If $R , X _{ L }$. and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta $. After some time the velocity of the ball attains a constant value known as terminal velocity ${v_T}$. The terminal velocity depends on $(i)$ the mass of the ball $m$, $(ii)$ $\eta $, $(iii)$ $r$ and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct

The dimension of $\frac{1}{2} \varepsilon_0 E ^2$, where $\varepsilon_0$ is permittivity of free space and $E$ is electric field, is

Identify the pair which has different dimensions

An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is

Dimensions of $\frac{1}{{{\mu _0}{\varepsilon _0}}}$, where symbols have their usual meaning, are