Types of Modulus of Elasticity:
Modulus of elasticity is of three types
- Young’s Modulus of Elasticity
- Bulk Modulus of Elasticity
- Modulus of Rigidity
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Types of Modulus of Elasticity in Physics | Definition, Formulas, Units – Elasticity
1. Young’s Modulus of Elasticity Definition:
Young’s Modulus of Elasticity is defined as the ratio of normal stress to the longitudinal strain within the elastic limit.
Young’s Modulus of Elasticity Formula:
Y = \(\frac{\text { Normal stress }}{\text { Longitudinal strain }}\)
Y = \(\frac{F \Delta l}{A l}=\frac{M g \Delta l}{\pi r^{2} l}\)
Young’s Modulus of Elasticity unit:
Young’s Modulus of Elasticity SI unit is N/m² or pascal
Young’s Modulus of Elasticity Dimensional Formula:
Its dimensional formula is [ML-1T-2].
Force Constant of Wire
Force required to produce unit elongation in a wire is called force constant of a material of wire. It is denoted by k
K = \(\frac{Y A}{l}\)
where, Y = Young’s modulus of elasticity
and A = cross-section area of wire.
2. Bulk Modulus of Elasticity Definition:
It is defined as the ratio of volumetric stress to the volumetric strain within the elastic limit.
Bulk Modulus of Elasticity Formula:
K = \(\frac{\text { Volumetric stress }}{\text { Volumetric strain }}\)
K = \(-\frac{F V}{A \Delta V}=-\frac{\Delta p V}{\Delta V}\)
where, Δp = F / A = Change in pressure.
Negative sign implies that when the pressure increases volume decreases and vice-versa.
Bulk Modulus of Elasticity unit:
Bulk Modulus of Elasticity SI unit is N/m² or pascal
Bulk Modulus of Elasticity Dimensional Formula:
The dimensional formula is [ML-1T-2].
Compressibility
Compressibility of a material is the reciprocal of its bulk modulus of elasticity.
Compressibility Formula:
Compressibility (C) = \(\frac{1}{K}\)
Compressibility unit:
Its SI unit is N-1m² and CGS unit is dyne-1 cm².
3. Modulus of Rigidity Definition: (η) (Shear Modulus)
It is defined as the ratio of tangential stress to the shearing strain, within the elastic limit. Modulus of Rigidity is also known as Shear Modulus.
Rigidity Modulus Formula:
η = \(\frac{\text { Tangential stress }}{\text { Shearing strain }}\)
η = \(\frac{F}{A \theta}\)
Modulus of Rigidity unit:
SI unit is N/m² or pascal
Modulus of Rigidity Dimensional Formula:
Its Dimensional formula is [ML-1T-2].
Factors Affecting Elasticity Physics
Factors Affecting Elasticity of a Material:
- Modulus of elasticity of materials decreases with the rise in temperature, except for invar.
- By annealing elasticity of material decreases.
- By hammering or rolling elasticity of material increases.
- Addition of impurities affects elastic properties depending on whether impurities are themselves more or less elastic.
Note:
- For liquids, modulus of rigidity is zero.
- Young’s modulus (V) and modulus of rigidity (rj) are possessed by solid materials only.
Elasticity:
Elasticity defines a property of an object that has the ability to regain its original shape after being stretched or compressed. Learn about the deforming force applied on an elastic object and how the stress and strain works on an object. What is a Hooke’s law and how it is applicable for the concept of elasticity.
| Deforming Force | Elasticity |
| Stress | Strain |
| Hooke’s Law | Elastic Modulus |
| Types of Modulus of Elasticity | Poisson’s Ratio |
| Stress and Strain Curve | Thermal Stress |
| Cantilever Beam | Torsion of a Cylinder |