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JEE Main 2003
Exam
JEE Main
Year
2003
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2003 · Physics · Units and Dimensions

Dimension of (1)/(μ_0 _0) , where symbols have their usual meaning,...

Dimension of 1μ0ε0\frac{1}{\mu_0 \varepsilon_0}, where symbols have their usual meaning, are

Options

  1. A[L−1 T]\left[\mathrm{L}^{-1} \mathrm{~T}\right]
  2. B[L−2 T2]\left[\mathrm{L}^{-2} \mathrm{~T}^2\right]
  3. C[L2 T−2]\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]
  4. D[LT−1]\left[\mathrm{LT}^{-1}\right]

Correct answer

C. [L2 T−2]\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]

Step-by-step solution

\frac{1}{\sqrt{\mu_0 \varepsilon_0}}=\mathrm{C} \Rightarrow \frac{1}{\mu_0 \varepsilon_0}=\mathrm{C}^2 \Rightarrow[1μ0ε0]=[C]2\left[\frac{1}{\mu_0 \varepsilon_0}\right]=[\mathrm{C}]^2 [C]=LT−1[\mathrm{C}]=\mathrm{LT}^{-1} \quad or [C]2=L2 T−2\quad[\mathrm{C}]^2=\mathrm{L}^2 \mathrm{~T}^{-2}
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