The dimensions of $\left(\mu_0 \varepsilon_0\right)^{-1 / 2}$ are

The dimensions of $\left(\mu_0 \varepsilon_0\right)^{-1 / 2}$ are
  1. $\left[\mathrm{L}^{1 / 2} \mathrm{~T}^{-1 / 2}\right]$
  2. $\left[\mathrm{L}^{-1} \mathrm{~T}\right]$
  3. $\left[\mathrm{LT}^{-1}\right]$
  4. $\left[\mathrm{L}^{1 / 2} \mathrm{~T}^{1 / 2}\right]$

Solution

$\left(\mu_0 \varepsilon_0\right)^{-1 / 2}$ is velocity of light Hence $\quad c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}=\left[\mathrm{LT}^{-1}\right]$

Asked in: NEET 2012 (Mains)

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