The dimensions of surface tension are

Identify the pair of physical quantities that have the same dimensions.

In the relation: $\frac{dy}{dx} = 2\omega \sin(\omega t + \phi_0)$,the dimensional formula for $(\omega t + \phi_0)$ is:

The dimensional formula of $\varepsilon_r$ is .......

Which two of the following five physical parameters have the same dimensions?
$(a)$ Energy density
$(b)$ Refractive index
$(c)$ Dielectric constant
$(d)$ Young's modulus
$(e)$ Magnetic field

$A$ temperature difference can generate $e.m.f.$ in some materials. Let $S$ be the $e.m.f.$ produced per unit temperature difference between the ends of a wire,$\sigma$ the electrical conductivity and $\kappa$ the thermal conductivity of the material of the wire. Taking $\text{M, L, T, I}$ and $K$ as dimensions of mass,length,time,current and temperature,respectively,the dimensional formula of the quantity $Z=\frac{S^2 \sigma}{\kappa}$ is :-