NEET • Class XI Physics

Syllabus Hub: Units & Chapters (2025–26)

Curated, NCERT-aligned table of contents for quick navigation. Start with measurement foundations, progress through mechanics and properties of matter, then wrap up with thermodynamics, kinetic theory, and waves.

Aligned to NCERT/CBSE Class XI Physics (Code 042), session 2025–26.

Unit I: Physical World & Measurement 1 chapter • 23 marks

Chapter 1: Units and Measurements

Unit II: Kinematics 2 chapters

Chapter 2: Motion in a Straight Line Chapter 3: Motion in a Plane

Unit III: Laws of Motion 1 chapter

Chapter 4: Laws of Motion

Unit IV: Work, Energy & Power 1 chapter • 17 marks

Chapter 5: Work, Energy and Power

Unit V: Motion of System of Particles & Rigid Body 1 chapter

Chapter 6: System of Particles and Rotational Motion

Unit VI: Gravitation 1 chapter

Chapter 7: Gravitation

Unit VII: Properties of Bulk Matter 3 chapters • 20 marks

Chapter 8: Mechanical Properties of Solids Chapter 9: Mechanical Properties of Fluids Chapter 10: Thermal Properties of Matter

Unit VIII: Thermodynamics 1 chapter

Chapter 11: Thermodynamics

Unit IX: Behaviour of Perfect Gases & Kinetic Theory 1 chapter

Chapter 12: Kinetic Theory

Unit X: Oscillations & Waves 2 chapters • 10 marks

Chapter 13: Oscillations Chapter 14: Waves

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Use the search box to quickly filter units/chapters.
Click a chapter to open your detailed post (update links as needed).
Stick to the NCERT sequence for NEET-aligned prep.

01 Units and Measurements

Conceptual Weightage: Low Updated: 04 Sep 2025

Chapter Notes

Need for measurement: Physical quantities must be measured to compare and quantify phenomena; measurements are reported with units and uncertainty.
Systems of units: Historical systems (CGS, FPS, MKS) → modern SI (International System of Units) with seven base quantities (m, kg, s, A, K, mol, cd) and derived units (e.g., N, J, W, Pa).
SI conventions: Standard symbols (italic for quantities, roman for units), spacing (value–unit with a space), prefixes (k, M, m, μ, n), and unit algebra (e.g., N = kg·m·s⁻²).
Significant figures: Counting rules (leading zeros not significant, captive zeros significant, trailing zeros significant if decimal point present); rounding after operations:
- Add/Subtract: limit by decimal places of the least precise term.
- Multiply/Divide: limit by significant figures of the least precise factor.
Uncertainty & errors: Absolute vs relative/percentage error; propagation of errors (sum/difference, product/quotient, powers); report results as value ± uncertainty with appropriate sig figs.
Dimensions & dimensional analysis: Dimensional formulae (e.g., [Force] = MLT⁻²); uses—check homogeneity of equations, derive relations, estimate dependence of variables; limitations—cannot yield dimensionless constants or functions (sin, exp, etc.).
Quick derived unit table: N (kg·m·s⁻²), J (kg·m²·s⁻²), W (kg·m²·s⁻³), Pa (kg·m⁻¹·s⁻²).

Important Figures

Table of SI base quantities and their base units — SI base quantities & units with symbols (m, kg, s, A, K, mol, cd).

Infographic summarizing rules for counting and rounding significant figures — Significant figures: counting and rounding rules for calculations.

Worked examples of dimensional analysis and homogeneity checks — Dimensional analysis: homogeneity checks and deriving relations.

Quick Summary

This chapter builds the language of Physics: standardized SI units, correct use of significant figures, and reporting of uncertainty. Dimensional analysis is a rapid tool to verify equations and infer how variables relate—powerful for eliminating wrong options in exams.

Practice Quiz (10 MCQs)

1) Which is not an SI base unit?

2) The dimensional formula of pressure (Pa) is:

3) In 0.02050, the number of significant figures is:

4) (2.31 × 1.4) should be reported with:

5) If a = (2.0 ± 0.1) and b = (3.00 ± 0.05), the relative error in (a·b) is approximately:

6) The dimensional formula of viscosity (μ) is:

7) Which statement about trailing zeros is correct?

8) Checking both sides of an equation for identical dimensions tests:

9) Which of the following is a derived unit?

10) Dimensional analysis cannot determine:

Downloads

SI Units & Prefixes (PDF) Significant Figures Rules (PNG) Error Propagation Cheatsheet (PDF)

Cross-links

Next topics: Motion in a Straight Line · Motion in a Plane

02 Motion in a Straight Line

Core Kinematics Weightage: Medium Updated: 04 Sep 2025

Chapter Notes

Frame of reference & position: Specify an origin and an axis (1D). Position x(t) locates a particle along a straight line; displacement Δx is path-independent.
Distance vs displacement: Distance = total path length (scalar); displacement = x₂ − x₁ (vector, signed).
Average speed & velocity: v̄_speed = total distance/Δt; v̄ = Δx/Δt (can be negative/zero).
Instantaneous velocity & acceleration: v = dx/dt, a = dv/dt = d²x/dt² (elementary calculus ideas).
Uniform vs non-uniform motion: Uniform → constant v (a = 0); non-uniform → v changes with time (a ≠ 0).
Graphs in 1D motion: x–t slope = v; v–t slope = a; area under v–t gives displacement; curvature hints at changing a.
Uniformly accelerated motion (UAM): For constant a:
- v = u + at
- x = ut + ½at²
- v² = u² + 2ax
- x = ((u + v)/2) t
Graphical derivations and calculus consistency checks recommended.
Free fall (near Earth): a = −g (downward). Use UAM with sign convention (up positive).
Typical pitfalls: Average speed ≠ magnitude of average velocity; reading slopes/areas correctly; consistent units & significant figures in numerical answers.

