Depending upon the type of strain in the body there are three different types of modulus of elasticity. They are
(i) Young's modulus
(ii) Bulk modulus
(iii) Rigidity modulus

*Three moduli of elasticity*

Depending upon the type of strain in the body
there are three different types of modulus of elasticity. They are

(i)
Young's modulus

(ii)
Bulk modulus

(iii)
Rigidity modulus

*(i) Young's modulus of elasticity*

*Consider a wire of length l
and cross sectional area A stretched by a force F acting along its length. Let
dl be the extension produced.*

* Longitudinal stress = Force / Area = F/A*

*Longitudinal strain = change
in length / original length = dl/l*

*Young's modulus of the
material of the wire is defined as the ratio of longitudinal stress to
longitudinal strain. It is denoted by q.*

*Young's modulus =
longitudinal stress / longitudinal strain*

*q =F/A / dl/l = Fl /Adl*

*(ii) Bulk modulus of elasticity*

*Suppose euqal forces act
perpendicular to the six faces of a cube of volume V as shown in Fig.. Due*

*to the action of these
forces, let the decrease in volume be dV. *

*Now, Bulk stress = Force/Are
= F/ A*

*Bulk Strain =* *change in volume / original volume = -dV/V*

*(The negative sign indicates
that volume decreases.)*

*Bulk modulus of the material
of the object is defined as the ratiobulk stress to bulk strain.*

*It is denoted by k*

*Bulk modulus = Bulk stress / Bulk strain*

*K = -PV/dV*

*(iii) Rigidity modulus or shear modulus*

*Let us apply a force
Ftangential to the top surface of a block whose bottom AB is fixed, as shown in
Fig..*

*Under the action of this
tangential force, the body suffers a slight change in shape, itsvolume
remaining unchanged.The side AD of the block is sheared through an angle θ to
the position AD'.*

*If the area of the top
surface is A, then shear stress = F/A.*

*Shear modulus or rigidity
modulus of the material of the object isdefined as the ratio of shear stress to
shear strain. It is denoted by n.*

*Rigidity modulus = shear
stress / shear strain*

*(i.e) n = F/Aθ*

*Table lists the values of the three moduli of
elasticity for some commonly used materials.*

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11th 12th std standard Class Physics sciense Higher secondary school College Notes : Three moduli of elasticity |

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