Young’s modulus is the ratio of longitudinal stress to longitudinal strain within the elastic range. It measures resistance to a change in length.
Learning Outcomes
Young’s modulus applies to tensile or compressive length deformation.
Y = FAΔL/L = FL/(AΔL).
Its SI unit is Pa and dimensions are ML⁻¹T⁻².
A larger Y means a stiffer material.
Intermediate Level
Elasticity and Elastic Modulus
Elasticity is the ability of a material to regain its original shape and size after the deforming stress is removed. Within the elastic range, stress divided by strain defines an elastic modulus.
Key equation
elastic modulus=stressstrain
Young's Modulus
Key equation
Y=FAΔ L/L=FLAΔ L
Symbol
Meaning
SI unit
F
axial force
N
A
cross-sectional area
m²
L
original length
m
ΔL
change in length
m
Y
Young’s modulus
Pa
Physical Meaning
For the same stress, a material with larger Y undergoes smaller longitudinal strain. Young’s modulus describes stiffness, not the breaking strength of the material.
Wire Extension
A wire 2.0 m long and area 1.0 × 10⁻⁶ m² is pulled by 100 N. If Y = 2.0 × 10¹¹ Pa, find extension.
1
Given
L = 2.0 m
A = 1.0 × 10⁻⁶ m²
F = 100 N
Y = 2.0 × 10¹¹ Pa
2
Working
ΔL = FL/(AY)
3
Step 2
ΔL = 100 × 2.0(1.0 × 10⁻⁶)(2.0 × 10¹¹)
Final answer:ΔL = 1.0 × 10⁻³ m = 1.0 mm
Textbook Material Values
Material
Y (10¹⁰ Pa)
Steel
20.0
Iron
19.0
Copper
12.0
Brass
10.0
Aluminium
7.0
Common Mistakes
Use the stress and strain of the same deformation type.
Convert all data to SI units.
Modulus has the same unit as stress because strain is dimensionless.
A larger modulus means greater stiffness, not greater strain.
Short-Question Preparation
Q. Define Young’s modulus.
A. The ratio of longitudinal stress to longitudinal strain within the elastic range.
Q. Write its working formula.
A.Y = FL/(AΔL).
Q. What does a large Y mean?
A. The material is stiff and shows small strain for a given stress.
Q. State its SI unit.
A. Pascal, Pa.
Sticky Notes
Young’s modulus applies to tensile or compressive length deformation.
Y = FAΔL/L = FL/(AΔL).
Its SI unit is Pa and dimensions are ML⁻¹T⁻².
A larger Y means a stiffer material.
60-Second Revision
Young’s modulus is the ratio of longitudinal stress to longitudinal strain within the elastic range. It measures resistance to a change in length.
Summary
Young’s modulus is the ratio of longitudinal stress to longitudinal strain within the elastic range. It measures resistance to a change in length.
Ask-the-Tutor Modes
Explain the modulus simply.
Derive its formula.
Solve a numerical problem.
Compare the elastic moduli.
Test me with an MCQ.
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Exam preparation
Exam Focus
Important points
Young’s modulus applies to tensile or compressive length deformation.
Y = FAΔL/L = FL/(AΔL).
Its SI unit is Pa and dimensions are ML⁻¹T⁻².
A larger Y means a stiffer material.
Common mistakes
Match the modulus to the deformation type.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Young's Modulus
Sticky Notes · Quick Revision
1.
Key Point 1
Young’s modulus applies to tensile or compressive length deformation.
