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

  • question_answer
    In terms of resistance R and time T, the dimensions of ratio\[\frac{\mu }{\varepsilon }\]of the permeability \[\mu \] and permittivity \[\varepsilon \] is:  [JEE ONLINE 11-04-2014]

    A) \[[R{{T}^{-2}}]\]

    B) \[[{{R}^{2}}{{T}^{-1}}]\]

    C) \[[{{R}^{2}}]\]

    D) \[[{{R}^{2}}{{T}^{2}}]\]

    Correct Answer: C

    Solution :

    [c] Dimensions of\[\mu =[ML{{T}^{-2}}{{A}^{-2}}]\]
    Dimensions of \[\in =[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]\]
    Dimensions of \[R=[M{{L}^{2}}{{T}^{-3}}{{A}^{-2}}]\]
    \[\therefore \]\[\frac{\text{Dimensionsof}\,\mu }{\text{Dimensionsof}\,\in }=\frac{[ML{{T}^{-2}}{{A}^{-2}}]}{[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]}\]
    \[=[{{M}^{2}}{{L}^{4}}{{T}^{-6}}{{A}^{-4}}]=[{{R}^{2}}]\]


You need to login to perform this action.
You will be redirected in 3 sec spinner