Vidaara.orgClass 11 · Physics
CodeVID-P11-08-MOE-01
Moduli of Elasticity — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- 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. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The SI unit of Young's modulus is:
- A.N
- B.N/m$^2$
- C.no unit
- D.m$^2$/N
2.
Compressibility is the reciprocal of:
- A.Young's modulus
- B.shear modulus
- C.bulk modulus
- D.Poisson's ratio
3.
Which modulus measures resistance to change in shape?
- A.Young's modulus
- B.bulk modulus
- C.shear modulus
- D.compressibility
4.
Poisson's ratio has the unit:
- A.N/m$^2$
- B.m$^2$/N
- C.no unit
- D.N
5.
For the same load, a longer wire of the same material and area stretches:
- A.less
- B.more
- C.by the same amount
- D.not at all
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
Define Young's modulus and write its formula.
7.
Why is there a negative sign in the formula for bulk modulus?
8.
Define Poisson's ratio.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
A wire of length 3 m and area $2\times10^{-6}\ \text{m}^2$ extends 1.5 mm under a 200 N load. Find Young's modulus.
10.
Distinguish between bulk modulus and shear modulus, stating which one fluids lack.
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
Define the three moduli of elasticity (Young's, bulk and shear) with their formulas and SI units, and explain Poisson's ratio with its typical range for metals.
Answer Key
Section A — Multiple Choice Questions
- (B) N/m$^2$
- (C) bulk modulus
- (C) shear modulus
- (C) no unit
- (B) more
Section B — Short Answer (2 marks)
- Ratio of longitudinal stress to longitudinal strain: $Y=\frac{FL}{A\,\Delta L}$.
- Because volume decreases as pressure increases ($\Delta V$ is negative); the sign makes $B$ a positive quantity.
- The ratio of lateral strain to longitudinal strain (taken positive): $\sigma=-\frac{\Delta d/d}{\Delta L/L}$; it is dimensionless.
Section C — Short Answer (3 marks)
- $Y=\frac{FL}{A\Delta L}=\frac{200\times3}{2\times10^{-6}\times1.5\times10^{-3}}=2\times10^{11}\ \text{N/m}^2$.
- Bulk modulus resists volume change under uniform pressure (all states have it); shear modulus resists shape change under tangential stress and is possessed only by solids — fluids at rest have zero rigidity.
Section D — Long Answer (5 marks)
- Young's: $Y=\frac{FL}{A\Delta L}$ (resists length change); bulk: $B=-\frac{\Delta P}{\Delta V/V}$ (resists volume change); shear: $\eta=\frac{F/A}{\theta}$ (resists shape change) — all in $\text{N/m}^2$. Poisson's ratio $\sigma=-\frac{\text{lateral strain}}{\text{longitudinal strain}}$ is dimensionless and lies between about $0.2$ and $0.4$ for most metals.
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