Question

What is the dimensional formula for compressibility?

Answer 1

Step 1: Definition

Compressibility would be defined as the change throughout the volume of material in proportion to continuous change in pressure.

The SI unit of compressibility is commonly expressed as $\raisebox{1ex}{$m^2$}\!\left/ \!\raisebox{-1ex}{$N$}\right.$.

Step 2: Dimension formula

The dimensional formula of the bulk modulus is $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]$.

We know that compressibility seems to be the reciprocal of bulk modulus, the dimension formula or compressibility is:

$\left[{\mathrm{M}}^{-1}{\mathrm{L}}^1{\mathrm{T}}^2\right]$

Therefore, the dimensional formula for compressibility is $\left[{\mathrm{M}}^{-1}{\mathrm{L}}^1{\mathrm{T}}^2\right]$.