Which of the following has the dimensions of pressure?

The correct answer is [ML⁻¹T⁻²].

To find the dimensional formula of pressure, we start with its basic definition:

$\text{Pressure}=\frac{\text{Force}}{\text{Area}}$

Let us find the dimensions of both force and area:

1. Force: Force is defined as mass multiplied by acceleration.
$\text{Force}=\text{Mass}\times \text{Acceleration}$
The dimension of mass is [M] and the dimension of acceleration is [LT^-2]. Therefore, the dimensional formula for force is:
$\left[\text{Force}\right]=\left[{\text{MLT}}^{-2}\right]$

2. Area: Area is the product of two length dimensions.
$\left[\text{Area}\right]=\left[{\text{L}}^2\right]$

Now, we substitute these dimensions back into the formula for pressure:
$\left[\text{Pressure}\right]=\frac{\left[{\text{MLT}}^{-2}\right]}{\left[{\text{L}}^2\right]}$

Simplifying the expression by dividing the powers of L:
$\left[\text{Pressure}\right]=\left[{\text{ML}}^{1-2}{\text{T}}^{-2}\right]$
$\left[\text{Pressure}\right]=\left[{\text{ML}}^{-1}{\text{T}}^{-2}\right]$

Thus, the dimensions of pressure are [ML⁻¹T⁻²].