Important Figures

Representative x–t and v–t graphs showing slopes and areas — x–t slope gives v; v–t slope gives a; area under v–t equals displacement.

Summary card of uniformly accelerated motion equations — Uniformly accelerated motion: v = u+at; x = ut+½at²; v² = u²+2ax.

Diagram of free fall with sign conventions and axes — Free fall: choose axis/signs consistently; a = −g for upward-positive axis.

Quick Summary

One-dimensional kinematics formalizes how position, velocity, and acceleration relate via graphs and calculus. Mastery of slopes/areas and the constant-acceleration equations lets you solve most straight-line motion problems, including free fall, average–instantaneous distinctions, and multi-interval motions.

Practice Quiz (10 MCQs)

1) The slope of the x–t graph at any instant equals:

2) Area under a v–t curve between t₁ and t₂ gives:

3) For uniform motion, which is constant?

4) If v = u + at, then x equals:

5) A particle moves with a = constant > 0 and v(t₀) > 0. Its v–t graph is:

6) In free fall (up positive), acceleration is:

7) Average speed equals magnitude of average velocity when:

8) From x = 4t − t² (SI), the instantaneous velocity is:

9) The relation v² = u² + 2ax is valid for:

10) If a v–t graph crosses the time axis, the particle:

Downloads

1D Kinematics Formula Sheet (PDF) x–t & v–t Graphs Quick Guide (PNG) Free-Fall Practice Set (PDF)

Cross-links

03 Motion in a Plane

Core Kinematics Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Scalars vs vectors: Scalars have magnitude only (e.g., speed); vectors have magnitude and direction (e.g., velocity, acceleration).
Position & displacement vectors: Position \u2192 arrow from origin to point; displacement is change of position. Equality of vectors and multiplication by a real number scale magnitude and may reverse direction.
Vector addition/subtraction: Triangle/parallelogram rules. \u2192 Component-wise: \u27e8x, y\u27e9; subtraction is addition with negative.
Unit vector & resolution: \u0302i, \u0302j are unit vectors along x, y. Any vector \u1d5f = A_x\u0302i + A_y\u0302j with A = \u221a(A_x²+A_y²) and \u03b8 = tan\u207b\u00b9(A_y/A_x).
Scalar (dot) product: \u1d5f\u00b7\u1d5f = AB\u2009cos\u03b8; work W = \u1d5f\u22c5\u1d5f. Zero when vectors are perpendicular.
Vector (cross) product: \u1d5f\u00d7\u1d5f = AB\u2009sin\u03b8 \u0302n (right-hand rule); magnitude equals area of the parallelogram; zero when vectors are parallel.
Projectile motion (no air drag): v₀ at angle \u03b8:
- Time of flight T = \u2212\; 2v₀sin\u03b8 / g
- Range R = v₀² sin2\u03b8 / g
- Maximum height H = v₀² sin\u00b2\u03b8 / (2g)
- Path: y(x) = x tan\u03b8 \u2212 (g x\u00b2)/(2 v₀² cos\u00b2\u03b8) (parabola)
Uniform circular motion (UCM): Speed constant, velocity changes direction; centripetal acceleration a_c = v\u00b2 / r toward the centre; angular variables relate via v = \u03c9r.
Problem cues: Break vectors into components; use dot/cross product judiciously; for projectiles, treat x and y motions independently; in UCM, acceleration is normal to velocity.

Important Figures

Vector resolution into rectangular components — Resolving \u1d5f into A_x\u0302i and A_y\u0302j; magnitude and direction from components.

Projectile trajectories showing range, time of flight and maximum height — Projectile motion in 2D: parabolic path, T, R, and H for angle \u03b8.

Uniform circular motion with velocity and centripetal acceleration vectors — UCM: velocity tangential, a_c toward centre; v = \u03c9r and a_c = v\u00b2/r.

Quick Summary

Plane motion extends 1D kinematics to two dimensions: represent vectors with components, apply dot/cross products for geometry and work/area, model projectiles by independent x–y motions, and treat uniform circular motion with constant speed but changing direction (centripetal acceleration).

Practice Quiz (10 MCQs)

1) The magnitude of A + B is maximum when the angle between A and B is:

2) If A = 3\u0302i + 4\u0302j, then |A| equals:

3) A\u00b7B = 0 implies that vectors are:

4) The magnitude of A\u00d7B equals:

5) For a projectile, the horizontal component of velocity (no air resistance) is:

6) The range is maximum for a projection angle of:

7) Centripetal acceleration for uniform circular motion is:

8) The direction of A\u00d7B is given by:

9) If R is resultant of two equal vectors A at angle 2\u03b1, then R equals:

10) Projectile’s equation y(x) is a parabola because acceleration is:

Downloads

Vectors & Components Quick Sheet (PDF) Projectile Motion Formula Card (PNG) Uniform Circular Motion Notes (PDF)

Cross-links

04 Laws of Motion

Mechanics Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Force & inertia: Intuitive concept of force; inertia as resistance to change of state. Mass quantifies inertia.
Newton’s Laws:
- I (Law of Inertia): A body remains at rest or moves with uniform velocity unless acted upon by a net external force.
- II: Net force F = m a; impulse = change in momentum.
- III: For every action, there is an equal and opposite reaction.
Momentum & its conservation: In absence of external force, total linear momentum of an isolated system remains constant (collisions, recoil).
Equilibrium of concurrent forces: For a particle in equilibrium, vector sum of all concurrent forces is zero; resolve forces along convenient axes.
Friction: Static vs. kinetic (sliding) friction; limiting friction; laws of friction; rolling friction & role of lubrication. Free-body diagrams (FBDs) essential.
Uniform circular motion (dynamics): Centripetal force requirement F_c = m v²/r; applications: vehicles on level circular roads and on banked roads.
Problem cues: Draw clear FBDs; identify constraints (no-slip, smooth surface); check limiting conditions; for circular motion, ensure required F_c is provided by available forces (normal/friction).

