Topic 7.2.25 min read
Young's Modulus
Young’s modulus is the ratio of longitudinal stress to longitudinal strain within the elastic range. It measures resistance to a change in length.
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Beginner Level
Young’s modulus compares how hard a material is pulled or compressed with the fractional change in its length. A stiff material has a large Young’s modulus.
Recommended for Class 11
Young's Modulus
Overview
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.
Young's Modulus
| 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.
- L = 2.0 m
- A = 1.0 × 10⁻⁶ m²
- F = 100 N
- Y = 2.0 × 10¹¹ Pa
ΔL = FL/(AY)
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.
Exam Focus
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 exam traps
- Wrong strain type
- Unit conversion
Long question structure
Definition → deformation → formula → unit → example.
Common Mistakes
Common Mistakes
- Mistake
Match the modulus to the deformation type.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
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.
Young’s modulus is the ratio of longitudinal stress to longitudinal strain within the elastic range. It measures resistance to a change in length.
- Definition
- Young’s modulus is the ratio of longitudinal stress to longitudinal strain within the elastic range. It measures resistance to a change in length.
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Exam Practice
Important Question
Q1. Define Young’s modulus.
Important Question
Q2. Write its working formula.
Important Question
Q3. What does a large Y mean?
Important Question
Q4. State its SI unit.