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NCERT SolutionsClass 11 Physics
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NCERT Solutions
Class 11 Physics

15 chapters · 76 important questions · Updated 2025-26

Ch 1

Physical World

Introduces the scope and excitement of physics, covering its fundamental forces and their relative strengths. Students learn about the scientific method and how physics underpins all natural phenomena. The chapter surveys major sub-fields of physics from mechanics to cosmology. It emphasises the unity of physics and the role of hypothesis, experiment, and theory.

Key Topics

Four fundamental forces: gravitational, electromagnetic, strong nuclear, weak nuclearRelative strengths and ranges of fundamental forcesNature of physical laws: conservation of energy, momentum, chargeScope of physics: macroscopic, microscopic, mesoscopicPhysics and technology: historical milestonesReductionism and unification as goals of physics

⚠️ Deleted from Syllabus 2025-26

  • Physics, technology and society (detailed section removed from CBSE 2025-26 syllabus)
  • Detailed discussion of physicists' contributions and Nobel prizes (removed)
  • Excitement of physics — narrative portion (reduced to brief introduction only)

Important Questions

Q1

Name the four fundamental forces of nature. Which is the strongest and which is the weakest?

Short Answer2M
Q2

What do you mean by the scope of physics? Give two examples each from macroscopic and microscopic domains.

Long Answer3M
Q3

What is the principle of conservation of energy? State its universal applicability.

Short Answer2M
Q4

Distinguish between the gravitational force and the electromagnetic force in terms of their range and relative strength.

Long Answer3M
Ch 2

Units and Measurements

Covers the SI system of units, dimensional analysis, and significant figures. Students learn to express measurements with correct precision and use dimensional analysis for checking equations and deriving relations. Error analysis including absolute, relative, and percentage errors is a key exam topic.

Key Topics

SI base units: m, kg, s, A, K, mol, cd — definitionsDimensional formulae and dimensional equationsApplications of dimensional analysis: checking homogeneity, deriving formulasSignificant figures: rules for arithmetic operationsTypes of errors: systematic, random, gross; absolute error, relative error, percentage errorCombination of errors: addition, subtraction, multiplication, division, powersParallax method for measuring large distances; vernier calliper and screw gauge

Important Questions

Q1

What are the limitations of dimensional analysis?

Short Answer2M
Q2

The period of a simple pendulum depends on length l and acceleration due to gravity g. Using dimensional analysis, derive the formula for the time period.

Long Answer3M
Q3

The resistance R = V/I, where V = (100 ± 2) V and I = (10 ± 0.2) A. Find the percentage error in R.

Long Answer3M
Q4

Explain with an example how significant figures indicate the precision of a measurement.

Short Answer2M
Q5

Distinguish between systematic errors and random errors. How can each be minimised?

Long Answer3M
Ch 3

Motion in a Straight Line

Introduces kinematics of a particle moving along a straight line. Students study average and instantaneous velocity, uniform and non-uniform acceleration, and the three equations of motion. Graphical analysis using position-time and velocity-time graphs is essential for board exams.

Key Topics

Equations of uniformly accelerated motion: v = u + at; s = ut + ½at²; v² = u² + 2asDisplacement in nth second: sₙ = u + a(2n−1)/2Position-time graph: slope = velocity; velocity-time graph: slope = acceleration, area = displacementRelative velocity: v_AB = v_A − v_BFree fall: a = g = 9.8 m/s² downward; terminal velocity conceptInstantaneous velocity = lim(Δt→0) Δx/Δt = dx/dt

Important Questions

Q1

A ball is thrown vertically upward with velocity 49 m/s. Find (i) maximum height reached, (ii) time of flight. (g = 9.8 m/s²)

Long Answer3M
Q2

Draw velocity-time graphs for uniform motion and uniformly accelerated motion. How is displacement calculated from the v-t graph?

Long Answer3M
Q3

A car starts from rest and accelerates uniformly at 2 m/s². Find its velocity and displacement after 10 s.

Short Answer2M
Q4

Define instantaneous velocity. How is it different from average velocity?

Short Answer2M
Q5

Two trains A and B are moving in the same direction with speeds 80 km/h and 50 km/h respectively. Find the velocity of train A relative to train B.

