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

  • question_answer
    The dimensions of angular momentum, latent heat and capacitance are, respectively.             [JEE ONLINE 22-04-2013]

    A) \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{1}}{{\operatorname{A}}^{2}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{2}}\]

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

    C)             \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},\operatorname{M}{{\operatorname{L}}^{2}}\operatorname{T}{{\operatorname{A}}^{2}}\]

    D)             \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{4}}{{\operatorname{A}}^{2}}\]

    Correct Answer: D

    Solution :

    [d] Angular momentum \[=m\times v\times r\]\[=M{{L}^{2}}{{T}^{-1}}\]
    Latent heat \[L=\frac{Q}{m}=\frac{M{{L}^{2}}{{T}^{-2}}}{M}={{L}^{2}}{{T}^{-2}}\]
    Capacitance\[C=\frac{Ch\arg e}{P.d.}={{M}^{-1}}{{L}^{-2}}{{T}^{-4}}{{A}^{2}}\]


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