QUESTION PAPER 1

Chapter 8: Mechanical Properties of Solids

Original chapter-specific practice paper

Maximum Marks: 40Suggested time: 60 minutes

Instructions: Answer all 20 questions. Marks are shown in brackets. Show calculation steps and units. These are original practice questions, not an official examination paper.

Section A · 1-mark questions — 8 × 1 = 8 marks

Define stress.[1]
SI unit of Young's modulus?[1]
Longitudinal strain?[1]
Hooke's law?[1]
Modulus for volume change?[1]
Is strain dimensionless?[1]
Meaning of large Young's modulus?[1]
Longitudinal stress?[1]

Section B · 2-mark questions — 6 × 2 = 12 marks

100 N on 2×10⁻⁴ m²: stress?[2]
2 m wire extends 1 mm: strain?[2]
Stress=2×10⁷ Pa, strain=10⁻⁴: Y?[2]
10 cm cube compresses by .1 cm: strain magnitude?[2]
L=1 m,A=2×10⁻⁶ m²,Y=2×10¹¹,F=40 N: extension?[2]
Why use steel reinforcement in concrete?[2]

Section C · 3-mark questions — 4 × 3 = 12 marks

Wire L=2m,A=10⁻⁶,Y=2×10¹¹,F=100N: extension?[3]
Stress 4×10⁷ Pa at strain 2×10⁻⁴. Estimate modulus.[3]
B=1.5×10⁹ Pa, volume strain=−2×10⁻⁴. Pressure increase?[3]
Why does doubling wire length double its extension if F,A,Y fixed?[3]

Section D · 4-mark questions — 2 × 4 = 8 marks

Distinguish proportional and elastic limits.[4]
Derive extension and calculate for F=50 N,L=1.5m,A=10⁻⁶,Y=2×10¹¹.[4]

End of paper — review signs, units and working.

Open marking scheme and model answers

Attempt the paper before opening the key. Model answers show the expected facts and results; mark allocation is a suggested guide and equivalent correct methods should receive credit.

Q1 · 1 mark
Restoring force per unit area.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q2 · 1 mark
Pa.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q3 · 1 mark
ΔL/L.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q4 · 1 mark
Within proportional limit, stress is proportional to strain.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q5 · 1 mark
Bulk modulus.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q6 · 1 mark
Yes.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q7 · 1 mark
Material is relatively stiff.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q8 · 1 mark
F/A.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q9 · 2 marks
5×10⁵ Pa.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q10 · 2 marks
5×10⁻⁴.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q11 · 2 marks
2×10¹¹ Pa.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q12 · 2 marks
0.01.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q13 · 2 marks
1×10⁻⁴ m.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q14 · 2 marks
Steel carries tensile stress effectively; concrete is strong in compression.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q15 · 3 marks
0.001 m.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.

Q16 · 3 marks
2×10¹¹ Pa.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.

Q17 · 3 marks
3×10⁵ Pa.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.

Q18 · 3 marks
ΔL∝L.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.

Q19 · 4 marks
Proportional limit ends linearity; elastic limit is the greatest stress for full recovery after unloading.
Suggested split: 1 for principle, 1 for equation, 1 for working and 1 for result/explanation. Accept an equivalent correct method.

Q20 · 4 marks
ΔL=FL/(AY)=3.75×10⁻⁴ m.
Suggested split: 1 for principle, 1 for equation, 1 for working and 1 for result/explanation. Accept an equivalent correct method.