Identify the pair of physical quantities that possesses the same...

Energy density is defined as energy per unit volume.

Dimensional formula of energy density = $\dfrac{[M L^2 T^{-2}]}{[L^3]} = [M L^{-1} T^{-2}]$

Pressure is defined as force per unit area.

Dimensional formula of pressure = $\dfrac{[M L T^{-2}]}{[L^2]} = [M L^{-1} T^{-2}]$

Bulk modulus is defined as the ratio of volumetric stress to volumetric strain.

Dimensional formula of bulk modulus = $\dfrac{[M L^{-1} T^{-2}]}{[M^0 L^0 T^0]} = [M L^{-1} T^{-2}]$

Thus, pressure and bulk modulus have the same dimensional formula as that of energy density.

Answer: Pressure and bulk modulus