CBSE Class 11 — Notes, Chapters & Practice Quizzes

Chapter 1: Mechanical Properties of Solids

Summary

Real solids are not perfectly rigid: a deforming force changes their shape or size, and elasticity is the property by which a body regains its original form when the force is removed, while plasticity is the opposite tendency to retain the deformed shape. Stress is the internal restoring force per unit area (SI unit pascal), and strain is the fractional change in dimension; there are three kinds — tensile or compressive (longitudinal), shearing, and hydraulic (volume). Hooke's law states that within the elastic limit stress is proportional to strain, the constant being a modulus of elasticity. The stress-strain curve shows a proportional region up to the yield point, then plastic deformation up to the ultimate tensile strength and fracture; materials are brittle or ductile, and elastomers like rubber do not obey Hooke's law. Young's modulus \(Y=\) stress/longitudinal strain, shear modulus \(G\) (modulus of rigidity), and bulk modulus \(B=-p/(\Delta V/V)\) describe the three deformations; compressibility is the reciprocal of \(B\). Poisson's ratio is the lateral to longitudinal strain. Elastic potential energy per unit volume of a stretched wire is \(\tfrac12\times\text{stress}\times\text{strain}\). These ideas guide the design of beams, columns, bridges and cranes, and explain the limit on mountain height.

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