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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2008

  • question_answer
    A string vibrates with a frequency of 200 Hz. When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 Hz. The ratio of the new tension to the original tension is

    A)  \[9:1\]                                 

    B)  \[1:9\]

    C)  \[3:1\]                                 

    D)  \[1:3\]

    Correct Answer: A

    Solution :

                    \[v=\frac{1}{2l}\sqrt{\frac{T}{m}}\] \[\Rightarrow \]               \[v\propto \frac{\sqrt{T}}{l}\]                 \[\frac{{{T}_{2}}}{{{T}_{1}}}={{\left[ \frac{{{v}_{2}}}{{{v}_{1}}} \right]}^{2}}{{\left[ \frac{{{l}_{2}}}{{{l}_{1}}} \right]}^{2}}={{\left[ \frac{300}{200} \right]}^{2}}{{\left[ \frac{2l}{l} \right]}^{2}}=\frac{9}{1}\]


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