AQA A-Level Physics Paper 1, June 2022: Question 28
1 mark · Medium difficulty · Multiple Choice
Determine the correct statement relating the stress, strain, and extension of two wires made of the same material with different lengths and subject to different tensile forces.
Practise this questionQuestion
Question text
28 Two wires P and Q are made of the same material and have the same cross-sectional
area.
P has an original length L and is subject to a tensile force F. P extends a distance x.
Q has an original length 2L and is subject to a tensile force 2F.
Which statement is correct?
[1 mark]
A The stress in P and the stress in Q are the same.
B The extension of Q is 2x.
C The strain of Q is double the strain of P.
stress
D The value of for P is half that of Q.
strain
Mark scheme
Show the mark scheme
28 C (AO3) The strain of Q is double the strain of P.
How to answer it
Comparing Tensile Properties of Wires P and Q
What this question tests
This question assesses your understanding of bulk material properties under tensile forces, specifically the definitions and proportional relationships of tensile stress, tensile strain, and Young modulus. It requires applying algebraic ratios to compare two distinct physical systems (wires P and Q) made of the same material.
Question 28 Analysis
Evaluating Options via Step-by-Step Proportional Reasoning
✅ Correct Answer: C
Statement C: The strain of Q is double the strain of P.
This is the correct choice because strain is defined as extension divided by original length ( strain = ΔL / L ). Analysing wire Q shows its extension is 4x and its original length is 2L , yielding a strain of 2x / L , which is double the strain of P ( x / L ).
💡 Key Knowledge
- Tensile Stress ( σ ): Force divided by cross-sectional area ( σ = F / A ).
- Tensile Strain ( ε ): Extension divided by original length ( ε = ΔL / L ).
- Young Modulus ( E ): The ratio of tensile stress to tensile strain ( E = σ / ε ), which remains constant for a given material.
🧠 Exam Technique
For ratio-based multiple choice questions, write out the defining formula for each variable in terms of the given parameters ( F , L , A ) before evaluating the options. Do not rely on intuition alone; work through each distractor methodically.
❌ Common Errors
- Confusing Stress and Force: Assuming stress is identical because wire Q has twice the force ( 2F ), forgetting to account for the fact that its length and resulting extension also change.
- Ignoring Original Length: Assuming extension is simply doubled because the force is doubled, overlooking Hooke's Law adjustments for different starting lengths.
📐 Step-by-Step Derivation for Wire Q
- Identify Material Consistency: Both wires have the same cross-sectional area ( A ) and are made of the same material, meaning they share the same Young modulus ( E ).
- Find Stress for P and Q:
• Stress in P: σ_P = F / A
• Stress in Q: σ_Q = 2F / A = 2σ_P (Stress in Q is actually double, ruling out Option A). - Determine Extension ( ΔL ) using Young Modulus:
• Rearranging E = (F / A) / (ΔL / L) gives ΔL = FL / (AE) .
• For wire P: x = FL / (AE) .
• For wire Q (using 2F and 2L ): ΔL_Q = (2F)(2L) / (AE) = 4FL / (AE) = 4x (Ruling out Option B). - Calculate Strain ( ε ) for Both Wires:
• Strain of P ( ε_P ) = x / L .
• Strain of Q ( ε_Q ) = ΔL_Q / original length = 4x / 2L = 2x / L .
• Comparing them: ε_Q = 2 × ε_P . Thus, strain of Q is double the strain of P, confirming Option C. - Check Option D: Since Young modulus ( stress / strain ) is a constant property of the material, it is identical for both wires P and Q, making Option D false.
Topics
Physics · 3.4 Mechanics and materials
Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.