CET Karnataka Medical CET - Karnataka Medical Solved Paper-2002

  • question_answer
    The tension of a stretched string is increased by 69%. In order to keep its frequency of vibration constant, its length must be increased by:

    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.    __ \[{{f}_{1}}=\frac{1}{2{{l}_{1}}}\sqrt{\frac{{{T}_{1}}}{\mu }}\] \[{{T}_{1}}=T+0.69T=1.69T\] \[{{l}_{1}}=?,f={{f}_{1}}\] \[\frac{1}{2l}\sqrt{\frac{T}{\mu }}=\frac{1}{2{{l}_{1}}}\sqrt{\frac{1.69T}{\mu }}\] \[\frac{1}{l}=\frac{1.3}{{{l}_{1}}}\] \[{{l}_{1}}=1.3l\] Increase in length \[=1.3l-l=0.3l\] \[=30%\]


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