MCQ / 1 Mark1M
Q6

Derive the three equations of uniformly accelerated motion using the velocity-time graph.

Long Answer5M
Ch 4

Motion in a Plane

Extends kinematics to two dimensions using vectors. Students learn vector addition, subtraction, and resolution into components. Projectile motion and uniform circular motion are the two major applications. Relative velocity in 2D is also covered.

Key Topics

Vector addition: triangle law, parallelogram law; resultant magnitude and directionResolution of vectors: A_x = A cos θ, A_y = A sin θScalar (dot) product: A·B = AB cos θ; vector (cross) product: |A×B| = AB sin θProjectile motion: T = 2u sinθ/g; R = u² sin 2θ/g; H = u² sin²θ/2gMaximum range at θ = 45°; R_max = u²/gUniform circular motion: centripetal acceleration a = v²/r = ω²r; v = rωAngular velocity ω = 2π/T; relationship v = rω

Important Questions

Q1

A projectile is launched with velocity 20 m/s at 30° to the horizontal. Find the maximum height, time of flight, and horizontal range. (g = 10 m/s²)

Long Answer5M
Q2

Prove that the trajectory of a projectile is parabolic.

Long Answer3M
Q3

Define centripetal acceleration. Derive an expression for centripetal acceleration for uniform circular motion.

Long Answer4M
Q4

Find the resultant of two vectors of magnitudes 3 N and 4 N acting at right angles to each other.

Short Answer2M
Q5

What is the angle of projection for which the horizontal range is equal to the maximum height?

Short Answer2M
Ch 5

Laws of Motion

Covers Newton's three laws of motion and their applications to everyday situations. Students study concepts of inertia, momentum, impulse, friction, and the dynamics of circular motion. Free body diagrams and solving problems involving multiple forces and constraints are central skills.

Key Topics

Newton's First Law: inertia; Newton's Second Law: F = ma; Newton's Third Law: action-reaction pairsLinear momentum: p = mv; impulse J = FΔt = ΔpConservation of linear momentum: ΣF_ext = 0 ⟹ Δp = 0Static friction f_s ≤ μ_s N; kinetic friction f_k = μ_k N; μ_s > μ_kFree body diagram: normal force, tension, friction, weightPseudo force in non-inertial framesMotion on inclined plane: a = g(sin θ − μ cos θ) for sliding

Important Questions

Q1

State Newton's Second Law of motion. How does it reduce to the First Law when F = 0?

Short Answer2M
Q2

A block of mass 5 kg is on a rough horizontal surface (μ_k = 0.3). A horizontal force of 25 N is applied. Find the acceleration. (g = 10 m/s²)

Long Answer3M
Q3

Derive the law of conservation of linear momentum from Newton's Third Law.

Long Answer3M
Q4

Explain why a person jumping from a moving bus should run in the direction of the bus after landing.

Short Answer2M
Q5

A bullet of mass 50 g moving at 400 m/s is embedded in a block of mass 950 g at rest. Find the common velocity after the collision.

Long Answer3M
Q6

What is the maximum acceleration with which a person can climb a rope if the rope can bear a maximum tension equal to 2/3 of his weight?

Long Answer3M
Ch 6

Work, Energy and Power

Introduces the scalar quantity work and its relationship with kinetic and potential energy. The work-energy theorem and conservation of mechanical energy are derived and applied. Elastic and inelastic collisions are analysed using energy and momentum principles.

Key Topics

Work done W = F·d = Fd cos θ; work by variable force W = ∫F dxKinetic energy KE = ½mv²; work-energy theorem: W_net = ΔKEPotential energy: gravitational PE = mgh; elastic PE = ½kx²Conservation of mechanical energy: KE + PE = constant (conservative forces)Power P = W/t = F·v; unit watts (W); 1 hp = 746 WElastic collision: both KE and momentum conserved; coefficient of restitution e = 1Perfectly inelastic collision: only momentum conserved; maximum KE loss

Important Questions

Q1

State and prove the work-energy theorem.

Long Answer4M
Q2

A spring of spring constant 1000 N/m is compressed by 10 cm. Find the elastic potential energy stored and the velocity of a 0.5 kg block when the spring is released.

