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Dimensional Analysis

Question

The dimensional formula of $\frac{1}{μ_{0} ϵ_{0}}$ is
$[M^{0} L^{2} T^{- 2}]$
$[M^{0} L^{- 2} T^{- 2}]$
$[M^{0} L T^{- 1}]$
$[M^{0} L T^{- 2}]$

A

[M^{0} L^{- 2} T^{- 2}]

B

[M^{0} L T^{- 1}]

C

[M^{0} L^{2} T^{- 2}]

D

[M^{0} L T^{- 2}]

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Solution

Verified by Toppr

Velocity of $E M$ waves, $v = \frac{1}{\sqrt{μ_{0} ϵ_{0}}}$
$\Rightarrow= \frac{1}{μ_{0} ϵ_{0}} = v^{2}$
$∴$ Dimensional formula of $\frac{1}{μ_{0} ϵ_{0}} = [M^{0} L T^{- 1}]^{2}$
$= [M^{0} L^{2} T^{- 2}]$ .

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