Young's Modulus Compared
Four wires (steel, copper, Al, brass) under same load — stiff materials stretch less.
Key Notes
Young's modulus Y measures a material's stiffness under TENSILE/COMPRESSIVE stress: Y = stress/strain = (F/A)/(ΔL/L).
Units: Pa (N/m²). Reported in GPa for typical solids.
Y values: steel ≈ 200 GPa, copper ≈ 110 GPa, aluminum ≈ 70 GPa, glass ≈ 70 GPa, rubber ≈ 0.01-0.1 GPa, wood (along grain) ≈ 12 GPa.
Wire of length L, cross-section A: extension ΔL = FL/(YA). Stiffer (higher Y) ⇒ smaller ΔL for given F.
Force constant of a wire viewed as a spring: k = YA/L. Long, thin wires are softer; short, thick ones are stiffer.
Used in structural engineering, materials selection, vibration analysis, and acoustics.
Y is approximately constant for moderate strains; varies slightly with temperature.
For composite or anisotropic materials (wood, carbon fibre), Y depends on direction.
Formulas
Young's modulus definition
Slope of stress vs strain in the elastic region.
Extension under load
Useful in problems with wires and rods.
Spring-equivalent constant
k of a wire seen as a Hookean spring.
Strain energy / volume
Energy stored per unit volume in elastic deformation.
Important Points
Y is a MATERIAL property — does NOT depend on the wire's size or shape.
Extension ΔL DOES depend on geometry: long thin wires extend more than short thick ones under the same load.
Steel (Y ≈ 200 GPa) is about 100,000× stiffer than rubber (Y ≈ 1-10 MPa).
Diamond has the highest Y (~1000 GPa) of any natural material.
Y varies slightly with temperature — usually decreases with rising T.
For ANISOTROPIC materials (wood, crystals), Y depends on direction of measurement.
Young's Modulus Compared notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.