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JCECE Medical JCECE Medical Solved Paper-2014

  • question_answer
    The frequency of vibration of string is given by \[v=\frac{p}{2l}{{\left[ \frac{F}{m} \right]}^{1/2}}\] Here, p is the number of segments in the string and \[l\]is the length. The dimensional formula for \[m\]will be

    A) \[[{{M}^{0}}L{{T}^{-1}}]\]

    B)  \[[M{{L}^{0}}{{T}^{-1}}]\]

    C)  \[[M{{L}^{-1}}{{T}^{0}}]\]

    D)  \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]

    Correct Answer: C

    Solution :

     \[v=\frac{p}{2l}{{\left[ \frac{F}{m} \right]}^{1/2}}\] Squaring the equation on either side, we have \[{{v}^{2}}=\frac{{{p}^{2}}}{4{{l}^{2}}}\left( \frac{F}{m} \right)\] \[m=\frac{{{P}^{2}}F}{4{{l}^{2}}{{v}^{2}}}\] \[[m]=\frac{[ML{{T}^{-2}}]}{[{{L}^{2}}]{{[{{T}^{-1}}]}^{2}}}=[M{{L}^{-1}}{{T}^{0}}]\]


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