Dimensions of 1/(μ0ε0) are (μ0 is magnetic permeability of free space and ε0 is permittivity of free space)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → [M0L2T−2]
The speed of light in vacuum is linked to the two constants by
\( \displaystyle c = \frac{1}{\sqrt{\mu_0\varepsilon_0}} \)
\( \displaystyle \frac{1}{\mu_0\varepsilon_0} = c^{2} \)
So \( 1/(\mu_0\varepsilon_0) \) has the dimensions of speed squared:
\( \displaystyle [c^{2}] = [\mathrm{LT^{-1}}]^{2} = [\mathrm{M^{0}L^{2}T^{-2}}] \)
NCERT (2026-27):
Summary – “… The speed c of electromagnetic wave in vacuum is related to \( \mu_0 \) and \( \varepsilon_0 \) (the free space permeability and permittivity constants) as follows:
\( \displaystyle c = 1/\sqrt{\mu_0 \varepsilon_0} \)”