A) \[{{2}^{1/3}}:1\]
B) \[1:{{2}^{1/3}}\]
C) \[{{3}^{1/2}}:1\]
D) \[1:{{3}^{1/2}}\]
Correct Answer: B
Solution :
Given: Velocity ratio \[({{v}_{1}}:{{v}_{2}})=2:1.\] We know that mass (m)\[\propto \]Volume\[\propto {{r}^{3}}\]. According to law of conservation of momentum,\[{{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}\] Therefore \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}=\frac{r_{2}^{3}}{r_{1}^{3}}\] or \[\frac{{{r}_{1}}}{{{r}_{2}}}={{\left( \frac{{{v}_{2}}}{{{v}_{1}}} \right)}^{1/3}}{{\left( \frac{1}{2} \right)}^{1/3}}=\frac{1}{{{2}^{1/3}}}\] or \[={{r}_{1}}:{{r}_{2}}=1:{{2}^{1/3}}\,.\]
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