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

Dimension of $\frac{1}{\mu_0 \varepsilon_0}$, where symbols have their usual meaning, are
  1. $\left[\mathrm{L}^{-1} \mathrm{~T}\right]$
  2. $\left[\mathrm{L}^{-2} \mathrm{~T}^2\right]$
  3. $\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]$
  4. $\left[\mathrm{LT}^{-1}\right]$

Solution

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

Asked in: JEE Main 2003

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