NCERT Class 11 Physics Chapter 9 Notes Mechanical Properties of Solids - Download PDF

The Mechanical Properties of Solids in Class 11 Physics help us understand how solids stretch, compress, or bend when force is applied. The NCERT notes give a clear summary of all the key concepts in this chapter.

In these notes, you’ll learn about:

• Stress and Strain
• Hooke’s Law
• Types of stress and strain
• The Stress-Strain Curve and what it tells us about the behavior of solids
• Important formulas and basic equations used in problems

You can easily download the PDF of these notes to revise at short notice at any time. Be informed that the above notes put extra emphasis on concepts and synopsis — complete step-by-step derivations may not be present. Just ideal to ace CBSE boards, or revise briefly prior to exams, or during numerical solutions!

This Story also Contains

1. NCERT Class 11 Physics Chapter 9 Notes
2. Strain
3. Hooke's Law
4. Stress-Strain Curve
5. Modulus of Elasticity
6. Significance of NCERT Class 11 Physics Chapter 9 Notes

Also, students can refer,

• NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties of Solids
• NCERT Exemplar for Class 11 Physics Solutions Chapter 9 Mechanical Properties of Solids

NCERT Class 11 Physics Chapter 9 Notes

The mechanical properties of solids tell us how strong a material is and how well it resists being stretched, compressed, or bent. In simple words, it shows how much stress an object can handle before it starts changing shape.

Some materials are easy to deform, like clay—you can mold it into different shapes, like an earthen pot. That’s because clay has a low resistance to deformation. On the other hand, materials like iron don’t change shape easily. They can only be bent or reshaped when heated, which means iron has high resistance to deformation and is stronger than clay.

Mechanical characteristics:-

1. Elasticity: Elasticity is a quality that allows an object to restore its original shape after an external force is removed. This implies it shows us how flexible a person's body is. Take, for example, a spring. When a spring is stretched, its shape changes, and when the external force is removed, the spring returns to its original position.

2. Plasticity is the opposite of elasticity. The term "property" refers to a state of permanent deformation. Even when the external force is eliminated, the object never returns to its previous shape. Plastic is the name for these types of items.

3. Ductility: It refers to the ability to be pulled into thin wires or sheets. for example:-Small gold

4. Strength: The ability to resist a high level of applied stress without failing.

Stress
The restoring force per unit area is known as stress.
When we apply an external force to the body in order to change its shape, the body creates a restoring force in the opposite direction.

As an example:

When an external force is applied to a rubber ball at the same time, the ball creates a force that acts in the opposite direction.

The restoring force is the opposite force that arises in the ball when an external force is applied. Both forces have the same magnitude.

Stress = F/A (mathematically)

Where F is the restoring force that emerges in the body as a result of the force we apply.

A=area

S.I. Unit:- N/m²

Longitudinal stress

When a force is applied to the cross-sectional area of a cylindrical body, longitudinal stress is defined as the restoring force per unit area.

Shearing or Tangential Stress

Force per unit area is restored when the applied force is parallel to the cross-sectional area of the body.

There is relative displacement between the opposing faces of the body.

Hydraulic Stress

Hydraulic stress is the restoring force per unit area when a fluid delivers force to the body.

Strain

Strain is a deformation measurement that represents the displacement of particles in the body in relation to a reference length.

It explains how and what happens to a body when it is put under stress.

Mathematically:

- Strain = ΔL/L, where ΔL is the length change.

L stands for the original length.

Because it is a ratio of two quantities, it is a dimensionless quantity.

Strain Types: Longitudinal Strain

The longitudinal tension causes a change in the original length of the body. When we apply longitudinal stress to a body, the body either elongates or compresses as a result of the change in length. Longitudinal Strain is a measurement of length change.

Longitudinal Strain = ΔL/L

Shearing Strain

Shearing strain is the measurement of the relative displacement of the body's opposed faces as a result of shearing force. If we apply force parallel to the cross-sectional area, the opposite faces of the body will be displaced relative to each other. Shearing strain is a measurement of how far the two opposing faces have moved away from each other.

Mathematically:-
Consider a cube with an initial length of L that is in a certain position and is shifted by an angle θ. Let x represent the modest relative displacement.

