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# 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 -2in 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-1m2in S.I.