Mechanical Properties of Solids | Class 11 Physics Notes

8.5 Elastic moduli

This section introduces three fundamental elastic moduli that characterize the elastic response of materials: Young's modulus (Y), shear modulus (G), and bulk modulus (B). These moduli quantify the stiffness of materials under different types of stress. Young's modulus relates tensile or compressive stress to longitudinal strain and is given by Y = stress / strain = (F/A) / (ΔL/L) = (F × L) / (A × ΔL). It has units of Pascal (Pa). Table 8.1 lists typical values of Young's modulus and yield strengths for various materials, showing metals have large values indicating high stiffness. Shear modulus G relates shearing stress to shearing strain: G = (F/A) / (Δx/L) = (F × L) / (A × Δx) or G = F / (A × θ), where θ is angular displacement. Shear modulus is generally smaller than Young's modulus. Table 8.2 gives values of G for common materials. Bulk modulus B relates hydraulic stress (pressure) to volume strain: B = -p / (ΔV/V), with negative sign indicating volume decreases with increasing pressure. Table 8.3 shows bulk moduli for solids, liquids, and gases; solids are least compressible, gases most compressible. The reciprocal of bulk modulus is compressibility. The section also introduces Poisson's ratio, the ratio of lateral strain to longitudinal strain in a stretched wire, typically 0.28–0.33 for metals. Finally, the section derives the elastic potential energy stored in a stretched wire as U = (1/2) × stress × strain × volume, representing work done against interatomic forces during deformation.

📊 Diagram: Table on page 4 (10×5); Table on page 6 (11×2); Table on page 7 (16×2)

🔗 Connection: Leads to the next section on practical applications of elastic behavior in engineering and everyday life.

Table on page 4 (10×5)

Table on page 6 (11×2)

Table on page 7 (16×2)

Table on page 7 (5×8)