac{1}{{{2}^{1/3}}}.\] Hence, the correction option is (d).
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