Long Answer3M
Q3

Distinguish between elastic and inelastic collisions. Give one example of each.

Long Answer3M
Q4

An engine pumps 500 kg of water per minute to a height of 10 m. Find the power of the engine. (g = 10 m/s²)

Short Answer2M
Q5

Show that in an elastic head-on collision, two equal masses exchange velocities.

Long Answer3M
Ch 7

System of Particles and Rotational Motion

Extends mechanics to systems of particles and rigid bodies. Concepts of centre of mass, torque, angular momentum, and moment of inertia are introduced and applied. The parallel and perpendicular axis theorems are used to calculate moment of inertia for standard shapes.

Key Topics

Centre of mass: x_cm = Σm_i x_i / Σm_i; for uniform bodies — geometric centreTorque: τ = r × F; |τ| = rF sin θ; unit N·mAngular momentum L = r × p = Iω; conservation of L when τ_ext = 0Moment of inertia I = Σm_i r_i²; I for ring = MR², disc = ½MR², rod (centre) = ML²/12Parallel axis theorem: I = I_cm + Md²; perpendicular axis theorem (laminar bodies): I_z = I_x + I_yEquations of rotational motion: ω = ω₀ + αt; θ = ω₀t + ½αt²; ω² = ω₀² + 2αθRolling without slipping: KE_total = ½mv² + ½Iω² = ½mv²(1 + k²/R²)

Important Questions

Q1

State and prove the theorem of parallel axes for moment of inertia.

Long Answer3M
Q2

A solid sphere and a hollow sphere of the same mass and radius roll down an inclined plane without slipping. Which reaches the bottom first and why?

Long Answer4M
Q3

Derive an expression for the kinetic energy of a rolling body.

Long Answer3M
Q4

Find the moment of inertia of a thin uniform rod of mass M and length L about an axis through one end perpendicular to the rod.

Short Answer2M
Q5

A diver pulls in her arms while performing a somersault. Explain using the law of conservation of angular momentum why her rate of rotation increases.

Short Answer2M
Ch 8

Gravitation

Covers Newton's law of universal gravitation and its applications, including satellite motion, orbital and escape velocities, and Kepler's laws. Gravitational potential energy and the variation of g with altitude and depth are also studied.

Key Topics

Newton's law of gravitation: F = Gm₁m₂/r²; G = 6.67 × 10⁻¹¹ N m² kg⁻²Acceleration due to gravity: g = GM/R²; variation with altitude g' = g(1 − 2h/R) and depth g' = g(1 − d/R)Gravitational potential energy U = −GMm/rOrbital velocity: v_o = √(GM/r) = √(gR²/(R+h)); for near orbit v_o ≈ 7.9 km/sEscape velocity: v_e = √(2GM/R) = √(2gR) ≈ 11.2 km/s for EarthKepler's three laws: law of orbits (ellipse), law of areas (equal areas in equal time), law of periods T² ∝ r³Geostationary satellite: T = 24 h, height ≈ 36,000 km above equator

Important Questions

Q1

Derive an expression for the orbital velocity of a satellite. What is the orbital velocity for a satellite close to the Earth's surface? (g = 9.8 m/s², R = 6400 km)

Long Answer5M
Q2

State Kepler's laws of planetary motion. Derive Kepler's Third Law using Newton's law of gravitation.

Long Answer5M
Q3

How does acceleration due to gravity vary with (i) altitude and (ii) depth below the Earth's surface?

Long Answer3M
Q4

Calculate the escape velocity from the surface of the Earth. (g = 9.8 m/s², R = 6.4 × 10⁶ m)

Short Answer2M
Q5

What is a geostationary satellite? State two conditions for a satellite to be geostationary.

Short Answer2M
Ch 9

Mechanical Properties of Solids

Studies the elastic behaviour of solid materials under stress and strain. Students learn Hooke's law, Young's modulus, Bulk modulus, and Shear modulus. Stress-strain curves reveal proportionality limit, elastic limit, yield point, and breaking point.

