A) \[\frac{n}{\sqrt{3}}\]
B) \[\frac{n}{3}\]
C) \[n\sqrt{3}\]
D) \[\frac{n}{3\sqrt{3}}\]
Correct Answer: D
Solution :
\[n=\frac{1}{2l}\sqrt{\frac{T}{\pi {{r}^{2}}\rho }}\Rightarrow n\propto \frac{\sqrt{T}}{lr}\] Þ \[\frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\times \frac{{{l}_{2}}}{{{l}_{1}}}\times \frac{{{r}_{2}}}{{{r}_{1}}}\] \[=\sqrt{\frac{T}{3T}}\times \frac{3l}{l}\times \frac{2r}{r}=3\sqrt{3}\]Þ \[{{n}_{2}}=\frac{n}{3\sqrt{3}}\]
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