CBSE Class 11 Physics Chapter 9: Mechanical Properties of Solids NCERT Solutions
This chapter delves into the fundamental concepts of the Mechanical Properties of Solids, crucial for Class 11 Physics students. The NCERT Solutions provide a comprehensive understanding of stress, strain, elasticity, and the various moduli of elasticity. Key topics covered include Young's modulus, bulk modulus, and shear modulus, along with their applications. The solutions also explain the stress-strain relationship, elastic limit, yield strength, and ultimate tensile strength, often illustrated with graphical representations. These meticulously solved problems are designed to help students grasp the theoretical aspects and apply them to practical scenarios, ensuring thorough preparation for their examinations by clarifying complex concepts and problem-solving techniques.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 11 |
| Subject | Physics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 9 |
Chapter summary
Chapter 9, Mechanical Properties of Solids, focuses on the elastic behavior of materials. The NCERT Solutions cover definitions of stress and strain, Hooke's Law, and Young's modulus, bulk modulus, and shear modulus. It also explores the concepts of elastic limit, yield strength, and the breaking stress of materials, often using stress-strain curves to illustrate these properties. The provided solutions offer step-by-step guidance for solving numerical problems related to these concepts.
Learning outcomes
- Understand the concepts of stress, strain, and elasticity.
- Calculate Young's modulus, bulk modulus, and shear modulus for different materials.
- Interpret stress-strain curves to determine material properties.
- Identify and calculate the yield strength and ultimate tensile strength of a material.
- Solve problems involving the stretching and deformation of solids under load.
Topics covered
Paper topics
- Mechanical Properties of Solids
- Elasticity
- Stress
- Strain
- Hooke's Law
- Young's Modulus
- Bulk Modulus
- Shear Modulus
- Stress-Strain Curve
- Elastic Limit
- Yield Strength
- Ultimate Tensile Strength
Important topics
- Stress and Strain definitions
- Hooke's Law and Young's Modulus calculation
- Interpretation of Stress-Strain Curves
- Yield Strength determination
PDF preview
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Questions and Solutions
Physics
(Chapter – 9) (Mechanical Properties of Solids)
(Class - XI)
Question 9.1:
A steel wire of length 4.7 m and cross-sectional area <math>3.0 \times 10^{-5}</math> m<sup>2</sup> stretches by the same
amount as a copper wire of length 3.5 m and cross-sectional area of <math>4.0 \times 10^{-5}</math> m<sup>2</sup> under
a given load. What is the ratio of the Young's modulus of steel to that of copper?
Answer 9.1:
Length of the steel wire, <math>L_1 = 4.7 \text{ m}</math>
Area of cross-section of the steel wire, <math>A_1 = 3.0 \times 10^{-5} \,\mathrm{m}^2</math>
Length of the copper wire, <math>L_2 = 3.5 \text{ m}</math>
Area of cross-section of the copper wire, <math>A_2 = 4.0 \times 10^{-5} \,\mathrm{m}^2</math>
Change in length = <math>\Delta L_1 = \Delta L_2 = \Delta L</math>
Force applied in both the cases = F
Young's modulus of the steel wire:
<math display="block">Y_{\rm l} = \frac{F_{\rm l}}{A_{\rm l}} \times \frac{L_{\rm l}}{\Delta L}</math>
<math display="block">=\frac{F\times 4.7}{3.0\times 10^{-5}\times \Delta L} \cdots (i)</math>
Young's modulus of the copper wire:
<math display="block">Y_2 = \frac{F_2}{A_2} \times \frac{L_2}{\Delta L_2}</math>
<math display="block">=\frac{F\times3.5}{4.0\times10^{-5}\times\Delta L}</math>
... (ii)
Dividing (i) by (ii), we get:
<math display="block">\frac{Y_1}{Y_2} = \frac{4.7 \times 4.0 \times 10^{-5}}{3.0 \times 10^{-5} \times 3.5} = 1.79:1</math>
The ratio of Young's modulus of steel to that of copper is 1.79: 1. 1
Question 9.2: Figure 9.11 shows the strain-stress curve for a given material. What are (a) Young's modulus and (b) approximate yield strength for this material? 300 250
Stress (106Nm<sup>-2</sup>) 200 150 100 50
0,001 0.002 0.003 0.004
Strain
Fig. 9.11
Answer 10.2:
It is clear from the given graph that for stress <math>150 \times 10^6</math> N/m<sup>2</sup>, strain is 0.002.
