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  4. The dimensions of (μ0 ε0)-1 / 2 are

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Q. The dimensions of $\left(\mu_{0} \varepsilon_{0}\right)^{-1 / 2}$ are

AIPMTAIPMT 2012Physical World, Units and Measurements

Solution:

The speed of the light in vacuum is
$ c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}=\left(\mu_{0} \varepsilon_{0}\right)^{-1 / 2}$
$\therefore \left[\left(\mu_{0} \varepsilon_{0}\right)^{-1 / 2}\right] =[c]=\left[\text { LT }^{-1}\right]$