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JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank Self Evaluation Test - Physical World, Units and Measurements

  • question_answer
    The speed of light in vacuum, c, depends on two fundamental constants, the permeability of free space, \[{{\mu }_{0}}\] d me permittivity of free space,\[{{\varepsilon }_{0}}.\] The speed of light is given by\[c=\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}\]. The units of \[{{\varepsilon }_{0}}\] are \[{{N}^{-1}}{{C}^{2}}{{m}^{-2}}\]. The units for \[{{\mu }_{0}}\] are

    A)  \[k{{g}^{-1}}{{m}^{-1}}{{C}^{2}}\]

    B)  \[kgm{{C}^{-2}}\]

    C)  \[kg\,m{{s}^{-4}}{{C}^{-2}}\]

    D)  \[k{{g}^{-1}}{{s}^{-3}}{{C}^{-2}}\]

    Correct Answer: B

    Solution :

    [b] We have, \[c=\frac{1}{\sqrt{{{\mu }_{0}}{{\in }_{0}}}}\Rightarrow {{\mu }_{0}}=\frac{1}{{{\in }_{0}}{{c}^{2}}}\] \[\therefore \]   units of \[{{\mu }_{0}}=\frac{1}{units\,of\,{{\in }_{0}}{{c}^{2}}}\] \[=\frac{1}{{{N}^{-1}}{{C}^{2}}{{m}^{-2}}{{(m{{s}^{-1}})}^{2}}}=N{{s}^{2}}{{C}^{-2}}\] \[=(kgm{{s}^{-2}}){{s}^{2}}{{C}^{-2}}=kgm{{C}^{-2}}\]


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