a) Young's modulus, <math>Y = \frac{Stress}{Strain}</math>
<math display="block">= \frac{150 \times 10^6}{0.002} = 7.5 \times 10^{10} \text{ N/m}^2</math>
Hence, Young's modulus for the given material is <math>7.5 \times 10^{10} \text{ N/m}^2</math>.
- The yield strength of a material is the maximum stress that the material can sustain without crossing the elastic limit.
It is clear from the given graph that the approximate yield strength of this material is 300 <math>\times 10^6 \,\text{Nm}/^2 \,\text{or} \, 3 \times 10^8 \,\text{N/m}^2.</math> 2
Common mistakes
- Confusing stress and strain values or units.
- Incorrectly applying Hooke's Law or the formula for Young's modulus.
- Misinterpreting the scale or data points from a stress-strain graph.
- Errors in unit conversions, especially when dealing with large or small numbers (e.g., powers of 10).
Revision tips
- Review the definitions of stress, strain, and elastic moduli thoroughly.
- Practice interpreting stress-strain curves to extract key material properties.
- Work through all numerical problems, paying close attention to units and calculations.
- Understand the relationship between different types of moduli and their applications.
Practice MCQs
Q1. What is the ratio of Young's modulus of steel to copper if a steel wire and a copper wire of specific lengths and cross-sectional areas stretch by the same amount under the same load?
Explanation: Young's modulus (Y) is given by (F/A) * (L/ΔL). For the same load (F) and same stretch (ΔL), Y is inversely proportional to L/A, meaning Y is proportional to A/L. Thus, the ratio Y_steel / Y_copper depends on the ratio of their areas and inverse ratio of their lengths.
Q2. In a stress-strain curve, what does the initial linear portion represent?
Explanation: The initial linear portion of the stress-strain curve represents the region where stress is directly proportional to strain, which is the domain of Hooke's Law and elastic behavior.
Q3. If a material's stress-strain curve shows a steep initial slope, what does this indicate about its Young's modulus?
Explanation: A steeper slope in the stress-strain curve signifies that a large stress is required to produce a small strain, which is characteristic of a material with a high Young's modulus (i.e., a stiff material).
Q4. What is the approximate yield strength of the material shown in Figure 9.11, based on the provided graph?
Explanation: The yield strength is the maximum stress a material can withstand before permanent deformation. From the graph, the curve reaches approximately 300 x 10^6 N/ before significant deviation from linearity or potential yielding.
Frequently asked questions
What is the main focus of Chapter 9, Mechanical Properties of Solids, for Class 11 Physics?
Chapter 9 focuses on the elastic behavior of solids, including concepts like stress, strain, Hooke's Law, and the different moduli of elasticity (Young's, bulk, and shear). It also covers the elastic limit, yield strength, and ultimate tensile strength.
How do these NCERT Solutions help students prepare for exams?
These solutions provide clear, step-by-step explanations for numerical problems and conceptual questions. They help students understand the application of formulas and interpret graphical data, which is essential for exam success.
What is Young's modulus, and how is it calculated?
Young's modulus (Y) is a measure of a solid's stiffness. It is defined as the ratio of tensile or compressive stress to the corresponding tensile or compressive strain within the elastic limit. The formula is Y = (Stress / Strain).
What is the difference between elastic limit and yield strength?
The elastic limit is the maximum stress a material can withstand without undergoing permanent deformation. Yield strength is the stress at which a material begins to deform plastically (permanently), often slightly beyond the elastic limit.
How can I use the stress-strain curve provided in the solutions?
The stress-strain curve helps visualize a material's response to applied stress. You can use it to determine Young's modulus (from the slope of the linear region), the elastic limit, and the yield strength.
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