Units & Dimensions

JEE Main level, single correct, medium

14 of 149

Question 14 of 149

In SISI units, the dimensions of ϵ0μ0\sqrt{\dfrac{{ϵ}_{0}}{{\mu }_{0}}} is:

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Answer: (B) A2T3M−1L−2{A}^{2}{T}^{3}{M}^{-1}{L}^{-2}

As we know, c=1μ0ϵ0c=\dfrac{1}{\sqrt{{\mu }_{0}{\epsilon }_{0}}}
∴ϵ0μ0=ϵ02μ0ϵ0=ϵ0c∴\sqrt{\dfrac{{\epsilon }_{0}}{{\mu }_{0}}}=\sqrt{\dfrac{{\epsilon }_{0}^{2}}{{\mu }_{0}{\epsilon }_{0}}}={\epsilon }_{0}c
∴[ϵ0μ0]=∴\left[\sqrt{\dfrac{{\epsilon }_{0}}{{\mu }_{0}}}\right]= [ϵ0][c]=[M−1L−3T4A2][LT−1]\left[{\epsilon }_{0}\right]\left[c\right]=\left[{M}^{-1}{L}^{-3}{T}^{4}{A}^{2}\right][L{T}^{-1}]
=[M−1L−2T3A2]=[{M}^{-1}{L}^{-2}{T}^{3}{A}^{2}]

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