Explain the different types of modulus of elasticity.

Explanation

From Hooke.s law, the stress in a body is proportional to the corresponding strain, provided the deformation is very small. Here we shall define the elastic modulus of a given material. There are three types of elastic modulus.
(a) Young.s modulus (6) Rigidity modulus (or Shear modulus) (c) Bulk modulus
Young.s Modulus: When a wire is stretched or compressed, then the ratio between tensile stress (or compressive stress) and tensile strain (or compressive strain) is defined as Young.s modules.
Young modulus of a material `=("Tensile stress or compressive stress ")/("Tensile strain or compressive strain ")`
` Y = (sigma_i )/( epsi_t) or Y = ( sigma _c )/( epsi_c)`
S.I. unit of Young modulus is `N m^(-2)` or pascal.
Bulk modulus: Bulk modulus is defined as the ratio of volume stress to the volume strain.
Bulk modulus K -`(" Normal (Perpendicular) stress or Pressure")/("Volume strain")`
The normal stress or pressure is `sigma _(n) = (F_n )/(Delta A )= Delta P`
The volume strain is `epsi_V =( Delta V )/(V )`
Therefore, Bulk modulus is `K = - ( sigma _n)/( epsi_v ) = ( Delta P )/((Delta V)/(V))`
The negative sign indicates when pressure is applied on the body, its volume decreases. Further, the equation implies that a material can be easily compressed if it has a small value of bulk modulus. In other words, bulk modulus measures the resistance of solids to change in their volume. For an example, we know that gases can be easily compressed than solids, which means, gas has a small value of bulk modulus compared to solids. The S.I. unit of K is the same as that of pressure i.e., `N m^(-2 )`or Pa (pascal).