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AMU Medical AMU Solved Paper-2010

  • question_answer
    If E, M, L and G denote energy, mass, angular  momentum  and  gravitational constant respectively, then the quantity \[({{\text{E}}^{\text{2}}}{{\text{L}}^{\text{2}}}/{{\text{M}}^{\text{5}}}{{\text{G}}^{\text{2}}})\]has the dimensions of

    A)  angle                                   

    B)  length

    C)  mass                                    

    D)  None of these

    Correct Answer: D

    Solution :

                     The dimensions of \[E=[M{{L}^{2}}{{T}^{-2}}]\] Dimensions of M = [M] Dimensions of \[L=[M{{L}^{2}}{{T}^{-1}}]\] Dimensions of \[G=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\] \[\therefore \] Dimensions of \[\left[ \frac{{{E}^{2}}{{L}^{2}}}{{{M}^{5}}{{G}^{2}}} \right]=\frac{{{[M{{L}^{2}}{{T}^{-2}}]}^{2}}{{[M{{L}^{2}}{{T}^{-1}}]}^{2}}}{{{[M]}^{5}}{{[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]}^{2}}}\]                 \[=[M{{L}^{2}}{{T}^{-2}}]\] So, option  is correct.


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