Important Figures

Example free-body diagrams for block on rough surface and on incline — Typical FBDs: forces on a block on rough horizontal surface and on an incline.

Static vs kinetic friction curves and limiting friction point — Static vs kinetic friction; limiting friction and transition to motion.

Centripetal force for vehicle on level and banked circular roads — Circular motion dynamics: level vs banked road; role of friction and normal components.

Quick Summary

Newton’s laws connect forces with motion. With clear free-body diagrams, the laws of friction, conservation of momentum, and centripetal-force requirements let you analyse equilibrium, linear motion under forces, and uniform circular motion (including vehicles on curves).

Practice Quiz (10 MCQs)

1) Newton’s second law defines force as:

2) Impulse equals:

3) In equilibrium of concurrent forces:

4) The coefficient of kinetic friction is:

5) For uniform circular motion, the direction of acceleration is:

6) On a banked road without friction, safe speed v satisfies:

7) An action–reaction pair:

8) Rolling friction is typically:

9) A block just starts to slide when horizontal pull reaches F_lim. The coefficient of static friction μ_s is:

10) Conservation of linear momentum holds when:

Downloads

FBD & Friction Cheatsheet (PDF) Impulse–Momentum Quick Guide (PNG) Banked & Level Road Formula Card (PDF)

Cross-links

05 Work, Energy and Power

Mechanics Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Work by a force: For a constant force along displacement, W = F·s = F s cosθ. For a variable force, W = ∫ F·dr along the path (area under F–x curve if collinear).
Kinetic energy (KE) & work–energy theorem: KE = ½ m v². Net work by all forces equals change in KE: W_net = Δ(½ m v²).
Power: Average power = W/Δt; instantaneous power P = dW/dt = F·v (dot product).
Potential energy (PE): Energy stored due to configuration. For a spring, PE = ½ k x². Gravitational near Earth: ΔU = m g Δh (independent of path).
Conservative vs non-conservative forces: Conservative forces have path-independent work and associated potential (W = −ΔU). Non-conservative (e.g., friction) dissipate mechanical energy to heat; mechanical energy changes by the work of non-conservative forces.
Vertical circle: Speed requirement at top: v_top ≥ √(g r) for just-taut string (T = 0). Use energy + dynamics to relate speeds and tensions at points.
Collisions: Elastic → both momentum and KE conserved; inelastic → momentum conserved, KE not (perfectly inelastic: bodies stick). Analyse in 1D and 2D via centre-of-mass or component method.
Problem cues: Choose a sign convention; draw energy bar charts; for variable force, integrate or use area; in mixed problems combine W–E theorem with Newton’s laws.

Important Figures

Area under F–x curve representing work for a variable force — Work from variable force: area under F–x gives W when F is collinear with displacement.

Flow chart of conservative vs non-conservative forces and energy changes — Conservative vs non-conservative forces: how mechanical energy changes.

Tension and speed at points in a vertical circular motion — Vertical circle: speed thresholds and tension at top/bottom using energy + dynamics.

Quick Summary

This chapter connects forces with energy methods. Compute work from forces (including variable forces), use the work–energy theorem to relate forces and speeds, distinguish conservative/non-conservative interactions, model springs and vertical circles with energy + Newton’s laws, and classify collisions by momentum/energy conservation.

Practice Quiz (10 MCQs)

1) Work done by a constant force at 60° to displacement s is:

2) The work–energy theorem states that net work equals:

3) Instantaneous power delivered by a force is:

4) Potential energy stored in a spring stretched by x is:

5) For conservative forces, the work done around any closed path is:

6) Minimum speed at the top of a vertical circle for a taut string is:

7) In a perfectly inelastic collision:

8) The area under an F–x curve (collinear case) represents:

9) If non-conservative work W_nc acts on a system, the change in mechanical energy ΔE_mech equals:

10) Power for a block pulled at constant speed v by horizontal force F on a frictionless surface is:

Downloads

Work–Energy & Power Formula Sheet (PDF) Conservative vs Non-Conservative Flowchart (PNG) Collisions (1D & 2D) Problem Set (PDF)

