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.
Key equation
A=π(d2)2=π d24
Key equation
Y=FAΔ L/L=FLAΔ L
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.
1
Given
L = 2.0 m
d = 1.0 × 10⁻³ m
ΔL = 1.27 × 10⁻³ m
F = 50 N
2
Working
A = πd²/4 = 7.85 × 10⁻⁷ m²
3
Step 2
Y = FL/(AΔL)
4
Step 3
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).
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Exam preparation
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 mistakes
Use the elastic-limit conditions.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Young's Modulus of a Metallic Wire: Experiment
Sticky Notes · Quick Revision
1.
Key Point 1
Measure original length L accurately.
2.
Key Point 2
Find diameter at several positions and calculate A = πd²/4.
3.
Key Point 3
Use a reference wire to remove support and temperature effects.
4.
Key Point 4
Measure extension ΔL for known force F.
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Exam Practice
Important Question
Q1. Describe the experiment to find Young’s modulus.
