Young's Modulus — Dimensional Formula and SI Unit

Young's Modulus (Y) is a measure of the stiffness of a solid material. It quantifies the relationship between stress (force per unit area) and strain (fractional change in length) in the elastic region.

Y = Stress / Strain

Y = (F/A) / (ΔL/L)

Where:

• F = Applied force (Newton)
• A = Cross-sectional area (m²)
• ΔL = Change in length (m)
• L = Original length (m)

Stress = Force / Area = F/A

• Dimension of Force = [MLT⁻²]
• Dimension of Area = [L²]
• Dimension of Stress = [MLT⁻²] / [L²] = [ML⁻¹T⁻²]

Strain = ΔL/L = length/length

• Strain is a dimensionless quantity = [M⁰L⁰T⁰] = [1]

Therefore: Y = Stress / Strain = [ML⁻¹T⁻²] / [1]

Dimensional Formula of Young's Modulus = [ML⁻¹T⁻²]

SI Unit: Pascal (Pa) = N/m² = kg/(m·s²)

Or equivalently: N/m²

Typical values:

Steel is much stiffer than rubber — its Young's modulus is about 200,000 times greater!

A high Young's modulus means the material is very stiff (resists deformation under stress). A low Young's modulus means the material is flexible/elastic (deforms easily).

Applications:

• Engineering: Choosing materials for bridges, buildings (steel has very high Y)
• Medicine: Bone has Y ≈ 14 GPa; artificial implants must match this