Cross-links

06 System of Particles and Rotational Motion

Mechanics Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Centre of mass (CM): For two particles, R = (m₁r₁ + m₂r₂)/(m₁+m₂); extends to many particles/continuous bodies. If external force is zero, CM moves with constant velocity. Momentum conservation ↔ motion of CM.
CM of rigid bodies: Locate CM by symmetry or integration; examples: uniform rod (midpoint), rectangular/square/triangular lamina (standard formulae).
Moment of a force (torque): τ = r × F; direction by right-hand rule. Angular momentum L = r × p; dL/dt = net external torque. Conservation of L when net external torque is zero (e.g., skater pulling arms in).
Rigid-body equilibrium: For a body to be in static equilibrium: ΣF = 0 and Στ = 0 about any point. Choose convenient pivot; use perpendicular distances and sign conventions.
Pure rotation & equations: For rotation about a fixed axis: Στ = Iα, with angular kinematics analogous to linear: θ ↔ x, ω ↔ v, α ↔ a. Power in rotation: P = τω.
Moment of inertia (MI): I = Σ mᵢ rᵢ² (discrete) or ∫ r² dm (continuous). Radius of gyration k via I = Mk². Parallel/Perpendicular axis theorems (for appropriate cases).
Typical MI values (no derivations): Uniform rod about centre (I = ML²/12), about end (I = ML²/3); ring about diameter/axis; disc about diameter/axis; solid/hollow cylinder and sphere (standard sets for quick reference).
Problem cues: Separate translation of CM and rotation about CM; check external torque for angular momentum changes; pick axis smartly for torque balance and MI simplification.

Important Figures

Centre of mass of two-particle system and uniform rod — Centre of mass: two particles & uniform rod; CM motion under external forces.

Torque as r cross F and angular momentum as r cross p — Torque and angular momentum; conservation when net external torque is zero.

Common moments of inertia for rod, disc, ring, sphere — Common MI formulae (no derivations) and radius of gyration k.

Quick Summary

Treat many-particle bodies via centre of mass and torque. For fixed-axis rotation, dynamics mirror linear motion (Στ = Iα). Angular momentum is conserved without external torque. Moments of inertia quantify rotational inertia; use symmetry and standard results to solve quickly.

Practice Quiz (10 MCQs)

1) For two masses m and m at ±a on x-axis, CM is at:

2) Net external force is zero but net external torque is non-zero. Then:

3) Condition for complete static equilibrium is:

4) The rotational analogue of F = ma is:

5) Radius of gyration k for a body of mass M is defined by:

6) MI of a uniform rod (length L, mass M) about an axis through its centre and perpendicular to length is:

7) Angular momentum of a particle about origin is:

8) Power in pure rotation under torque τ and angular speed ω is:

9) When net external torque is zero, angular momentum about that axis is:

10) Parallel axis theorem (for a rigid body) states:

Downloads

Rotational Dynamics Formula Sheet (PDF) Common Moments of Inertia (PNG) CM & Torque Problems Set (PDF)

Cross-links

07 Gravitation

Mechanics Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Newton’s law of gravitation: F = G m₁m₂ / r²; universal constant G, acts along line joining centres, attractive force with infinite range.
Gravitational field & intensity: Field strength g = F/m = GM/r² (for point mass). Superposition applies.
Acceleration due to gravity (g): g at Earth’s surface = GM/R². Variation with altitude (g' ≈ g(1-2h/R)), depth (g' ≈ g(1-d/R)), and latitude (due to rotation).
Gravitational potential energy (U): U = −GMm/r; negative indicates bound state. ΔU = −∫F·dr.
Gravitational potential (V): V = U/m = −GM/r; scalar; work per unit mass to bring body from infinity.
Escape speed: vₑ = √(2GM/R); independent of mass of body. For Earth ≈ 11.2 km/s.
Orbital velocity: For satellite near Earth’s surface: v₀ = √(GM/R). Period T = 2π√(r³/GM).
Geostationary orbit: Circular orbit with period 24 h over equator, fixed relative to Earth’s surface; altitude ≈ 36000 km.
Weightlessness: Apparent weight zero in free fall (satellites, space station); g-effective = 0.
Problem cues: Distinguish U, V, and field; use conservation of mechanical energy in satellite motion; signs critical (negative PE).

Important Figures

Graph showing inverse square variation of gravitational force with distance — Inverse-square law: F ∝ 1/r²; field lines radial and symmetric.

Diagram showing derivation of escape velocity — Escape velocity: energy conservation to leave gravitational field.

Geostationary satellite orbit around Earth — Satellite motion: orbital speed, period, and geostationary orbit.

Quick Summary

Gravitation is a universal attractive force acting between all masses. Newton’s law gives F ∝ 1/r². Potential energy is negative for bound systems. Escape velocity and orbital parameters follow directly from conservation of mechanical energy and centripetal force relations.

Practice Quiz (10 MCQs)

1) Gravitational force between two masses is:

2) The value of G was first measured by:

3) Variation of g with height h (h≪R) is approximately:

4) Gravitational potential energy of two masses is negative because:

5) Escape velocity on Earth is about:

6) Weightlessness in a satellite is due to:

7) Orbital speed near Earth’s surface is approximately:

8) A geostationary satellite’s period is:

9) The potential at infinity is taken as:

10) Kepler’s third law states:

Downloads

Gravitation Formula Sheet (PDF) Variation of g Charts (PNG) Satellite Motion Practice Set (PDF)

Cross-links

08 Mechanical Properties of Solids

Properties of Matter Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Elasticity: Ability of a material to regain shape after deforming force is removed; perfectly elastic vs plastic idealisations.
Stress–strain: Stress = force per area (normal/shear); strain = fractional deformation (ΔL/L, ΔV/V, or shear γ). Hooke’s law (within elastic limit): stress ∝ strain.
Elastic moduli:
- Young’s modulus (Y): normal stress/linear strain (tension/compression of rods, wires).
- Bulk modulus (K): volumetric stress/volumetric strain (uniform compression).
- Shear modulus (η or G): shear stress/shear strain (qualitative idea).
- Poisson’s ratio (ν): lateral strain / longitudinal strain (0 ≤ ν < 0.5 for most solids).
Stress–strain curve (qualitative): Proportional limit → elastic limit → yield → ultimate tensile strength → fracture; slope in linear region ≈ Y.
Elastic potential energy: U = ½ kx² in a stretched spring; energy density in a stretched wire ≈ ½ (stress × strain).
Applications (qualitative): Material selection (stiffness vs toughness), bridges & cables, safety factors, springs, design against excessive strain.
Problem cues: Keep units consistent (Pa, N·m⁻²); choose correct modulus from boundary conditions; convert wire data to stress/strain; use series/parallel spring analogies where appropriate.

