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BCECE Engineering BCECE Engineering Solved Paper-2008

  • question_answer
    If E = energy, G = gravitational constant, \[I=\]impulse and \[M=\]mass, then dimensions of \[\frac{GI{{M}^{2}}}{{{E}^{2}}}\]are same as that of

    A) time                                      

    B)  mass

    C)  length                 

    D)         force

    Correct Answer: A

    Solution :

    Dimensions of \[E=[M{{L}^{2}}{{T}^{-2}}]\] Dimensions of \[G=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]         Dimensions of \[I=[ML{{T}^{-1}}]\] and dimensions of \[M=[M]\] So, dimensions of\[\frac{G{{\operatorname{IM}}^{2}}}{{{E}^{2}}}\] \[=\frac{[G][I][{{M}^{2}}]}{[{{E}^{2}}]}\] Substituting the dimensions for each physical quantity, we get Dimensions of\[\frac{GI{{M}^{2}}}{{{E}^{2}}}\]                 \[=\frac{[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}][ML{{T}^{-1}}][{{M}^{2}}]}{{{[M{{L}^{2}}{{T}^{-2}}]}^{2}}}\]                 \[=[T]\]                 = Dimensions of time


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