A) \[\frac{\text{3}}{8}\]
B) \[\frac{2}{3}\]
C) \[\frac{8}{9}\]
D) \[\frac{9}{4}\]
Correct Answer: D
Solution :
The frequency\[n=\frac{1}{2l}\sqrt{\frac{T}{m}}\] \[n\propto \frac{\sqrt{T}}{l}\] The ratio of tensions \[\frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{n}_{1}}}{{{n}_{1}}} \right)}^{2}}{{\left( \frac{{{l}_{2}}}{{{l}_{1}}} \right)}^{2}}\] \[={{(2)}^{2}}\times {{\left( \frac{3}{4} \right)}^{2}}\] \[=\frac{9}{4}\]
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