Properties of Matter
Introduction
A body can be changed in shape or size by the suitable application of external force on it.
The property of a body to regain its original state on the removal of the applied force is called
elasticity.
The materials which have elasticity are known as elastic materials.
Classification of Elastic Materials
Elastic materials are classified into the following two categories:

Elastic materials

Plastic materials
Elastic material If materials regain their original shape or size, when the applied forces are
removed are called as elastic materials.
Example: Quartz fiber.
Plastic materials If materials does not regain their original shape or size, when the applied
forces are removed are called as plastic materials.
Example: Glass.
Stress
The restoring force per area is known as stress.
Stress =
Force
Area
𝐹
=𝐴
Its dimensions are ML-1T-2. Its unit is Nm-2.
Stress is classified as,

Shearing stress

Tangential stress

Compressive or expansive stress
Strain
The ratio of the change in any dimension to its original dimension is called as strain. It
has no unit.
Strain is classified as,

Longitudinal strain

Shearing strain

Bulk Strain
Hooke’s Law
Robert Hooke introduced a relation between stress and strain. This law states that stress
is proportional to strain within the elastic limit.
Stress α strain
𝑠𝑡𝑟𝑒𝑠𝑠
𝑠𝑡𝑟𝑎𝑖𝑛
= 𝐸(𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)
This constant is called as coefficient of elasticity or modulus of elasticity. It depends on
the nature of the material.
The dimension formula of E is ML-2T-2 and unit is Nm-2.
Types of Modulus
Corresponding to the three types of strains, there are three elastic modulus:
1. Young’s modulus : It corresponds to linear or tensile strain.
2. Bulk modulus : It corresponds to volumetric strain.
3. Rigidity modulus : It corresponds to shearing strain.
Young’s Modulus (Y)
It is defined as the ratio of longitudinal stress to longitudinal strain within elastic limits.
Let a wire of length ‘L’ and area of cross section ‘a’. one end of the wire is fixed in the top and a
load is applied on the bottom of the wire as shown in Fig.2.
Fig.2 Change in Length
The force which is acting along the length of the wire is ‘F’. Let the increase in length is
‘l’ when a stretching force ‘F’ is applied in the direction of its length. The force applied per unit
area of cross section is known as longitudinal or linear stress. The ratio of the longitudinal stress
to linear strain within the elastic limit is known as Young’s modulus.
Longitudinal strain = l/L
Stress = F/a
... Young’s modulus Y = stress/ strain
Y = FL/al
Unit of the Young’s modulus is Nm-2 or Pascal.
Bulk Modulus (K)
It is defined as the ratio between volume stress to the volume strain. Consider a body of
volume ‘V’ and area of cross section ‘a’ as shown in Fig.3. Let ‘F’ be the force applied under
normal condition to the whole surface of the body. This results in change in volume but there is
no change shape of the body.
Fig.3 Change in Volume
When three equal stresses (F/a) are act on a body in mutually perpendicular directions,
such that there is a change of volume ΔV in its original volume.
Volume stress = F/a
Volume strain = - (ΔV/V)
... Bulk modulus K = Volume stress/ Volume strain
= - (PV/ΔV)
The negative sign indicates that the pressure is increased with increasing volume.
Rigidity Modulus
It is defined as the ratio of tangential stress to shearing strain.
Consider a solid cube ABCDEFGH as shown in Fig.4. The lower face CDEF is fixed and
a tangential force F is applied over the upper face ABEF. The result is that each horizontal layer
of the cube is displaced, the displacement being proportional to its distance from the fixed plane.
Point A is shifted to A’, B to B’, E to E’ and F to F’ through an angle ϕ, where AA’ = EE’ = l.
Fig.4 Change in Angle
Clearly ϕ = (l/L), where l is the relative displacement of the upper face of the cube with respect
to the lower fixed face, The angle ϕ is a measure of the shearing strain.
Now, Rigidity modulus (G) =
𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙 𝑠𝑡𝑟𝑒𝑠𝑠
𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑡𝑟𝑎𝑖𝑛
𝐹
Rigidity modulus (G) = 𝑎𝜙
Here, a = L2 = Area of face ABEF.
Rigidity modulus (G) =
𝑇
𝜙
Where T is a tangential stress.