Important Figures

Qualitative stress–strain curve showing linear (Hooke’s law), yield, UTS and fracture regions — Qualitative stress–strain curve: elastic region, yield, UTS, fracture.

Schematic showing Young’s, bulk and shear deformation modes with definitions — Elastic moduli: Young’s (tension), bulk (volume), shear (shape change).

Illustration of Poisson’s effect and elastic energy density in a stretched wire — Poisson’s ratio (lateral vs longitudinal strain) and elastic energy density.

Quick Summary

Solids deform under applied forces; within the elastic limit, stress is proportional to strain (Hooke’s law). Young’s, bulk and shear moduli quantify stiffness for different deformations, while Poisson’s ratio links lateral and longitudinal strains. Elastic energy stored during deformation underpins many engineering applications.

Practice Quiz (10 MCQs)

1) Hooke’s law holds:

2) SI unit of stress is:

3) Young’s modulus is the ratio of:

4) Bulk modulus relates to change in:

5) Poisson’s ratio is defined as:

6) In the linear region of the stress–strain curve, the slope equals:

7) Elastic potential energy stored in a stretched spring of extension x is:

8) Which statement is qualitative only in the syllabus?

9) Energy density in a stretched wire (linear elasticity) is proportional to:

10) When a wire is stretched, its diameter reduces due to:

Downloads

Stress–Strain Curve (PDF) Elastic Moduli Quick Sheet (PNG) Elastic Energy Problems (PDF)

Cross-links

09 Mechanical Properties of Fluids

Properties of Matter Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Pressure due to a fluid column: For static fluids, p = p₀ + ρ g h. Pressure acts normal to surfaces and increases with depth (hydrostatic law).
Pascal’s law & applications: Pressure applied to an enclosed fluid is transmitted undiminished. Hydraulic lift and hydraulic brakes use area ratios to amplify force.
Effect of gravity on fluid pressure: In a gravitational field, pressure varies linearly with depth; free surface is an equipotential (horizontal) in equilibrium.
Viscosity: Internal friction in fluids; η (Pa·s). Stokes’ law for small spheres in laminar flow: F_visc = 6π η r v; terminal velocity when net force becomes zero.
Flow regimes: Streamline (laminar) vs turbulent flow; critical velocity (threshold for transition). Reynolds number as a guide (qualitative mention).
Bernoulli’s theorem: For incompressible, non-viscous, steady flow along a streamline: p + ½ρv² + ρgh = constant. Simple applications: Torricelli’s law (efflux v = √(2 g h)), dynamic lift (airfoils, spinning ball—Magnus effect, qualitative).
Surface energy & surface tension: Work required to create surface area; S.T. = force per unit length (N·m⁻¹). Angle of contact characterizes wetting.
Excess pressure across a curved surface: For a bubble (two surfaces), Δp = 4S/R; for a liquid drop (one surface), Δp = 2S/R.
Capillarity: Capillary rise/depression h = 2S cosθ/(ρ g r) (in thin tubes); dependence on tube radius and wetting (θ).
Problem cues: Identify regime (static vs steady flow); choose proper model (Bernoulli vs Stokes); mind units and assumptions (inviscid/steady/incompressible); use sign conventions for pressure differences.

Important Figures

Hydrostatic pressure increasing with depth in a fluid — Hydrostatic pressure: p = p₀ + ρgh; normal force on surfaces increases with depth.

Bernoulli tube and Torricelli efflux illustration — Bernoulli’s theorem and Torricelli’s law: faster flow → lower static pressure; v = √(2gh).

Surface tension forces, angle of contact, capillary rise — Surface tension & capillarity: angle of contact, excess pressure in drops/bubbles, capillary rise.

Quick Summary

Fluids at rest create hydrostatic pressure (ρgh), while moving fluids obey Bernoulli’s relation under ideal conditions. Viscosity governs drag and terminal velocity in laminar flow. Interfacial phenomena—surface tension, angle of contact, excess pressure, and capillarity—explain drops, bubbles, and wetting effects in daily life.

Practice Quiz (10 MCQs)

1) Hydrostatic pressure at depth h is:

2) Pascal’s law states that pressure applied to an enclosed fluid:

3) Stokes’ law for a sphere of radius r moving slowly in a viscous fluid is:

4) Bernoulli’s equation along a streamline (for ideal fluid) is:

5) Torricelli’s law gives efflux speed from a hole at depth h as:

6) Excess pressure inside a spherical drop (one interface) is:

7) In steady ideal flow through a constriction, the static pressure:

8) Terminal velocity occurs when:

9) Capillary rise in a narrow tube varies:

10) Dynamic lift on an airfoil is explained using:

Downloads

Hydrostatics & Bernoulli Formula Sheet (PDF) Stokes’ Law & Terminal Velocity Examples (PNG) Surface Tension & Capillarity Problems (PDF)

