Introduction
HSA Notes brings complete, exam-focused solved notes to help Class 11 (1st Year, HSSC-I) students score high marks in their FBISE Physics board exam.
This page covers Unit 7, Physics of Solids, prepared strictly according to the FBISE New Book/Course syllabus for the current academic session, covering the properties and classification of solids, deformation, stress and strain, and elastic potential energy, along with fully solved MCQs, short and long responses, numericals, and assignments from HSA Notes.
Physics of Solids
Definition: Physics of Solids is the branch of Physics that studies the mechanical, electrical, thermal, and optical properties of solid materials.
Solids maintain a fixed shape and volume because strong interatomic forces hold their particles in relatively fixed positions, where the particles can vibrate but not move freely as in liquids or gases.
Examples: Crystalline solids, such as salt and metals, have an ordered internal structure, while amorphous solids, such as glass and rubber, lack this long-range order.
Deformation behavior also varies widely between materials; a rubber band demonstrates elastic deformation, returning to its original shape after the applied force is removed, while a bent paperclip demonstrates plastic deformation, remaining permanently bent.
Classification
Solids are classified into three main categories based on the arrangement of their particles.
- Crystalline solids: Have an ordered, repeating lattice structure, are anisotropic, meaning their properties vary with direction, and exhibit a sharp, well-defined melting point.
- Polycrystalline solids: Consist of many small crystalline grains oriented randomly, making the material isotropic on a macroscopic scale despite being crystalline at the microscopic level. Common examples include metals and ceramics.
- Amorphous solids: Have a disordered internal structure with no long-range order, are isotropic, and undergo a gradual glass transition rather than a sharp melting point. Common examples include glass and plastics.
Crystal Lattice: A three-dimensional, regularly repeating array of points representing the positions of atoms, ions, or molecules within a crystalline solid.
Unit Cell: The smallest repeating structural unit of a crystal lattice, which, when repeated in three dimensions, generates the entire crystal structure.
Deformation
Stress (σ): Defined as the internal restoring force per unit area developed within a material when it is deformed, given by:
σ = F/A
Stress can be tensile, compressive, or shear, depending on the type of force applied, and is measured in Pascals (Pa).
Strain (ε): Defined as the fractional change in dimension of a material under stress, given by:
ε = ΔL / L₀
where ΔL is the change in length and L₀ is the original length. Strain is a dimensionless quantity, since it is a ratio of two lengths.
Hooke’s Law: Within the elastic limit of a material, stress is directly proportional to strain, given by:
σ = Yε
where Y is a constant of proportionality known as the modulus of elasticity for that particular type of deformation.
Moduli of Elasticity: Depending on the type of deformation involved, three different moduli are defined: Young’s modulus (Y) for tensile or compressive deformation, Shear modulus (G) for shear deformation, and Bulk modulus (K) for volumetric deformation under uniform pressure.
Stress-Strain Curve
The stress-strain curve for a material passes through several distinct regions as increasing stress is applied: the proportional limit, where stress and strain remain directly proportional.
The elastic limit, beyond which the material no longer returns fully to its original shape; the yield point, where the material begins to deform plastically with little additional stress.
The plastic region, where permanent deformation occurs; the ultimate tensile strength (UTS), the maximum stress the material can withstand; and finally the fracture point, where the material breaks.
Elastic Potential Energy
The elastic potential energy stored in a deformed material can be expressed in two equivalent forms:
U = ½kx² = ½σεV
where k is the spring constant, x is the extension, σ is stress, ε is strain, and V is the volume of the material. The elastic potential energy density, meaning energy stored per unit volume, is given by:
u = ½σε
Young’s Modulus Experiment: This standard laboratory experiment involves measuring the extension produced in a wire under different applied loads. By recording the extension for a range of known masses and using the wire’s original length and cross-sectional area, Young’s modulus can be calculated from the slope of the stress-strain graph.
Exercises Solved
This session’s Unit 7 exercise solutions from HSA Notes cover every question type set by FBISE, with full working shown for each answer.
Solved MCQs
a. Amorphous (glue)
b. Glass-transition
c. Network structure (silicon)
d. [W₁ + (3W/4)] / S
e. mg/A
f. 400π N
g. Bending
h. 1 × 10¹²
i. Resilience
j. Constant
Short Responses
7.1 Crystalline solids are more stable due to their low internal energy arrangement, while the glass transition in amorphous solids is a reversible process that occurs without any latent heat being absorbed or released.
