The dimensions of pressure is equal to

To determine which of the given options has the same dimensions as pressure, let's analyze their dimensional formulas step-by-step.

First, we find the dimensions of pressure.
Pressure is defined as force per unit area:
$Pressure\; =\; \backslash frac\{Force\}\{Area\}$
The dimensional formula for Force ($F$) is:
$[F]\; =\; [M\; L\; T^\{-2\}]$
The dimensional formula for Area ($A$) is:
$[A]\; =\; [L^2]$
Therefore, the dimensional formula for Pressure ($P$) is:
$[P]\; =\; \backslash frac\{[M\; L\; T^\{-2\}]\}\{[L^2]\}\; =\; [M\; L^\{-1\}\; T^\{-2\}]$

Now, let's check the options:

1. Energy per unit volume:
Energy has the same dimensions as work, which is Force × Displacement:
$[Energy]\; =\; [M\; L^2\; T^\{-2\}]$
Volume ($V$) has the dimensional formula:
$[Volume]\; =\; [L^3]$
So, the dimensions of energy per unit volume are:
$[\backslash frac\{Energy\}\{Volume\}]\; =\; \backslash frac\{[M\; L^2\; T^\{-2\}]\}\{[L^3]\}\; =\; [M\; L^\{-1\}\; T^\{-2\}]$
This is identical to the dimensional formula of pressure.

2. Force per unit volume:
The dimensions are:
$[\backslash frac\{Force\}\{Volume\}]\; =\; \backslash frac\{[M\; L\; T^\{-2\}]\}\{[L^3]\}\; =\; [M\; L^\{-2\}\; T^\{-2\}]$
This does not match the dimensions of pressure.

3. Force:
The dimensions are:
$[Force]\; =\; [M\; L\; T^\{-2\}]$
This does not match the dimensions of pressure.

4. Energy:
The dimensions are:
$[Energy]\; =\; [M\; L^2\; T^\{-2\}]$
This does not match the dimensions of pressure.

Thus, the dimensions of pressure are equal to energy per unit volume.