MIND GROW Magazine

Properties of Matter – Stage 1 (Page 3)

Elastic Moduli – Young’s, Bulk & Shear (JEE Core)

1. Elastic Modulus – What Does It Measure?

Elastic modulus measures the resistance of a material to deformation. Higher the modulus → more rigid the material.

General Formula:
Elastic Modulus = Stress / Strain

2. Young’s Modulus (Y)

Young’s modulus relates longitudinal stress and longitudinal strain.

Y = (F / A) ÷ (ΔL / L)

Y = (F L) / (A ΔL)

Unit: Pascal (N/m²)
Dimension: ML⁻¹T⁻²

JEE Insight:
Greater Young’s modulus → material stretches less.

3. Bulk Modulus (K)

Bulk modulus measures resistance to uniform compression.

K = − (ΔP) ÷ (ΔV / V)

Negative sign → volume decreases with pressure
Important for fluids

Special Case:
Liquids have bulk modulus but no Young’s modulus.

4. Shear Modulus (η or G)

Shear modulus measures resistance to shape change.

η = Shearing Stress / Shearing Strain

Solids only
Liquids cannot sustain shear stress

5. Relation Between Elastic Constants

For isotropic materials:

Y = 9Kη / (3K + η)

JEE Note:
Knowing any two elastic constants → third can be calculated.

6. Poisson’s Ratio (ν)

Ratio of lateral strain to longitudinal strain.

ν = (Lateral Strain) / (Longitudinal Strain)

No unit
0 ≤ ν ≤ 0.5 (stable materials)

Extreme Case:
ν = 0.5 → perfectly incompressible material.

7. Typical Values (Approximate)

Material	Young’s Modulus (GPa)
Steel	200
Copper	110
Rubber	0.01

Stage 1 – Page 3 Summary

Three elastic moduli and their meaning
Units & physical interpretation
Relation between elastic constants
Poisson’s ratio limits

Stage 1 – Page 3 Completed ✅
Next: Elastic Energy, Stress in Wires & Applications – Page 4

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