NCERT Solutions for Class 11 Physics Chapter 9 – Mechanical Properties of Solids
Chapter 9 of Class 11 Physics, Mechanical Properties of Solids, introduces students to the behaviour of solid materials under applied forces. This chapter is essential for understanding how engineering structures, machines, and everyday objects respond to stress. Students learn the fundamental concepts of stress (force per unit area) and strain (fractional change in dimension), and explore the relationship between them through Hooke's Law. The chapter introduces three moduli of elasticity — Young's Modulus for longitudinal stress-strain, Bulk Modulus for volumetric changes, and Shear (Rigidity) Modulus for shape changes — each applicable in different engineering contexts.
The stress-strain curve is a critical concept that reveals the elastic limit, yield point, ultimate tensile strength, and fracture point of a material. Students also study elastic fatigue, elastic potential energy stored in stretched wires, and why materials like rubber behave differently from metals. Applications to real-life problems such as designing bridges, selecting cables for elevators, and determining the bending of beams are integral to this chapter. The NCERT solutions for Chapter 9 provide clear, step-by-step explanations of all textbook problems, helping Class 11 students build confidence for board exams and competitive entrance tests like JEE Main and NEET.
NCERT Solutions PDF – Class 11 Physics Chapter 9 (All Exercises)
The PDF includes complete solutions to all exercises in Chapter 9, covering problems on stress, strain, moduli of elasticity, and applications. Prepared as per the latest CBSE guidelines.
| Resource Name | Description | Best For |
|---|---|---|
| NCERT Solutions | Detailed answers and explanations for NCERT textbook questions across all classes and subjects. | Homework, assignments, and exam preparation |
| NCERT Solutions for Class 11 | Chapter-wise solutions for all Class 11 subjects including Physics, Chemistry, Mathematics, Biology, and English. | Class 11 board exam preparation |
| NCERT Solutions for Class 11 Physics | Step-by-step solutions covering all chapters such as Motion, Laws of Motion, Work Energy and Power, Thermodynamics, and Waves. | Concept building and numerical problem-solving |
| NCERT Exemplar Class 11 Physics | Advanced and application-based questions designed to strengthen conceptual understanding and analytical skills. | JEE, NEET, Olympiads, and higher-order practice |
| Physics Formula | Chapter-wise collection of important formulas, equations, and derivations for quick revision. | Last-minute revision and numerical practice |
Important Formulas – Chapter 9: Mechanical Properties of Solids
| Formula | Expression | Description |
|---|---|---|
| Stress | σ = F / A | Force per unit cross-sectional area; unit: Pa (N/m²) |
| Longitudinal Strain | ε = ΔL / L | Change in length per unit original length (dimensionless) |
| Volumetric Strain | ε_v = ΔV / V | Change in volume per unit original volume |
| Shear Strain | θ = Δx / L | Tangential displacement per unit height |
| Hooke's Law | σ = E · ε | Valid within elastic limit; stress ∝ strain |
| Young's Modulus (Y) | Y = (F/A) / (ΔL/L) | Ratio of longitudinal stress to strain; unit: Pa |
| Bulk Modulus (B) | B = −P / (ΔV/V) | Negative sign for compression; K = 1/B = compressibility |
| Shear Modulus (G) | G = (F/A) / θ | Ratio of shear stress to shear strain; also called Rigidity Modulus |
| Elastic Potential Energy | U = ½ · F · ΔL = ½ · stress × strain × volume | Energy stored in a deformed wire |
| Poisson's Ratio (σ) | σ = −(lateral strain) / (longitudinal strain) | Dimensionless; typically 0.2–0.5 for metals |
| Elongation of wire | ΔL = FL / (AY) | Derived from Young's Modulus definition |
Subtopics Explained – Chapter 9: Mechanical Properties of Solids
Elastic Behaviour and Stress-Strain Relationship
Solids resist deformation due to interatomic bonding forces. When stressed within the elastic limit, solids return to their original shape — this is elasticity. Beyond the elastic limit comes the plastic region, where permanent deformation occurs. The stress-strain graph for metals shows: (1) proportional limit, (2) elastic limit, (3) yield point, (4) ultimate strength, and (5) fracture point. Understanding this graph is critical for exam success.
Hooke's Law
Within the proportional limit, stress is directly proportional to strain. This forms the basis of all elastic moduli. Hooke's Law breaks down at larger strains, and the material either yields or fractures. Springs, wires, and rubber bands are common examples used in NCERT numericals.
Young's Modulus
Young's Modulus (Y) quantifies a material's resistance to elongation under tensile or compressive stress. Metals like steel have high Y (~2 × 10¹¹ Pa), making them ideal for structural use. Rubber has much lower Y, allowing large deformations. Typical NCERT problems involve finding the elongation of wires under known loads.
Bulk Modulus and Compressibility
Bulk modulus measures resistance to uniform compression (change in volume). It applies to all states of matter. Liquids and solids have very high B values (hard to compress). The reciprocal of bulk modulus is compressibility. This concept is important for understanding behaviour of materials under high pressure.
Shear Modulus (Rigidity Modulus)
Shear modulus describes a solid's resistance to shape change (without volume change). It is relevant in problems involving twisting, cutting, and shearing forces. Fluids have zero shear modulus — they cannot resist shear stress at all.
Elastic Potential Energy in Stretched Wires
When a wire is stretched, work done is stored as elastic PE: U = ½ × stress × strain × volume. This is analogous to the energy stored in a spring (½kx²). This energy is recovered when the load is removed (within elastic limit).
Quick Reference Table – Elastic Moduli of Common Materials
| Material | Young's Modulus Y (GPa) | Bulk Modulus B (GPa) | Shear Modulus G (GPa) |
|---|---|---|---|
| Steel | 200 | 160 | 84 |
| Aluminium | 70 | 75 | 26 |
| Copper | 120 | 140 | 45 |
| Rubber | 0.01–0.1 | 1–2 | ~0.0006 |
| Glass | 65–70 | 40–55 | 26–32 |
| Bone (cortical) | 15–25 | — | 3–5 |
| Wood (along grain) | 1–15 | — | 0.6–1.3 |