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CMC Medical CMC-Medical Ludhiana Solved Paper-2008

  • question_answer
    In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to \[\frac{3}{4}\]th of the original length and the tension is changed. The factor by which the tension is to be changed, is

    A)  \[\frac{3}{8}\]                                  

    B)  \[\frac{2}{3}\]

    C)  \[\frac{8}{9}\]                                  

    D)  \[\frac{9}{4}\]

    Correct Answer: D

    Solution :

                    \[n=\frac{1}{2l}\sqrt{\frac{T}{m}}\] \[\Rightarrow \]               \[n\propto \frac{\sqrt{T}}{l}\] \[\therefore \]  \[\frac{{{T}_{2}}}{{{T}_{1}}}={{\left[ \frac{{{n}_{2}}}{{{n}_{1}}} \right]}^{2}}{{\left[ \frac{{{l}_{2}}}{{{l}_{1}}} \right]}^{2}}\]      \[={{(2)}^{2}}\left[ \frac{3}{4} \right]=\frac{9}{4}\]


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