Physics Part II

Mechanical Properties of Solids covers stress, strain, elasticity, and Hooke's law — how materials deform under force and regain shape. Understanding these properties is essential for engineering design of buildings, bridges, and structural elements.

• 1Elasticity is the property by which bodies regain original shape/size when external force is removed; plasticity is permanent deformation
• 2Stress = F/A (force per unit area, SI unit Pa); Strain = ΔL/L (dimensionless ratio of dimension change)
• 3Hooke's law: stress = k × strain (valid for small deformations within elastic limit); three types—longitudinal, shearing, hydraulic
• 4Young's modulus Y = (F/A)/(ΔL/L); metals have large Y values (steel > copper > aluminium); shear modulus G ≈ Y/3
• 5Bulk modulus B relates pressure to volume change; solids least compressible, gases ~1 million times more compressible

Class 11 Physics Chapter 9 covers mechanical properties of fluids—pressure, streamline flow, Bernoulli's principle, viscosity, and surface tension. The NCERT Class 11 Physics Chapter 9 PDF is free to download.

• 1Pressure is a scalar quantity defined as normal force per unit area (P = F/A), measured in pascals (Pa); 1 atm = 1.01 × 10⁵ Pa
• 2Pascal's law: pressure in a fluid at rest is uniform at the same height and transmitted undiminished in all directions throughout an enclosed fluid
• 3Pressure increases with depth in a fluid according to P = Pa + ρgh, where ρ is density, g is gravity, and h is depth below surface
• 4Continuity equation (Av = constant) conserves mass in incompressible fluid flow; velocity increases where cross-sectional area decreases
• 5Bernoulli's equation (P + ½ρv² + ρgh = constant) applies to streamline flows and relates pressure changes to velocity and elevation changes

Thermal properties of matter encompass heat, temperature, thermal expansion, specific heat capacity, calorimetry, change of state, and heat transfer mechanisms. This chapter explains how heat flows between systems through conduction, convection, and radiation, and covers Newton's law of cooling.

• 1Heat is energy transferred between systems due to temperature differences; measured in joules (J), temperature in Kelvin (K)
• 2Absolute temperature scale: T = tc + 273.15, with 0 K as absolute zero where molecular activity ceases
• 3Thermal expansion: linear (∆l/l = αl∆T) and volume (∆V/V = αv∆T); relation αv = 3αl applies to uniform expansion
• 4Specific heat capacity s = (1/m)(∆Q/∆T) determines temperature change when heat is absorbed; water has highest capacity among common substances
• 5Latent heat (L = Q/m) represents energy for state changes—fusion Lf = 3.33×10⁵ J/kg and vaporization Lv = 22.6×10⁵ J/kg for water

Thermodynamics is the branch of physics dealing with heat, temperature, and energy conversion. It studies laws governing thermal energy transformation between heat and work, exemplified by processes like friction producing heat or steam engines converting heat to work.

• 1Zeroth Law: two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other; establishes temperature concept
• 2Heat (energy transfer via temperature difference) and work (energy transfer via other means) are two distinct modes of changing system internal energy
• 3First Law: ∆Q = ∆U + ∆W states that heat supplied equals internal energy change plus work done by system
• 4Internal energy is a state variable depending only on system state (pressure, volume, temperature), independent of path taken
• 5Second Law: no heat engine can achieve 100% efficiency; Carnot engine provides maximum theoretical efficiency of η = 1 − T₂/T₁ between hot (T₁) and cold (T₂) reservoirs

Kinetic theory explains the behaviour of gases by considering them as collections of rapidly moving atoms or molecules in incessant random motion, with elastic collisions determining pressure, temperature, and other macroscopic properties based on molecular parameters.

• 1Kinetic theory derives pressure from elastic molecular collisions: P = ⅓nmv², linking it directly to molecular mass m, number density n, and mean squared speed v²
• 2Temperature is the average translational kinetic energy per molecule: ½m⟨v²⟩ = (3/2)kBT; independent of gas type or pressure, it depends only on absolute temperature T
• 3Ideal gas equation PV = µRT (or PV = kBNT) emerges from kinetic theory; real gases obey it at low pressures and high temperatures when molecular interactions become negligible
• 4Law of equipartition of energy: each translational and rotational degree of freedom contributes ½kBT; each vibrational mode contributes kBT (both kinetic and potential energy)
• 5Root mean square speed vrms = √(3kBT/m); at same temperature, lighter molecules move faster; this governs diffusion rates and explains isotope separation

Oscillations is periodic motion in which objects move back and forth about an equilibrium position, with displacement described by sinusoidal functions like x(t) = A cos(ωt + φ) in simple harmonic motion.

• 1Periodic motion repeats at regular intervals; oscillatory motion is to-and-fro about equilibrium with an equilibrium position where no net force acts
• 2Simple harmonic motion (SHM) has displacement x(t) = A cos(ωt + φ) where amplitude A is maximum displacement, angular frequency ω = 2π/T, and phase constant φ determines initial conditions
• 3Velocity v(t) = –ωA sin(ωt + φ) and acceleration a(t) = –ω²x(t) in SHM; both are periodic with period T/2 for velocity magnitude and T for displacement
• 4Force in SHM is restoring: F = –kx = –mω² x, always directed toward equilibrium; k = mω² relates spring constant to mass and angular frequency
• 5Energy in SHM conserves total mechanical E = ½kA² = K + U; kinetic energy peaks at equilibrium, potential energy peaks at maximum displacement

Waves are patterns of disturbance that propagate through a medium without physical transfer of matter—they transport energy and information. Mechanical waves include transverse waves (oscillations perpendicular to propagation) and longitudinal waves (oscillations parallel to propagation), with speeds determined by the medium's elastic and inertial properties.

• 1Mechanical waves propagate disturbances through elastic media without transferring matter; they transport energy and depend on medium properties (tension/density for strings, bulk modulus/density for fluids).
• 2Transverse waves (oscillation ⊥ to propagation) occur in solids; longitudinal waves (oscillation ∥ to propagation) occur in all elastic media; wave speed is independent of frequency in non-dispersive media.
• 3Sinusoidal wave equation y(x,t) = a sin(kx − ωt + φ) describes position-time evolution with amplitude a, angular wave number k = 2π/λ, angular frequency ω = 2πν, and initial phase φ.
• 4Wave speed on a string: v = √(T/μ) where T is tension and μ is linear mass density; for sound in media: v = √(B/ρ) (bulk modulus/density) or v = √(γP/ρ) for ideal gases (Laplace correction).
• 5Principle of superposition: net displacement = sum of individual wave displacements; produces interference (amplitudes add if in-phase, cancel if π out-of-phase), standing waves on bounded strings, and beats (frequency = |ν₁ − ν₂|).