Mechanical Properties Of Solids Class 11 Notes Physics Chapter 9 - CBSE

• Elasticity is the property of a solid by virtue of which it regains its original shape or size after the externally applied deforming force has been removed.
• Restoring force per unit area is called stress.
• Magnitude of the stress =

$$\frac{\text{F}}{\text{A}}$$

• The SI unit of stress in Nm^–2.
• When a deforming force acts normally over a surface of a body, then the internal restoring force set up per unit area of the body is called normal stress.
• Strain is the deformation per unit of the relevant dimensions of the substance.
• Hooke's law states that, within proportionality limit, stress ∝  strains or stress = k × strains

The proportionality constant k is called the modulus of elasticity. It is denoted as:

1. Young's modulus (Y) in case of longitudinal stress.
2. Shear Modulus or Modulus of Rigidity (n) in case of tangential stress.
3. Bulk Modulus (K) in case of volumetric stress.

• The limiting deforming force below which a body retains its property of elasticity and above which it loses its property of elasticity is called the limit of elasticity.
• The point on the stress-strain curve beyond the elastic limit where after the material continues to deform without an increases in load in known as the field point.
• The stress at yield point Y is called yield strength/stress.
• If there is large plastic deformation in between yield point and breaking point, the metal is said to be ductile.
• If the wire breaks into piece on reaching beyond elastic limit, it is called brittle.
• Tension and compression (Young's modulus) $$\text{Y} = \frac{\frac{\text{F}}{\text{A}}}{\frac{\Delta l}{l_{0}}}.\\\text{The unit of Y is Nm}^{\normalsize-2}.$$
• Work done is stretching a wire,

$$\text{W} =\frac{1}{2}×\text{F}×\Delta l$$

• Energy stored per unit volume of the specimen

$$=\frac{1}{2}×\text{stress × strain}$$

• Bulk modulus

$$\text{k} =\frac{\text{stress}}{\text{strain}}=\frac{\Delta p}{(-\Delta \text{V}/\text{V})}$$

• Modulus of Rigidity (η),

$$η =\frac{\text{F/A}}{\Delta \space \text{l/l}}$$

• Compressibility is reciprocal of bulk modulus,

$$\text{C} =\frac{1}{k}$$

• Poisson's ratio is defined as,

$$\sigma =\frac{\text{Lateral strain}}{\text{Longitudinal strain}}\\=\bigg(-\frac{\Delta \text{r/r}}{\Delta\space l/l_{0}}\bigg)$$

• Factor affecting elasticity of a material

(i) Hammering and rolling

(ii) Annealing

(iii) Effect of the presence of impurities

(iv) Effect of temperature

• Application of Elastic Behaviour of Materials

(i) In designing a building, the structural design of columns, beams and supports

(ii) Use of wire-ropes in cranes

(iii) Design of bridges