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CodeVID-P11-08-CH-01
Mechanical Properties of Solids — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks. Show all working for Sections B, C and D.
Section A — Multiple Choice Questions
6 × 1 = 6 marks
1.
The SI unit of stress is:
- A.N
- B.N/m
- C.N/m$^2$
- D.no unit
2.
Strain is:
- A.measured in pascal
- B.measured in newton
- C.dimensionless
- D.measured in m$^3$
3.
Young's modulus is the ratio of:
- A.shear stress to shear strain
- B.volume stress to volume strain
- C.longitudinal stress to longitudinal strain
- D.lateral to longitudinal strain
4.
Compressibility is the reciprocal of:
- A.Young's modulus
- B.shear modulus
- C.bulk modulus
- D.Poisson's ratio
5.
The elastic energy stored per unit volume is:
- A.$\text{stress}\times\text{strain}$
- B.$\frac{1}{2}\times\text{stress}\times\text{strain}$
- C.$\frac{\text{stress}}{\text{strain}}$
- D.$\text{stress}+\text{strain}$
6.
Only solids possess a non-zero:
- A.bulk modulus
- B.Young's modulus
- C.shear (rigidity) modulus
- D.density
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
7.
State Hooke's law.
8.
Define Young's modulus and write its formula.
9.
Why does the bulk modulus formula carry a negative sign?
10.
Distinguish between elastic after-effect and elastic fatigue.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
11.
A wire of length 2 m and area $2\times10^{-6}\ \text{m}^2$ extends 1 mm under a 200 N load. Find Young's modulus.
12.
Show that the energy stored per unit volume in a stretched wire is $\frac{1}{2}\times\text{stress}\times\text{strain}$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
13.
Explain the stress–strain curve for a ductile metal up to the breaking point, marking the proportional limit, elastic limit, yield point and fracture point, and state how it distinguishes ductile from brittle materials.
14.
Define the three moduli of elasticity with their formulas, and discuss two applications of elasticity in engineering design.
Answer Key
Section A — Multiple Choice Questions
- (C) N/m$^2$
- (C) dimensionless
- (C) longitudinal stress to longitudinal strain
- (C) bulk modulus
- (B) $\frac{1}{2}\times\text{stress}\times\text{strain}$
- (C) shear (rigidity) modulus
Section B — Short Answer (2 marks)
- Within the elastic limit, stress is directly proportional to strain, so $\frac{\text{stress}}{\text{strain}}=E$ (modulus of elasticity).
- Ratio of longitudinal stress to longitudinal strain: $Y=\frac{FL}{A\,\Delta L}$.
- Because volume decreases as pressure increases; the sign makes $B$ positive.
- After-effect is a delay in full recovery of shape; fatigue is loss of strength under repeated stress cycles.
Section C — Short Answer (3 marks)
- $Y=\frac{FL}{A\Delta L}=\frac{200\times2}{2\times10^{-6}\times1\times10^{-3}}=2\times10^{11}\ \text{N/m}^2$.
- $U=\frac{1}{2}F\Delta L=\frac{1}{2}(\text{stress}\cdot A)(\text{strain}\cdot L)$; dividing by volume $AL$ gives $u=\frac{1}{2}\times\text{stress}\times\text{strain}$.
Section D — Long Answer (5 marks)
- From O the curve is straight (Hooke's law) to the proportional limit; up to the elastic limit recovery is complete. Beyond the yield point the material deforms plastically (permanent set) to the ultimate strength, then breaks at the fracture point. A large yield-to-fracture region marks a ductile material; a small one marks a brittle material.
- Young's $Y=\frac{FL}{A\Delta L}$ (length), bulk $B=-\frac{\Delta P}{\Delta V/V}$ (volume), shear $\eta=\frac{F/A}{\theta}$ (shape). Applications: ropes use many thin twisted strands for flexibility and safety; beams are made deep with an I-section because sag $\delta\propto\frac{1}{d^3}$, giving stiffness with minimum weight, and a factor of safety keeps working stress below the breaking stress.
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