# Bulk Modulus

It is defined as the ratio of normal stress to the volumetric strain. It is denoted by K.K = (i)

Consider a sphere of volume V and surface area a [Figure]. Suppose that the force F that acts uniformly over the whole surface of the sphere decreases its volume by Î” V. Then,

Normal stress =

Volumetric strain = -

The negative sign indicates that on increasing the stress, volume of the sphere decreases.

K = -(ii)

Now, = p, the pressure applied over the sphere.

Therefore,

K = - -----------(iii)

The units of bulk modules are **Pa **or **Nm ^{-2}**in S.I.

**Compressibility**

The reciprocal of the bulk modulus of a material is called its compressibility. Therefore,

Compressibility = ---------(iv)

The units of compressibility are reciprocal of those bulk modules i.e. the units of compressibility are **Pa ^{-1}** or

**N**in S.I.

^{-1}m^{2}