Physics Mechanical Properties of Solids: Overview, Questions, Preparation

Stress: When external forces act on a body in equilibrium, internal restoring forces develop within the material. Stress measures the intensity of these internal forces.

Basically, Stress is the restoring force per unit area.

Stress (σ) = Force (F) / Area (A)

Unit: N/m² or Pascal (Pa)

Types of Stress

Tensile Stress

Occurs when forces try to stretch or pull apart a material. For example: Pulling a rubber band.

Compressive Stress

Develops when forces try to compress the material. For example, pressing a sponge.

Shearing Stress

When forces are applied parallel to surfaces, it causes one layer to slide over another. For example: Using scissors to cut paper.

Strain: Strain measures how much a material has deformed relative to its original dimensions due to applied stress. It’s a dimensionless quantity.

Types of Strain

Longitudinal Strain

Change in length compared to the original length. Formula: Strain = ΔL/L

Shearing Strain

Angular deformation when shearing forces are applied. Formula: Shearing strain = Δx/L = tan θ ≈ θ (for small angles)

Volumetric Strain

Change in volume compared to the original volume. Formula: Volume strain = ΔV/V

The relationship between stress and strain for many materials within their elastic limits is Hooke’s law.

“For small deformations, stress is directly proportional to strain.”

Stress = k × Strain

Where k is called the modulus of elasticity.

Some materials (like rubber) don’t follow Hooke’s Law perfectly

Beyond the elastic limit, the relationship becomes non-linear

The stress-strain curve graphically shows how a material responds to increasing stress. This curve reveals important information about material behavior.

1. Linear Region (O to A)

- Stress and strain are directly proportional

- Hooke’s Law is perfectly valid

- Material behaves elastically

- Slope gives Young’s modulus

 

2. Elastic Region (A to B)

- Stress and strain are no longer proportional

- Material still returns to its original shape when unloaded

- Point B is called the elastic limit or yield point

 

3. Plastic Region (B to D)

- Permanent deformation begins

- Material cannot return to its original dimensions

- Point D represents the ultimate tensile strength

 

Fracture Point (E)

- Material breaks completely

- End of the material’s load-bearing capacity

Elastic moduli are material constants that measure resistance to deformation. They help engineers select appropriate materials for specific applications.

 

Young’s Modulus (Y)

Measures resistance to longitudinal (stretching or compression) deformation.

Y = Tensile Stress / Tensile Strain

Formula: Y = (F/A) / (ΔL/L) = (F × L) / (A × ΔL)

 

- High Young’s modulus = Material is stiff and resists stretching

- Low Young’s modulus = Material is flexible and stretches easily

 

Shear Modulus (G)

Measures resistance to shearing deformation. Also called modulus of rigidity.

G = Shearing Stress / Shearing Strain

Formula: G = (F/A) / θ = F / (A × θ)

It is generally less than Young’s modulus. For most materials: G ≈ Y/3

 

Bulk Modulus (B)

Measures resistance to volume change under uniform pressure.

B = Volume Stress / Volume Strain

Formula: B = -P / (ΔV/V)

-The negative sign indicates that an increase in pressure causes a decrease in volume.

 

Compressibility: The reciprocal of bulk modulus (k = 1/B)

Measures how easily a material can be compressed.

Understanding elastic properties is essential for practical engineering applications.

Building Design

Engineers must ensure structures can withstand loads without surpassing elastic limits

Safety factors are added to prevent failure

Material selection will be based on required strength and flexibility

 

Bridge Construction

Must support traffic loads, wind forces, and self-weight

Beam shapes are designed to minimize bending

I-shaped cross-sections provide strength with reduced weight

 

Crane Design

Steel ropes must support heavy loads without permanent deformation

Rope thickness calculated based on yield strength

Multiple thin wires braided together for flexibility and strength

 

Beam Design Principles

Bending in Beams, The amount a beam bends (sag) depends on:

Material properties (Young’s modulus)

Load applied

Beam dimensions (length, width, depth)

Below, we’ve covered all the formulas of the 11th class 9th chapter Mechanical Properties of Solid. The formula table helps you revise the chapter in less time and also helps you prepare for the JEE exam and NEET.

Concept	Formula	Notes
Stress	σ = F / A	Restoring force per unit area (Pa)
Longitudinal Strain	ε = ΔL / L	Fractional change in length
Shearing Strain	Shear strain = Δx / L = tan θ	Ratio of displacement to length
Volume Strain	Volume strain = ΔV / V	Fractional change in volume
Hooke’s Law	σ = k × Strain	Valid for small deformations
Young’s Modulus	Y = (F × L) / (A × ΔL)	Tensile/compressive stress
Shear Modulus	G = (F × L) / (A × Δx) = F / (A × θ)	Modulus of rigidity
Bulk Modulus	B = – p / (ΔV / V)	Negative sign: volume decreases under pressure
Compressibility	k = 1 / B	Reciprocal of bulk modulus
Poisson’s Ratio	ν = (Δd / d) ÷ (ΔL / L)	Pure number, no units

Elastic Potential Energy per Unit Volume	u = 1/2 × σ × ε	Energy stored in the stretched body
Deflection of Beam	δ = (W × l³) / (4 × b × d³ × Y)	Sag under central load
Rope Condition (Cranes)	A ≥ W / σy	Minimum cross-sectional area needed

What are the Mechanical Properties of a Solid?

Mechanical properties of a solid can be elasticity, plasticity, toughness, resilience, fatigue, tensile strength, etc.

 

Is Mechanical properties of solids easy chapter?

Yes, the Mechanical properties of solids are one of the easiest and highest-scoring chapters in class 11th physics. You can prepare the complete chapter from the class 11 NCERT Solutions Chemistry.

 

Are the Mechanical Properties of Solids in JEE?

Yes, the Mechanical Properties of Solid class 11th physics is in the JEE syllabus with approximately 6% weightage in the exam.

 

What is Hooke’s law in solid mechanics?

For a small deformation of the material, stress and strain are proportional to each other. This is Hooke’s law.

 

stress ∝ strain stress = k × strain

Where K is a constant and known as the modulus of elasticity.