IITJEE Study Material:Elasticity

-Elasticity is the property of material body to regain its original condition on removal of deforming forces.
-Bodies which can recover their original condition on removal of deforming forces are perfectly elastic bodies .
-Bodies which does not have tendency to recover their original condition on removal of deforming forces are called plastic bodies.
-There are no perfectly elastic or plastic bodies and actual bodies lie between two extremes.
(1) STRESS
-Stress is the restoring force per unit area set up inside the body and is measured by the magnitude of deforming force acting on unit area of the body within the elastic limits of the body.
Magnitude of stress=F/A where, Fis the force applied and A is the area of crosssection of the body.
-S.I. unit of sterss is N/m2.-Dimensional formula of stress is[ML1T-2].
(A) Normal Stress:- If elastic forces developed are perpandicular to the area of cross-section of the body then the stress developed is known as normal stress.
(B) Tangential Stress:- Tangential or shearing stress developes in a body when elastic restoring forces are parallel to the cross-sectional area of the body and the body gets sheared through a certain angle.
(2) STRAIN
-When a body is under a system of forces or couples in equilibrium then a change is produced in dimensions of the body and this fractional change produced in the body is called Strain.
(A) longitudinal strain=Δl/l, where l is the original length and Δl is the change in length.
(B) volume strain=ΔV/V, where V is the original volume and ΔV is the change in volume.
(C) if the deforming forces produces change in shape of the body then the strain is called shearing strain.
-Strain is an dimensionless quantity.
(3)HOOK'S LAW
-Hook's law states that 'For small deformations, within elastic limits, stress is directly proportional to strain'.
Thus, stress ∝ strain
or, stress/strain=constant-This constant is known as modulus of elasticity of given material.
(4)MODULUS OF ELASTICITY
(A) Young's modulus of elasticity:-
-Young's modulus of elasticity is given by
Y=longitudinal Stress/longitudinal Stress
= (F/A)/(Δl/l)
=Fl/AΔl
-It has dimensions of pressure.
(B) Bulk modulus of elasticity:-
-Bulk modulus of elasticity is the ratio of normal stress to volume strain within elastic limits.
-It is denoted by k and
K=FV/AΔV
(C) Modulus of rigidity:-
-When a body is sheared , the ratio of tangential stress to the shearing strain within elastic limits is called modulus of rigidity.

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