Mechanical Properties of Solids Revision Notes for NEET Physics PDF Download
🔧 MECHANICAL PROPERTIES OF SOLIDS · Elasticity
Stress • Strain • Hooke's Law • Young's Modulus • Bulk Modulus • Shear Modulus • NEET problems
📏 STRESS & STRAIN
Stress = Restoring force per unit area: σ = F/A
Types:
• Tensile/Compressive stress (normal to area)
• Shear stress (tangential to area)
Strain = Fractional deformation (dimensionless)
• Longitudinal strain = ΔL/L
• Volumetric strain = ΔV/V
• Shear strain = Δx/L = tanθ ≈ θ (for small angles)
✏️ Tensile stress on a rod
⚡ HOOKE'S LAW & ELASTIC MODULI
Within elastic limit, stress ∝ strain → Stress = Modulus × Strain
Young's Modulus (Y)
Y = (Longitudinal stress)/(Longitudinal strain) = (F/A) / (ΔL/L) = FL/(AΔL)
For a wire: ΔL = FL/(AY)
Bulk Modulus (B)
B = – (ΔP) / (ΔV/V) = –V ΔP/ΔV
Compressibility = 1/B
Shear Modulus (G or η)
G = (Shear stress)/(Shear strain) = (F/A) / (Δx/L) = FL/(AΔx)
📈 STRESS-STRAIN CURVE
🖍️ Hand-drawn stress-strain graph for a ductile metal
Points on curve:
A: Proportional limit (Hooke's law valid)
B: Elastic limit (up to B, elastic)
C: Yield point (plastic deformation starts)
D: Ultimate tensile strength
E: Fracture point
💾 ELASTIC POTENTIAL ENERGY
Energy stored per unit volume: u = ½ × stress × strain = ½ Y (strain)² = ½ (stress)² / Y
For a stretched wire: U = ½ × (Force) × (extension) = ½ F ΔL = ½ (YA/L) (ΔL)²
📐 POISSON'S RATIO (σ)
σ = – (Lateral strain)/(Longitudinal strain) = – (Δd/d) / (ΔL/L)
Theoretical range: –1 < σ < 0.5. For most metals: σ ≈ 0.3
Relation between Y, B, G: Y = 3B(1 – 2σ), Y = 2G(1 + σ)
💡 NEET TIPS & SHORTCUTS
- For a wire under load, Young's modulus is constant for a material, independent of dimensions.
- Bulk modulus of a gas is isothermal (B = P) or adiabatic (B = γP).
- Shear modulus for liquids is zero (they cannot sustain shear).
- Breaking stress is constant for a material, not breaking force.
⚠️ COMMON MISTAKES
- Confusing stress with pressure (pressure is isotropic, stress is directional).
- Using ΔL = FL/AY without checking elastic limit.
- Forgetting that strain is dimensionless.
- Assuming Poisson's ratio is always 0.5 for all materials.
📌 QUICK REVISION CARD
Young's modulus: Y = FL/(AΔL)
Bulk modulus: B = –V ΔP/ΔV
Shear modulus: G = FL/(AΔx)
Energy density: u = ½ σ ε = ½ Y ε²
Poisson's ratio: σ = –(lateral strain)/(longitudinal strain)
Relation: Y = 3B(1 – 2σ), Y = 2G(1 + σ)