JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions JEE PYQ - Mathematical Tools Units and Dimensions

  • question_answer
    In the formula \[X=5Y{{Z}^{2}},X\] and \[Z\] have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?        [JEE Main 10-4-2019 Afternoon]

    A) \[[{{M}^{-2}}{{L}^{-2}}{{T}^{6}}{{A}^{3}}]\]

    B) \[[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}]\]

    C) \[[{{M}^{-3}}{{L}^{-2}}{{T}^{8}}{{A}^{4}}]\]    

    D) \[[{{M}^{-2}}{{L}^{0}}{{T}^{-4}}{{A}^{-2}}]\]  

    Correct Answer: C

    Solution :

    [c] \[X=5Y{{Z}^{2}}\]
                \[Y=\frac{X}{5{{Z}^{2}}}\]
                \[[Y]=\frac{[X]}{[{{Z}^{2}}]}\]
                \[=\frac{{{A}^{2}}.{{M}^{-1}}{{L}^{-2}}.{{T}^{4}}}{{{(M{{A}^{-1}}{{T}^{-2}})}^{2}}}\]     
    \[={{M}^{-3}}.\,{{L}^{-2}}.\,{{T}^{8}}.\,{{A}^{4}}\]


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