7.2 Glass can turn milky due to devitrification or surface leaching, and it does not flow at room temperature despite being classified as an amorphous solid.
7.3 Strain is a fundamental kinematic quantity describing deformation, while stress is the material’s internal response to the applied force.
7.4 Yes, stretching a material in one direction can cause a corresponding contraction in the perpendicular direction, a relationship described by Poisson’s ratio.
7.5 The slope of a force-extension graph represents the stiffness (spring constant, k) of the material.
7.6 Elastic potential energy density is always positive, regardless of whether the material is under tension or compression.
7.7 Different types of loading, axial, bending, shear, and torsion, each have their own specific stress formulas depending on the geometry and direction of the applied force.
7.8 Repeated stress cycles can be dangerous due to fatigue, and material degradation can also occur due to corrosion over time.
7.9 Plastic deformation is associated with strain hardening and the formation of microscopic cracks within the material.
7.10 Stiffness refers to a material’s resistance to elastic deformation under an applied load.
Long Responses
7.1 A detailed explanation of the classification of solids into crystalline, polycrystalline, and amorphous categories, including their defining structural and physical properties.
7.2 A description of the different types of unit cells found in crystal lattices and how they determine the overall structure of a crystalline solid.
7.3 A full explanation of stress, strain, and the modulus of elasticity, including their formulas and physical significance.
7.4 A stage-by-stage explanation of the stress-strain curve for a ductile material, from the proportional limit through to fracture.
7.5 A comparison of elastic deformation, which is recoverable, and plastic deformation, which results in a permanent change in shape.
7.6 An explanation of how the area under a force-extension graph represents the work done in deforming the material.
7.7 A full derivation of the elastic potential energy formula, U = ½kx², starting from the work done against a restoring force.
7.8 A step-by-step description of the standard Young’s modulus experiment, including the procedure, measurements taken, and calculation method.
Numericals
7.1 Force ≈ 51 N, mass ≈ 5.2 kg.
7.2 Diameter of copper wire ≈ 2.29 mm.
7.3 Extension ΔL ≈ 0.279 mm, elastic potential energy U ≈ 0.011 J.
7.4 Elastic potential energy U = 60.75 J.
7.5 Stress σ ≈ 2.55 kPa.
Assignments
7.1 Extension ΔL ≈ 23 m.
7.2 Strain ε ≈ 10⁻⁴.
7.3 Work done W = 0.02 J.
HSA Notes Features
- Complete solved MCQs based on the FBISE paper pattern
- Short and long-response questions with clear, detailed answers
- Solved numericals with full working and correct units
- Solved assignments matching the current session’s syllabus
- Solved textbook exercises covering every question
- Full Physics of Solids notes for Class 11, based on the FBISE new book/course, available in PDF form at hsanotes.com
Why This Unit Matters
Physics of Solids bridges the gap between abstract material classification and practical, numerical problem-solving, both of which are tested heavily in the FBISE board exam.
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Frequently Asked Questions
What is the difference between crystalline, polycrystalline, and amorphous solids?
Crystalline solids have an ordered lattice structure with a sharp melting point, polycrystalline solids consist of many randomly oriented crystalline grains, and amorphous solids have a disordered structure with a gradual glass transition instead of a sharp melting point.
What is the difference between stress and strain?
Stress is the internal restoring force per unit area developed within a material, while strain is the fractional change in dimension the material undergoes as a result of that stress.
What is the difference between ductile and brittle materials?
Ductile materials undergo a large amount of plastic deformation before fracturing, while brittle materials undergo very little plastic deformation and fracture soon after their elastic limit is exceeded.
How is elastic potential energy calculated?
Elastic potential energy can be calculated using U = ½kx², based on the spring constant and extension, or equivalently using U = ½σεV, based on stress, strain, and volume.
Conclusion
With Unit 7, Physics of Solids, fully covered, Class 11 FBISE students now have a clear understanding of solid classification, deformation, stress-strain behavior, and elastic potential energy, along with fully solved MCQs, short and long responses, numericals, and assignments for this session. Practice these solved exercises alongside past papers, and consider joining our online classes for guided, exam-focused preparation, to build the accuracy and confidence needed for your board exam.
Best of luck for your Class 11 Physics exam!