MIND GROW Magazine

Properties of Matter – Stage 1 (Page 6)

Poisson’s Ratio, Bulk Modulus & Volume Elasticity (IIT-JEE Level)

1. Poisson’s Ratio (ν)

When a material is stretched longitudinally, it contracts laterally. The ratio of lateral strain to longitudinal strain is called Poisson’s ratio.

ν = (Lateral Strain) / (Longitudinal Strain)

Dimensionless quantity
Depends on nature of material

Sign Convention:
Lateral strain is negative, longitudinal strain is positive, so Poisson’s ratio is taken as positive.

2. Range of Poisson’s Ratio

Material	Poisson’s Ratio (ν)
Perfectly rigid	0
Steel	≈ 0.3
Rubber	≈ 0.5
Cork	≈ 0

IIT Fact:
Maximum possible value of Poisson’s ratio = 0.5

3. Bulk Modulus (K)

Bulk modulus measures resistance offered by a body to uniform compression.

K = (Increase in Pressure) / (Volumetric Strain)

K = − ΔP / (ΔV / V)

Unit: Pascal (Pa)
Applies to solids, liquids & gases

4. Compressibility

Compressibility is reciprocal of bulk modulus.

Compressibility (β) = 1 / K

Liquids → very low compressibility
Gases → high compressibility

5. Volume Elasticity

Volume elasticity refers to change in volume of a body under uniform pressure.

Related only to bulk modulus
No shape change involved

Key Idea:
Bulk modulus deals with volume change, Young’s modulus deals with length change.

6. Relation between Elastic Constants

For isotropic and homogeneous materials:

Y = 3K (1 − 2ν)

Y = 2η (1 + ν)

K = Y / [3 (1 − 2ν)]

IIT-JEE Favourite:
At ν = 0.5 → Bulk modulus → ∞ (incompressible material)

Stage 1 – Page 6 Summary

Poisson’s ratio definition & range
Bulk modulus & compressibility
Volume elasticity
Relations among Y, K, ν

Stage 1 – Page 6 Completed ✅
Next: Elastic Energy, Resilience & Numerical Concepts – Page 7

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