Cross-links

10 Thermal Properties of Matter

Properties of Matter Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Temperature & heat: Temperature measures thermal state (degree of hotness); heat is energy in transit due to temperature difference. Zeroth law defines thermal equilibrium and forms basis of thermometry.
Thermal expansion: For solids (approx. small changes): linear, area and volume expansion with coefficients α, β ≈ 2α, and γ ≈ 3α. Liquids show apparent expansion in a container; water exhibits anomalous expansion near 4 °C.
Specific heat capacity (c): Heat required per unit mass per degree rise: Q = m c ΔT. Molar heat capacity C = n c. (At this level, Cp/Cv distinction is qualitative for gases.)
Calorimetry & mixing: Thermal equilibrium uses heat balance: heat lost = heat gained (ignoring losses). Calorimeter principle; account for water equivalent if given.
Change of state & latent heat: During phase change temperature stays constant while heat is absorbed/released: Q = m L (L_f for fusion, L_v for vaporisation). Cooling/heating curves illustrate plateaus.
Heat transfer mechanisms:
- Conduction: Rate Q/t = k A (ΔT/L) in steady state; thermal conductivity k depends on material; composite slabs in series/parallel.
- Convection: Bulk motion of fluid transports heat; depends on buoyancy and flow (qualitative treatment).
- Radiation: Transfer via EM waves; blackbody concepts, emissivity e, absorptivity a, and qualitative Stefan–Boltzmann law P ∝ e A T⁴; Kirchhoff’s law (good absorbers are good emitters).
Newton’s law of cooling: For small temperature differences, rate of cooling is proportional to the temperature excess: dT/dt ∝ −(T − T_env).
Problem cues: Choose the correct model (Q = mcΔT vs Q = mL); watch units (°C vs K—differences are same); for conduction use thermal resistance analogies; in mixtures include calorimeter heat capacity if specified.

Important Figures

Linear, area and volume thermal expansion schematics — Thermal expansion: linear (α), area (β≈2α) and volume (γ≈3α) coefficients.

Heat balance diagram for mixing of hot and cold substances in a calorimeter — Calorimetry: heat lost = heat gained; include calorimeter’s water equivalent when given.

Conduction through composite slab and blackbody radiation schematic — Conduction rate Q/t = kAΔT/L; radiation power ~ eAT⁴ (qualitative), Newton’s law for small ΔT.

Quick Summary

Thermal properties link temperature, heat, and material response. Use expansion coefficients for size changes, Q = mcΔT and Q = mL in calorimetry and phase changes, and the appropriate transfer mechanism— conduction, convection, or radiation—to model heat flow. Newton’s law of cooling applies for small temperature gaps.

Practice Quiz (10 MCQs)

1) The zeroth law of thermodynamics establishes the concept of:

2) For small temperature changes in solids, the volume expansion coefficient γ is approximately:

3) Heat required to raise temperature of mass m by ΔT is:

4) During melting of ice at 0 °C, the heat supplied:

5) In steady one-dimensional conduction, the heat current is proportional to:

6) A good absorber at a given wavelength is, by Kirchhoff’s law, also a:

7) For small (T − T_env), Newton’s law of cooling predicts temperature falls:

8) The SI unit of specific heat capacity is:

9) If two slabs (k₁, L₁) and (k₂, L₂) are in series with equal area, the equivalent conductivity k_eq satisfies:

10) The heat needed to convert liquid at its boiling point to vapour at the same temperature is:

Downloads

Thermal Expansion & Calorimetry (PDF) Conduction–Convection–Radiation Cheat Card (PNG) Newton’s Law of Cooling Practice (PDF)

Cross-links

11 Thermodynamics

Thermal Physics Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Thermodynamic system & state variables: System, surroundings, boundary; macroscopic variables (P, V, T, U, S). Equation of state (ideal gas: PV = nRT).
Thermal equilibrium & Zeroth law: If A is in thermal equilibrium with B and B with C, then A and C are in equilibrium → defines temperature scale and thermometry.
Internal energy (U), heat (Q) & work (W): U is a state function; Q and W are path functions (energy in transit). Work by a gas in quasistatic process: W = ∫ P dV (area under P–V curve).
First law of thermodynamics: ΔU = Q − W (with W taken as work done by the system). Sign conventions matter.
Specific heats: C_V = (∂Q/∂T)_V, C_P = (∂Q/∂T)_P; for ideal gas, C_P − C_V = R and γ = C_P/C_V.
Thermodynamic processes: Isothermal (ΔT=0), adiabatic (Q=0), isobaric (ΔP=0), isochoric (ΔV=0); quasistatic vs non-quasistatic; reversible (idealised) vs irreversible (real).
Work/Heat in common processes (ideal gas):
- Isothermal: PV = constant; W = nRT ln(V₂/V₁).
- Adiabatic: PV^γ = constant; W = (P₁V₁ − P₂V₂)/(γ−1).
- Isochoric: W = 0, Q = ΔU = nC_VΔT.
- Isobaric: W = PΔV, Q = nC_PΔT.
Second law of thermodynamics: Clausius statement (heat doesn’t flow from cold to hot spontaneously) and Kelvin–Planck statement (no engine converts all heat into work in a cycle).
Heat engine & efficiency: η = W/Q_H = 1 − Q_C/Q_H. Refrigerator/heat pump performance via COP = Q_C/W or Q_H/W.
Carnot engine (ideal): Reversible cycle between T_H and T_C; maximum efficiency η_max = 1 − T_C/T_H (temperatures in kelvin); real engines have η < η_max.
Problem cues: Sketch P–V/T–S qualitatively; pick proper process model; apply sign convention consistently; use first law; for engines, track Q_H, Q_C, W over a complete cycle.

