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JCECE Engineering JCECE Engineering 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 m 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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