RBSE Class 11 Physics Notes Chapter 9 Mechanical Properties of Solids

These comprehensive RBSE Class 11 Physics Notes Chapter 9 Mechanical Properties of Solids will give a brief overview of all the concepts.

RBSE Class 11 Physics Chapter 9 Notes Mechanical Properties of Solids

→ The property of the material of a body, due to which it regains its original size and shape after the removal of the deforming force, is called elasticity.

→ No body is perfectly elastic or perfectly plastic. All the bodies that are found in nature lie between these two limits.

→ Stress is the restoring force per unit area.

→ There are three types of stress, namely ;

• Normal stress (tensile stress and compressive stress)
• Bulk stress/volumetric stress/hydraulic stress,
• Shearing stress/tangential stress.

→ Strain is defined as the fractional change in dimensions.

 

→ There are three types of strain, namely:

• Longitudinal strain
• Volumetric strain
• Shearing strain

→ Hooke’s law states that;
“ Stress is directly proportional to strain, with in the elastic limit.”
Thus under the elastic limit,
Stress ∝ Strain
\(\frac{\text { Stress }}{\text { Strain }}\) = constant
The constant of proportionality is called as the ‘modulus of elasticity’ or ‘coefficient of elasticity’.

→ Three elastic moduli are used to describe the elastic behaviour of the objects, which are as follows:

• Young’s modulus
• Bulk modulus
• Shear modulus

→ Elastometers which are a class of solids, do not obey Hooke’s law.

→ Stress = \(\frac{\text { Restoring force }}{\text { Area }}\)
The SI unit of stress is Nm^-2 and the C.G.S. unit is dyne cm^-2. The dimensional formula of stress is [ML^-1T^-2]

→ Strain = \(\frac{\text { Changeindimension }}{\text { Originaldimension }}\)

→ Modulus of elasticity, E = \(\frac{\text { Stress }}{\text { Strain }}\)
The SI unit of modulus of elasticity is Nm^-2 and its dimensions are [ML^-1T^-2].

→ Young’s modulus of elasticity:
Y = \(\frac{\text { Normal stress }}{\text { Longitudinal strain }}=\frac{F / A}{\Delta L / L}=\frac{F L}{A \Delta L}\)

The SI unit of Young’s modulus of elasticity is Nm^-2 or pascal (Pa) and its CGS unit is dyne cm^-2
The dimensional formula is [ML^-1T^-2].

→ Bulk modulus, K = \(\frac{\text { Volumetric stress }}{\text { Volumetric strain }}=-\frac{F / A}{\Delta V / V} K = -\frac{F V}{A \Delta V}\)
The negative sign in the above formula indicates that the volume decreases with the increase in stress. The SI unit is Nm^-2 or pascal (Pa) and CGS unit is dyne cm^-2.
Its dimensional formula is given as [ML^-1T^-2].

→ Shear modulus,
η = \(\frac{\text { Tangential stress }}{\text { Shear strain }}=\frac{F / A}{\theta}=\frac{F}{A \theta}\)
where, [θ = \(\frac{\Delta x}{L}\)]
The SI unit is Nm^-2 and its CGS unit is dyne cm^-2. The dimensional formula is [ML^-1T^-2].

→ Poisson's ratio, σ = \(\frac{\text { Lateral strain }}{\text { Longitudinal strain }}\)
= \(\frac{-\Delta D / D}{\Delta L / L}=-\frac{L \cdot \Delta D}{D \cdot \Delta L}\)
The negative sign in the formula indicates that longitudinal and lateral strains are opposite. It has no units and dimensions.

→ Deforming force:
A force which when applied changes the shape or size of the body is called a deforming force.

→ Elasticity:
It is the property of a body due to which it regains its original shape and size back after removing the deforming force, is called elasticity.

→ Plasticity:
The property of a body in which it does not regain its original shape and size back even after the removal of the deforming force, is called plasticity.

→ Stress:
The restoring force per unit area is defined as stress.

→ Normal stress:
The restoring force per unit area normal to the surface of a body is called as normal stress.

→ Tensile stress:
It is defined as the restoring force per unit area in reference to the increase in length (or elongation) of the body.

→ Compressive stress:
It is defined as the restoring force per unit area in case of decrease in length (or contraction) of the body.

→ Tangential shearing stress:
It is defined as the restoring force per unit area developed due to tangentially applied deforming force.

→ Strain:
Strain is defined as the ratio of the change in any dimension produced in the body to the original dimension.

→ Longitudinal strain:
When deforming force is applied on a body, the ratio of increase in length per unit original length is called the longitudinal strain.

→ Volumetric strain:
When deforming force is applied on a body, the change in volume per unit original volume is defined as volumetric strain.

→ Shear strain:
It is defined as the angle 0 (in radian) through which a face originally perpendicular to the fixed face gets turned on applying tangential deforming force.

→ Ductile materials:
Those materials which show large amount of plastic deformation between the elastic limit and the breaking point are called ductile materials.

→ Brittle materials:
Brittle materials show small amount of plastic deformation between the elastic limit and the breaking point.

→ Elastometers:
Elastometers are those materials for which the strain and stress variation in non linear or not a straight line with the limits of elasticity.

→ Modulus of elasticity:
The ratio of stress to strain is defined as the modulus of elasticity.

→ Compressibility:
Compressibility is defined as the reciprocal of bulk modulus of elasticity.

→ Modulus of rigidity:
The ratio of shearing (tangential) stress to shear strain is defined as modulus of rigidity.

→ Elasticity after effect:
The temporary delay caused in regaining the original size and shape by the body, when the deforming force is removed, is termed as the elastic after effect.

→ Elastic fatigue:
Elastic fatigue is defined as the property of a body due to which it loses the strength of being elastic under the influence of repeated alternating forces.

→ Elastic hysteresis:
It is defined as the lagging of strain behind the stress, when a deforming force is applied.

→ Elastic potential energy:
Potential energy stored as a result of deformation of an elastic object; is defined as the elastic potential energy.