A) \[1\ :\ 3\sqrt{2}\]
B) \[1\ :\ 2\sqrt{2}\]
C) \[1\ :\ 2\]
D) \[\sqrt{2}\ :\ 1\]
Correct Answer: B
Solution :
\[v=\sqrt{\frac{T}{m}}=\sqrt{\frac{T}{\pi {{r}^{2}}\rho }}\] \[v\propto \frac{\sqrt{T}}{r}\Rightarrow \frac{{{v}_{A}}}{{{v}_{B}}}=\sqrt{\frac{{{T}_{A}}}{{{T}_{B}}}}.\frac{{{r}_{B}}}{{{r}_{A}}}=\sqrt{\frac{1}{2}}.\frac{1}{2}=\frac{1}{2\sqrt{2}}\]
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