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

The dimensional formula for latent heat is

Match Column-$1$ with Column-$2$.

Column-$1$	Column-$2$
$(a)$ Wave vector	$(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density	$(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave	$(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient	$(iv)$ $M^1L^{-1}T^0$

The force of interaction between two atoms is given by $F = \alpha \beta \exp \left( - \frac{x^2}{\alpha kt} \right)$,where $x$ is the distance,$k$ is the Boltzmann constant,$T$ is temperature,and $\alpha$ and $\beta$ are two constants. The dimension of $\beta$ is:

Let $x = \pi R \left( \frac{P^2 - Q^2}{2} \right)$,where $P, Q$ and $R$ are lengths. The physical quantity $x$ is

Write the dimensional formula for energy density.