Vidaara.orgClass 11 · Physics
CodeVID-P11-08-EBA-01
Elastic Behaviour & Applications — 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 work done in stretching a wire is stored as:
- A.heat only
- B.elastic potential energy
- C.kinetic energy
- D.sound
2.
Elastic energy per unit volume equals:
- A.$\text{stress}\times\text{strain}$
- B.$\frac{1}{2}\times\text{stress}\times\text{strain}$
- C.$\frac{\text{stress}}{\text{strain}}$
- D.$\text{stress}+\text{strain}$
3.
The weakening of a material under repeated stress is:
- A.elastic after-effect
- B.elastic fatigue
- C.creep
- D.ductility
4.
Beams are made deep rather than wide because the sag varies as:
- A.$\frac{1}{d}$
- B.$\frac{1}{d^2}$
- C.$\frac{1}{d^3}$
- D.$d^3$
5.
Cranes use ropes of many thin strands mainly for:
- A.lower cost only
- B.greater flexibility and safety
- C.higher Young's modulus
- D.lower breaking stress
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
Write the expression for elastic potential energy stored in a stretched wire.
7.
Distinguish between elastic after-effect and elastic fatigue.
8.
A wire stretches by 1 mm under a 60 N force. Find the energy stored.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
Show that the energy stored per unit volume in a stretched wire is $\frac{1}{2}\times\text{stress}\times\text{strain}$.
10.
Explain why a deep beam with an I-section is preferred for bridges over a shallow rectangular one.
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
Discuss the applications of elasticity in engineering design, covering the choice of ropes for cranes, the shape of beams and girders, and the role of the factor of safety.
Answer Key
Section A — Multiple Choice Questions
- (B) elastic potential energy
- (B) $\frac{1}{2}\times\text{stress}\times\text{strain}$
- (B) elastic fatigue
- (C) $\frac{1}{d^3}$
- (B) greater flexibility and safety
Section B — Short Answer (2 marks)
- $U=\frac{1}{2}\times F\times\Delta L=\frac{1}{2}\times\text{stress}\times\text{strain}\times\text{volume}$.
- After-effect: a time delay before a body fully recovers its shape. Fatigue: loss of strength after repeated stress cycles.
- $U=\frac{1}{2}\times60\times1\times10^{-3}=0.03\ \text{J}$.
Section C — Short Answer (3 marks)
- Work $=\frac{1}{2}F\Delta L=\frac{1}{2}(\text{stress}\times A)(\text{strain}\times L)=\frac{1}{2}\times\text{stress}\times\text{strain}\times(AL)$; dividing by volume $AL$ gives $u=\frac{1}{2}\times\text{stress}\times\text{strain}$.
- The sag $\delta=\frac{WL^3}{4bd^3Y}$ varies as $\frac{1}{d^3}$, so increasing depth $d$ greatly reduces sag; an I-section concentrates material at top and bottom where bending stress is greatest, giving high stiffness with low weight.
Section D — Long Answer (5 marks)
- Ropes are made of many thin twisted strands for flexibility, the same load capacity (load $=$ safe stress $\times$ area) and easy fault detection. Beams are made deep and I-shaped because sag $\propto\frac{1}{d^3}$, giving stiffness with low weight. A factor of safety keeps the working stress well below the breaking stress to allow for fatigue, flaws and overloads, ensuring structures stay within the elastic limit.
Generated by Vidaara.org · Assignment VID-P11-08-EBA-01 · vidaara.org