Shearing strain= x/

Volume Strain

The ratio of change in volume to the original volume as a result of hydraulic stress is known as volume strain. When a fluid applies stress to a body, the volume of the body changes without changing the shape of the body.

Volume strain = ΔV/V

Hooke's Law

Within the elastic limit, Hooke's law asserts that the stress developed is directly proportional to the strain produced in a body. Consider a situation in which the body is subjected to external force. As a result, tension arises in the body, and this stress causes a strain in the body, implying that the body will deform. Strain is formed as a result of stress.
According to Hooke's law, as strain rises, so does stress, and vice versa. All elastic substances are subject to Hooke's law. It does not apply to the deformation of plastic. In terms of mathematics:

stress ∝ strain
stress = k × strain

The proportionality constant, k, is also known as the modulus of elasticity.

Stress-Strain Curve

It's a curve that depicts the relationship between stress and strain. The stress (which is the same magnitude as the applied force per unit area) and the strain produced are represented on a graph. The graph demonstrates how a specific material deforms as the load increases. The line that connects O and A is a straight line. This suggests that strain is directly related to stress. Hooke's Law is relevant in this area. The material behaves like an elastic body in this area. Stress and strain are not directly related in the region between A and B. However, as the force is withdrawn, the material returns to its original dimensions. They have elasticity to them.

The yield point B(also known as elastic limit) in the curve indicates that the material will be elastic until this point, and the stress corresponding to point B is known as the material's yield strength (Sy). The elastic region refers to the area between O and B. We can observe that even tiny changes in stress cause strain to increase rapidly from point B to point D. Even when the force is removed, the material does not return to its former location. Stress is zero at this stage, but strain is not since the body has changed shape. Plastic deformation has occurred in the material. It is claimed that the substance is permanently fixed. The ultimate tensile strength (Su) of the material is shown by point D on the graph. We can observe that as we progress from D to E, tension reduces while strain increases. Finally, a fracture occurs at point E. This indicates that the body has broken down.

Modulus of Elasticity

The elastic modulus is defined as the ratio of tension to strain. The elastic modulus is a property of each material.

This means that gold will have a specific elastic modulus value, rubber will have a specific elastic modulus value, and so on.

Young’s Modulus

Young's modulus is named after the physicist who first defined it.

The ratio of longitudinal stress to longitudinal strain is known as the longitudinal stress-to-strain ratio.

Y is the symbol for it.

Y can be written as longitudinal stress/longitudinal strain

= σ/ ε

Modulus of Shear (Modulus of Rigidity)

The ratio of shearing stress to shearing strain is known as the shear modulus.

Modulus of Rigidity is another name for it.

The letter 'G' stands for it.

G=shearing stress/shearing strain

= (F/A)/( Δx/L)

= FL/A Δx

Relation between Young’s Modulus and Shear Modulus

Young's modulus is greater than the shear modulus.

G = Y/3 is there for most material

Bulk Modulus

The ratio of hydraulic stress to matching hydraulic strain is known as the bulk modulus.

The letter 'B' stands for this.

B = -p/(ΔV/V)

Here represents p =hydraulic stress, ΔV/V = hydraulic strain

B(solids) > B(liquids) >B(gases)

Compressibility

Compressibility refers to a substance's ability to withstand compression. Compressibility is the reciprocal of the bulk modulus.

The letter 'K' stands for this.

k=1/B = - (1/p) (ΔV/V)

k(solids)<k(liquids)<k(gases)

Significance of NCERT Class 11 Physics Chapter 9 Notes

• Quick Concept Clarity
  The notes explain tough topics like stress, strain, Hooke’s law, and elastic limits in a simple and easy-to-understand way.

• Easy Revision
  Perfect for last-minute revision before exams as all key formulas, definitions, and graphs are neatly summarized.

• Helps with Numericals
  Understanding concepts like Young’s modulus, shear modulus, and bulk modulus becomes easier with formula-based notes.

• Visual Learning
  Includes diagrams like the stress-strain curve, making it easier to understand how solids behave under force.

• Printable & Portable
  Notes are available in PDF format, so you can read them on your phone or take a printout for offline study.

• Supports Exam Prep
  Great for scoring well in school exams, and also useful as a base for competitive exams like JEE, NEET and many more.

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