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RAJASTHAN PMT Rajasthan - PMT Solved Paper-2007

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

    A)  time                                     

    B)  mass

    C)  length                 

    D)         force

    Correct Answer: A

    Solution :

    \[S\], Dimensions or\[\frac{GI{{M}^{2}}}{{{E}^{2}}}\]                 \[=\frac{[G][I][{{M}^{2}}]}{[{{E}^{2}}]}\] 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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