Topic 7.3.16 min read
Young's Modulus of a Metallic Wire: Experiment
Young’s modulus of a metallic wire is determined by measuring its original length and cross-sectional area, applying known loads, measuring the small extension with a vernier arrangement, and using Y = FL/(AΔL).
Choose Your Level
Beginner Level
A wire stretches slightly when weights are added. Measuring that tiny extension, together with force, length and area, reveals how stiff its material is.
Recommended for Class 11
Young's Modulus of a Metallic Wire: Experiment
Overview
Young’s modulus of a metallic wire is determined by measuring its original length and cross-sectional area, applying known loads, measuring the small extension with a vernier arrangement, and using Y = FL/(AΔL).
Learning Outcomes
- Measure original length L accurately.
- Find diameter at several positions and calculate A = πd²/4.
- Use a reference wire to remove support and temperature effects.
- Measure extension ΔL for known force F.
- Calculate Y = FL/(AΔL) within the elastic range.
Intermediate Level
Apparatus
- Test metallic wire and identical reference wire.
- Rigid support.
- Variable load hanger and known weights.
- Vernier scale for small extension.
- Micrometer screw gauge for diameter.
- Metre scale for original length.
Experimental Arrangement
The test wire carries the variable load. The reference wire provides a stable zero reference for the vernier scale so common changes, such as support movement or temperature expansion, are reduced.
Procedure
- Measure the effective length L of the test wire.
- Measure diameter d at several positions and in perpendicular directions; use the mean.
- Calculate cross-sectional area.
- Set the vernier scale to zero using the reference wire.
- Add loads gradually and record extension after the wire settles.
- Remain below the elastic limit and repeat readings while unloading.
- Use the force and extension data to calculate Y or find a best-fit relation.
Worked Example
Calculating Young’s Modulus
A 2.0 m wire of diameter 1.0 mm extends 1.27 mm under 50 N. Find Y.
- L = 2.0 m
- d = 1.0 × 10⁻³ m
- ΔL = 1.27 × 10⁻³ m
- F = 50 N
A = πd²/4 = 7.85 × 10⁻⁷ m²
Y = FL/(AΔL)
Y = 50 × 2.0(7.85 × 10⁻⁷)(1.27 × 10⁻³)
Final answer: Y ≈ 1.00 × 10¹¹ Pa
Precautions
- Keep the wire straight and free from kinks.
- Avoid parallax when reading scales.
- Add and remove loads gently.
- Do not exceed the elastic limit.
- Use the mean diameter because area depends on d².
- Allow oscillations to stop before reading.
Common Mistakes
- Keep force, length, area and extension in SI units.
- Use the original wire length in the modulus formula.
- Work and stored energy are equal only for deformation within the elastic limit when energy is recoverable.
Short-Question Preparation
Q. Describe the experiment to find Young’s modulus.
A. Measure L and d, calculate A, apply known F, measure ΔL with the reference/vernier arrangement, then use Y = FL/(AΔL).
Q. Why is a reference wire used?
A. It provides a stable comparison and reduces errors due to support movement or temperature.
Q. Why measure diameter several times?
A. Small diameter errors become larger area errors because A depends on d².
Q. State two precautions.
A. Do not exceed the elastic limit and take readings without parallax after oscillations stop.
Sticky Notes
- Measure original length L accurately.
- Find diameter at several positions and calculate A = πd²/4.
- Use a reference wire to remove support and temperature effects.
- Measure extension ΔL for known force F.
- Calculate Y = FL/(AΔL) within the elastic range.
60-Second Revision
Young’s modulus of a metallic wire is determined by measuring its original length and cross-sectional area, applying known loads, measuring the small extension with a vernier arrangement, and using Y = FL/(AΔL).
Summary
Young’s modulus of a metallic wire is determined by measuring its original length and cross-sectional area, applying known loads, measuring the small extension with a vernier arrangement, and using Y = FL/(AΔL).
Ask-the-Tutor Modes
- Explain the setup simply.
- Derive the formula.
- Solve the textbook-style numerical.
- Explain the graph.
- Test me with an MCQ.
Exam Focus
Exam Focus
Important points
- Measure original length L accurately.
- Find diameter at several positions and calculate A = πd²/4.
- Use a reference wire to remove support and temperature effects.
- Measure extension ΔL for known force F.
- Calculate Y = FL/(AΔL) within the elastic range.
Common exam traps
- Wrong axes or units
Long question structure
Setup → measurements → observation → formula → calculation → precautions.
Common Mistakes
Common Mistakes
- Mistake
Use the elastic-limit conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Measure original length L accurately.
Find diameter at several positions and calculate A = πd²/4.
Use a reference wire to remove support and temperature effects.
Measure extension ΔL for known force F.
Young’s modulus of a metallic wire is determined by measuring its original length and cross-sectional area, applying known loads, measuring the small extension with a vernier arrangement, and using Y = FL/(AΔL).
- Definition
- Young’s modulus of a metallic wire is determined by measuring its original length and cross-sectional area, applying known loads, measuring the small extension with a vernier arrangement, and using Y = FL/(AΔL).
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Exam Practice
Important Question
Q1. Describe the experiment to find Young’s modulus.
Important Question
Q2. Why is a reference wire used?
Important Question
Q3. Why measure diameter several times?
Important Question
Q4. State two precautions.