A) \[30%\]
B) \[~20%\]
C) \[~69%\]
D) \[\sqrt{69%}\]
Correct Answer: A
Solution :
\[f=\frac{1}{2l}\sqrt{T/\mu }\] \[T=\]tension \[\mu =\]mass/length \[l=\]length. \[{{f}_{1}}=\frac{1}{2{{l}_{1}}}\sqrt{\frac{{{T}_{1}}}{\mu }}\] \[{{T}_{1}}=T+0.69\,T=1.69\,T\] \[{{l}_{1}}=?,f={{f}_{1}}\] \[\frac{1}{2l}.\sqrt{\frac{T}{\mu }}=\frac{1}{2{{l}_{1}}}\sqrt{\frac{1.69\,T}{\mu }}\] \[\frac{1}{l}=\frac{1.3}{{{l}_{1}}}\] \[{{l}_{1}}=1.3\,l\] Increase in length\[=1.3\,l-l=0.3l\] \[=30%\]
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