A) \[2v\]
B) \[\sqrt{2v}\]
C) \[{{2}^{2/3}}v\]
D) \[\frac{v}{\sqrt{2}}\]
Correct Answer: C
Solution :
\[\frac{4}{3}\pi {{R}^{3}}=2.\frac{4}{3}\pi {{r}^{3}}\] \[R=r{{(2)}^{1/3}}\] \[v\propto {{r}^{2}}\] \[\therefore \] \[\frac{{{v}_{R}}}{{{v}_{r}}}=\frac{{{R}^{2}}}{{{r}^{2}}}\] Or \[\frac{{{v}_{R}}}{v}=\frac{{{r}^{2}}{{(2)}^{2/3}}}{{{r}^{2}}}\] \[{{v}_{R}}={{2}^{2/3}}v\]
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