Dimensions of bulk modulus are

The correct option is [ML⁻¹T⁻²].

Step-by-step Explanation:

Bulk modulus ($B$) is defined as the ratio of volumetric stress (which is equivalent to pressure) to volumetric strain.
The formula is:
$B=-\frac{\Delta P}{\frac{\Delta V}{V}}$
where $\Delta P$ represents the change in pressure, $\Delta V$ is the change in volume, and $V$ is the original volume.

Since volumetric strain ($\frac{\Delta V}{V}$) is the ratio of two identical physical quantities (volume divided by volume), it is dimensionless:
$\left[\text{Volumetric Strain}\right]=\left[M^0{L}^0{T}^0\right]$

Therefore, the dimensions of Bulk Modulus ($B$) must be the same as the dimensions of pressure ($P$):
$\left[B\right]=\left[\text{Pressure}\right]$

Pressure is defined as Force per unit Area:
$\text{Pressure}=\frac{\text{Force}}{\text{Area}}$

Let's determine the dimensions of Force and Area:
1. Force ($\text{Mass}\times \text{Acceleration}$) has the dimensions:
$\left[\text{Force}\right]=\left[M\right]\times \left[L{T}^{-2}\right]=\left[ML{T}^{-2}\right]$
2. Area has the dimensions:
$\left[\text{Area}\right]=\left[L^2\right]$

Now, we substitute these dimensions back into the formula for pressure:
$\left[\text{Pressure}\right]=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}=\left[M{L}^{-1}{T}^{-2}\right]$

Thus, the dimensional formula of the bulk modulus is:
$\left[B\right]=\left[M{L}^{-1}{T}^{-2}\right]$