Class 12 > Unit # 21:Physics of Solids > Modulus of Elasticity, Modulus of Rigidity & Modulus of Comprehensibility

 

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Young’s Modulus, Shear Modulus, and Bulk Modulus

Video Lecture

"Watch the complete lecture on the modulus of elasticity, rigidity, and comprehensibility exploring Young's Modulus, Shear Modulus, and Bulk Modulus."

Watch on YouTube: Modulus of Elasticity, Rigidity & Comprehensibility | Talha's Physics Academy

(i) Young’s Modulus

"It is a mechanical property of solids that measures the stiffness or elasticity of a solid material and it computes how much a material will deform (stretch or compress) under a given force."

It is a measure of a material's resistance to elastic deformation when subjected to an external force. The higher the Young's Modulus, the stiffer the material.

Symbol: Denoted by the symbol $Y$ (or $E$) and typically expressed in Pascals ($\text{Pa}$) or GigaPascals ($\text{GPa}$).

Formula

Mathematically, it is the ratio between tensile/compressive stress and longitudinal strain:

$$Y = \frac{\text{Stress}}{\text{Longitudinal Strain}} = \frac{F / A}{\Delta L / L_0} = \frac{F \cdot L_0}{A \cdot \Delta L}$$

(ii) Shear Modulus

"Shear modulus, also known as the modulus of rigidity, is a mechanical property that describes a material's resistance to shear deformation when a force is applied perpendicular to the material's surface."

Shear modulus measures the rigidity of the body, defined as the ratio of shear stress to shear strain.

Symbol: Denoted by the symbol $G$ or $S$, expressed in Pascals ($\text{Pa}$) or GigaPascals ($\text{GPa}$).

Formula

Mathematically, it is the ratio between shear stress and shear strain:

$$G = \frac{\text{Shear Stress}}{\text{Shear Strain}} = \frac{F / A}{\Delta x / L} = \frac{F \cdot L}{A \cdot \Delta x}$$

(iii) Bulk Modulus

"Bulk modulus, also known as the modulus of compressibility, is a mechanical property that describes the resistance of a material to compression under uniform external pressure."

Bulk modulus is defined as the ratio of the change in pressure applied to a material to the resulting fractional change in volume that occurs in the material.

Symbol: Denoted by the symbol $K$ (or $B$), expressed in Pascals ($\text{Pa}$) or GigaPascals ($\text{GPa}$).

Formula

Mathematically, it is the ratio between the change in pressure and volumetric strain:

$$K = -\frac{\Delta P}{\Delta V / V_0} = -\frac{V_0 \cdot \Delta P}{\Delta V}$$

Note: The negative sign indicates that an increase in pressure leads to a decrease in volume.

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