Important Figures

P–V curves for isothermal, adiabatic, isobaric and isochoric processes — P–V sketches: isothermal vs adiabatic (γ > 1 → steeper), isobaric and isochoric processes.

Schematic of a heat engine with reservoirs QH and QC and work output — Heat engine: absorbs Q_H at T_H, rejects Q_C at T_C, delivers work W; η = 1 − Q_C/Q_H.

Carnot cycle on a P–V diagram with two isotherms and two adiabats — Carnot cycle: two isotherms + two adiabats; ideal reversible engine, η_max = 1 − T_C/T_H.

Quick Summary

Thermodynamics links heat, work and internal energy via the first law, classifies processes by constraints (isothermal, adiabatic, etc.), and limits energy conversion through the second law. Carnot’s result sets an upper bound on engine efficiency determined solely by reservoir temperatures.

Practice Quiz (10 MCQs)

1) The first law of thermodynamics is:

2) For a reversible Carnot engine, efficiency equals:

3) In an isochoric process for an ideal gas:

4) For an ideal gas, C_P − C_V equals:

5) A process with Q = 0 is:

6) In an isothermal expansion of an ideal gas:

7) Kelvin–Planck statement forbids:

8) Work done by a gas in a quasistatic process equals:

9) The coefficient of performance (COP) of a refrigerator is:

10) For an adiabatic process of an ideal gas:

Downloads

Thermodynamics Formula Sheet (PDF) P–V Process Summary Cards (PNG) Carnot & Engines Practice Set (PDF)

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12 Kinetic Theory

Thermal Physics Weightage: Low Updated: 06 Sep 2025

Chapter Notes

Historical background: Boyle’s, Charles’s, and Avogadro’s laws; ideal gas equation PV = nRT; Avogadro number (N_A).
Molecular nature of matter: Atoms and molecules are in constant motion; collisions are elastic; intermolecular forces are negligible at large separations.
Kinetic theory assumptions:
- Gas is a collection of identical molecules in random motion.
- Volume of molecules negligible compared to container volume.
- No intermolecular forces except during elastic collisions.
- Collisions are perfectly elastic; obey Newton’s laws.
Derivation of pressure equation: P = (1/3) ρ ; where ρ is mass density and is mean square speed.
Kinetic interpretation of temperature: Mean translational KE per molecule is (3/2)k_BT, linking temperature with microscopic motion.
Degrees of freedom & specific heats: Energy equipartition theorem: each degree of freedom has energy (½k_BT). Monatomic (3), diatomic (5 at room T), polyatomic (6+); implications for C_V, C_P, and γ.
Mean free path: Average distance travelled between collisions; depends on number density and molecular diameter (λ ∝ 1/(√2 π d² n)).
Real gases: Deviations from ideality at high pressure/low temperature due to molecular volume and intermolecular forces (qualitative).
Problem cues: Use ideal gas law to convert between P, V, T; derive RMS speed v_rms=√(3kT/m); understand scaling with molecular mass and temperature.

Important Figures

Schematic of gas molecules in random motion colliding with walls — Kinetic theory model: gas as molecules in random motion; elastic collisions with walls explain pressure.

Maxwell-Boltzmann distribution curve of molecular speeds — Maxwell-Boltzmann distribution of speeds; most probable, average and rms speeds.

Diagram of translational, rotational, vibrational degrees of freedom — Degrees of freedom and energy contribution per mode (equipartition theorem).

Quick Summary

Kinetic theory links macroscopic properties of gases with microscopic motion. Pressure arises from elastic collisions; temperature is proportional to average kinetic energy. Degrees of freedom explain specific heats, and real gases deviate due to finite molecular size and attractions.

Practice Quiz (10 MCQs)

1) RMS speed of gas molecules is given by:

2) According to kinetic theory, pressure of an ideal gas is:

3) The mean kinetic energy of a molecule is:

4) Number of degrees of freedom for a linear diatomic molecule (room temperature) is:

5) Mean free path of a molecule varies:

6) Energy equipartition theorem assigns per degree of freedom:

7) Avogadro’s number (N_A) is approximately:

8) At high pressure and low temperature, real gases deviate due to:

9) The constant k in kinetic theory is:

10) Kinetic theory neglects:

Downloads

Kinetic Theory Summary (PDF) Maxwell Distribution Curve (PNG) Degrees of Freedom Quick Sheet (PDF)

Cross-links

Related: Thermodynamics · Oscillations

13 Oscillations

Oscillations Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Periodic & oscillatory motion: Motion that repeats after a fixed interval T; frequency f=1/T; angular frequency ω=2πf.
Simple Harmonic Motion (SHM): Restoring force proportional to displacement and directed towards mean position: F = −kx ⇒ x(t) = A sin(ωt+φ), with ω = √(k/m). Velocity v=ω√(A²−x²); acceleration a=−ω²x.
Energy in SHM: U=½k x², K=½k(A²−x²); total energy E=½kA² = ½mω²A² (constant). Exchange between K and U during oscillation.
Mass–spring systems: Horizontal/vertical SHM; for vertical spring, use extension at equilibrium x₀=mg/k, then small oscillations with same ω=√(k/m). Series/parallel springs: k_eq = (k₁k₂)/(k₁+k₂) (series), k_eq=k₁+k₂ (parallel).
Simple pendulum (small oscillations): T=2π√(L/g) for small angle; factors affecting period (L, g). Effective length includes suspension point to centre of bob.
Phase & superposition: Phase φ fixes initial state; superposition of two SHMs of same ω can yield a resultant SHM (phasor idea, qualitative).
Damped & forced oscillations (qualitative): Damping reduces amplitude over time; forced oscillations lead to steady state; resonance occurs when driving frequency ≈ natural frequency (large amplitude, limited by damping).
Problem cues: Identify mean position and restoring force; write equation of motion mẍ + kx = 0; use energy methods to get amplitude/turning points; check units (rad·s⁻¹) and small-angle approximation for pendulum.

