Dimensions of 1/μ₀ₚε₀, where symbols have their usual meaning, are

The correct option is [L² T⁻²].

To find the dimensions of the expression, we recall the relationship between the speed of light in a vacuum ($c$), the permeability of free space (${\mu }_0$), and the permittivity of free space (${\epsilon }_0$). This fundamental relationship is given by the formula:

$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

Squaring both sides of this equation, we get:

$c^2=\frac{1}{{\mu }_0{\epsilon }_0}$

Since $c$ represents speed (velocity of light), its dimensional formula is:

$\left[c\right]=\left[{\text{LT}}^{-1}\right]$

Substituting the dimensional formula of $c$ into the equation for $c^2$, we obtain:

$\left[\frac{1}{{\mu }_0{\epsilon }_0}\right]={\left[{\text{LT}}^{-1}\right]}^2=\left[{\text{L}}^2{\text{T}}^{-2}\right]$

Thus, the dimensional formula of $\frac{1}{{\mu }_0{\epsilon }_0}$ is [L² T⁻²].