Young’s modulus:
Within the elastic limit, longitudinal stress divided by longitudinal strain is called Young’s modulus.
Young’s modulus (Y) = longitudinal stress / longitudinal strain
If longitudinal stress tends to infinity and longitudinal strain tends to zero. Young’s modulus tends to infinity. For a perfectly rigid body, the longitudinal stress is infinite and the longitudinal strain zero. So, Young’s modulus Y is infinite. on the other hand, if any external force is applied to a plastic body, its longitudinal stress is zero and Young’s modulus (Y) to becomes zero.
Bulk modulus:
Within the elastic limit, volume stress divided by volume strain is called the bulk modulus of elasticity.
Bulk moudulus (K) = volume stress / volume strain
Every substance – solid, liquid or gas has some volume and hence the bulk modulus is meaningful for all substances. The bulk moduli of a perfectly rigid body and a perfectly plastic body are infinite and zero respectively.
Since liquid and gaseous substances undergo only volume strain, the bulk modulus is the only elastic modulus for them. Among the different bulk moduli of gas very useful is its isothermal and adiabatic bulk moduli. The isothermal bulk modulus of air = 1.01 x 105Pa and the adiabatic bulk modulus of air = 1.42 x 105Pa.