Important Figures

Graphs of displacement, velocity, and acceleration vs time in SHM — SHM kinematics: x(t), v(t), a(t) with phase relations; a = −ω²x.

Mass–spring system and simple pendulum with period formulas — ω = √(k/m) for spring; T = 2π√(L/g) for small–angle pendulum.

Amplitude decay in damping and resonance peak under forced oscillation — Damped decay and resonance peak (qualitative) under external driving.

Quick Summary

Oscillations quantify periodic motion. In SHM, restoring force ∝ displacement, giving sinusoidal motion with ω = √(k/m). Energy swaps between kinetic and potential while total remains constant. Springs and pendulums are standard SHM models; damping and forcing introduce amplitude decay and resonance (qualitative).

Practice Quiz (10 MCQs)

1) In SHM, acceleration is proportional to:

2) The angular frequency of a mass–spring system is:

3) For SHM, velocity is maximum at:

4) Total energy in SHM equals:

5) The time period of a simple pendulum (small angle) is proportional to:

6) In vertical spring SHM, the equilibrium extension x₀ equals:

7) Series combination of two springs (k₁, k₂) has equivalent:

8) Resonance in a driven oscillator occurs when driving frequency equals:

9) Damping primarily affects:

10) The displacement in SHM can be written as x = A sin(ωt + φ). Here φ is:

Downloads

SHM Formula Sheet (PDF) Spring & Pendulum Problems (PDF) Damped/Forced Oscillations (PNG)

Cross-links

Related: Kinetic Theory · Waves

14 Waves

Oscillations & Waves Weightage: Medium Updated: 06 Sep 2025

Chapter Notes

Types of waves: Mechanical (require medium) vs electromagnetic (no medium). Mechanical waves can be transverse (oscillations ⟂ direction of propagation) or longitudinal (oscillations ∥ direction).
Displacement relation for a progressive wave: For a harmonic wave moving in +x, y(x,t) = A sin(kx − ωt + φ). Here A = amplitude, k = 2π/λ (wavenumber), ω = 2πf (angular frequency), phase speed v = ω/k = λf.
Wave on a stretched string: Speed v = √(T/μ), where T is tension and μ is linear mass density.
Sound waves in a fluid: Longitudinal; speed v = √(B/ρ) (≈ √(γP/ρ) for ideal gas), where B is bulk modulus, ρ density.
Principle of superposition: Net displacement equals vector (algebraic in 1D) sum of individual displacements. Interference patterns arise from superposition of coherent waves.
Reflection & transmission at boundaries (strings): Fixed end → inversion (phase shift π); free end → no inversion. Partial reflection/transmission at change of medium (μ, T).
Standing waves: Superposition of two counter-propagating waves of same f and λ: y = 2A sin(kx) cos(ωt). Nodes at sin(kx) = 0; antinodes at maxima of |sin(kx)|. Node–node spacing = λ/2; node–antinode = λ/4.
Normal modes in strings & air columns:
- String fixed at both ends (length L): fₙ = n·(v/2L), n = 1,2,3,… (harmonics).
- Open pipe (open–open): fₙ = n·(v/2L), n = 1,2,3,…
- Closed pipe (open–closed): fₙ = (2n−1)·(v/4L), n = 1,2,3,… (only odd harmonics).
Beats (qualitative): Superposition of two close frequencies produces intensity variations at beat frequency |f₁ − f₂|.
Doppler effect (qualitative): Apparent frequency changes due to relative motion of source and observer; increases on approach, decreases on recession.
Problem cues: Identify wave type and boundary conditions; use v = λf; for strings, compute μ and use √(T/μ); draw mode shapes to count nodes/antinodes; watch units.

Important Figures

Sine wave showing wavelength, amplitude and phase — Progressive harmonic wave: A, λ, k, ω and phase speed v = ω/k.

Standing wave pattern with nodes and antinodes on a string — Standing waves on a string: nodes/antinodes; node spacing λ/2.

Harmonics in open and closed organ pipes — Harmonics in air columns: open–open (all harmonics), open–closed (odd harmonics).

Quick Summary

Waves transport energy without transporting matter. A sinusoidal progressive wave is described by y(x,t)=A sin(kx−ωt+φ) with v=λf. Boundary conditions set up standing waves and discrete normal modes in strings and air columns. Superposition explains interference and beats; Doppler effect and reflection rules are treated qualitatively.

Practice Quiz (10 MCQs)

1) For a wave y=A sin(kx−ωt), the phase velocity v equals:

2) Transverse waves have particle motion:

3) Speed of a wave on a stretched string is:

4) In a standing wave, distance between two adjacent nodes is:

5) Frequencies of a string of length L fixed at both ends are:

6) For a closed pipe (one end closed), the allowed harmonics are:

7) Beat frequency produced by 256 Hz and 260 Hz tuning forks is:

8) At a fixed end of a string, the reflected wave undergoes:

9) The relation between v, f and λ is:

10) Doppler effect (qualitative) explains change in:

Downloads

Waves & Standing Waves Formula Sheet (PDF) Modes in Strings & Pipes (PNG) Wave Problems Set (PDF)

Cross-links

Related: Oscillations · Back to Unit Index