NEET Physics Mathematical Tools, Units & Dimensions Question Bank Dimensions

  • question_answer
    If \[L,\,C\] and \[R\] denote the inductance, capacitance and resistance respectively, the dimensional formula for \[{{C}^{2}}LR\] is                                                                           [UPSEAT 2002]

    A)             \[[M{{L}^{-2}}{{T}^{-1}}{{I}^{0}}]\]

    B)             \[[{{M}^{0}}{{L}^{0}}{{T}^{3}}{{I}^{0}}]\]

    C)             \[[{{M}^{-1}}{{L}^{-2}}{{T}^{6}}{{I}^{2}}]\]      

    D)             \[[{{M}^{0}}{{L}^{0}}{{T}^{2}}{{I}^{0}}]\]

    Correct Answer: B

    Solution :

                    \[{{C}^{2}}LR=[{{C}^{2}}{{L}^{2}}]\times \left[ \frac{R}{L} \right]=[{{T}^{4}}]\times \left[ \frac{1}{T} \right]=[{{T}^{3}}]\]                         As \[\left[ \frac{L}{R} \right]=T\] and \[\sqrt{LC}=T\]


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