Question

The compressibility of a substance is the reciprocal of
A) Young’s modulus
B) Bulk modulus
C) Modulus of rigidity
D) Poisson’s ratio

Answer 1

Hint
Compressibility refers to the change in volume of a substance due to exertion of pressure.
The ratio of change in volume to original volume is nothing but strain.

Complete step by step answer
Compressibility is directly proportional to strain caused by stress. Generally, Compressibility is written as $\beta = - \left( {\dfrac{1}{V}} \right)\left( {\dfrac{{dV}}{{dP}}} \right)$ . The negative is to make it a positive value since dV is negative. Here $\left( {\dfrac{{dV}}{V}} \right)$ is the ratio of change in volume per unit volume and dP is pressure applied which is equal to Force applied per unit area which is also called as stress, which implies Compressibility $(\beta ) = \left( {\dfrac{{strain}}{{stress}}} \right)$ .
We know that Bulk modulus is ratio of pressure increased to volume change which is stress / strain which implies
Compressibility $ = \left( {\dfrac{{strain}}{{stress}}} \right)$ = 1/stress/strain = 1/ Bulk modulus.
Hence the correct answer is option (B).

Note
Compressibility is different from Compressibility factor (Z) which refers to the correction factor used to describe deviation of real gas from ideal behavior. Compressibility is also known as coefficient of Compressibility. Generally, Gases are more compressible, liquids and solids are less compressible.