Key Topics

Stress = F/A (N/m²); Strain = ΔL/L (dimensionless)Hooke's Law: stress ∝ strain (within elastic limit)Young's modulus Y = (F/A)/(ΔL/L) = FL/AΔL; unit Pa (N/m²)Bulk modulus B = −VΔP/ΔV; compressibility = 1/BShear modulus (rigidity modulus) G = shear stress/shear strainStress-strain curve: proportional limit, elastic limit, yield point, ultimate stress, fractureElastic potential energy stored in a wire: U = ½ × stress × strain × volume

Important Questions

Q1

Define Young's modulus, Bulk modulus, and Shear modulus. In which situation is each relevant?

Long Answer3M
Q2

A wire of length 2 m and cross-sectional area 10⁻⁶ m² is stretched by 1 mm under a force of 200 N. Find Young's modulus of the material.

Long Answer3M
Q3

Draw and explain the stress-strain curve for a ductile material. Mark all important points.

Long Answer4M
Q4

What is elastic fatigue? How does it affect the choice of materials in engineering?

Short Answer2M
Q5

Why are girders used in construction made in the I-shape cross-section?

Short Answer2M
Ch 10

Mechanical Properties of Fluids

Covers the behaviour of fluids at rest (hydrostatics) and in motion (hydrodynamics). Pressure in fluids, Pascal's law, Archimedes' principle, and Bernoulli's theorem are derived and applied. Surface tension, capillarity, and viscosity complete the chapter.

Key Topics

Pressure: P = F/A; pressure in a fluid: P = P₀ + ρgh; Pascal's lawArchimedes' principle: buoyant force = weight of displaced fluidEquation of continuity: A₁v₁ = A₂v₂ (for incompressible flow)Bernoulli's equation: P + ½ρv² + ρgh = constantApplications of Bernoulli's theorem: venturimeter, aerofoil lift, Torricelli's theoremSurface tension T = F/L; excess pressure inside drop: ΔP = 2T/r; bubble: ΔP = 4T/rViscosity: Stokes' law F = 6πηrv; terminal velocity v_t = 2r²(ρ−σ)g/9η

Important Questions

Q1

State and derive Bernoulli's theorem. List two applications of Bernoulli's principle.

Long Answer5M
Q2

A raindrop of radius 1 mm falls with terminal velocity 5 m/s. Find the coefficient of viscosity of air. (ρ_water = 10³ kg/m³, ρ_air ≈ 0)

Long Answer3M
Q3

Prove that the excess pressure inside a soap bubble is 4T/r.

Long Answer3M
Q4

Water flows through a pipe of diameter 4 cm at 2 m/s. It narrows to 2 cm diameter. Find the velocity in the narrower section.

Short Answer2M
Q5

State Archimedes' principle. A solid of mass 500 g has an apparent weight of 4.5 N when fully submerged in water. Find its volume. (g = 10 m/s²)

Long Answer3M
Ch 11

Thermal Properties of Matter

Covers temperature measurement, thermal expansion, specific heat, calorimetry, and modes of heat transfer. Students study linear, superficial, and volumetric expansion, latent heat, Newton's law of cooling, and the mechanisms of conduction, convection, and radiation.

Key Topics

Thermal expansion: linear α = ΔL/LΔT; superficial β = 2α; volumetric γ = 3αAnomalous expansion of water: maximum density at 4°CSpecific heat capacity c = Q/mΔT; molar specific heat C = McCalorimetry: heat gained = heat lost; Q = mcΔT; latent heat Q = mLConduction: H = kA(T₁−T₂)/d; k = thermal conductivity (W/m K)Newton's law of cooling: dT/dt ∝ (T − T₀); rate of coolingStefan's law: E = σT⁴; Wien's displacement law: λ_m T = b = 2.898 × 10⁻³ m K

Important Questions

Q1

A steel rod of length 1 m is heated from 20°C to 120°C. Find the increase in length. (α_steel = 1.2 × 10⁻⁵ /°C)

Short Answer2M
Q2

State Newton's law of cooling. A body cools from 80°C to 60°C in 5 minutes. How long will it take to cool from 60°C to 40°C in a room at 20°C?

Long Answer4M
Q3

Distinguish between conduction, convection, and radiation. Give two examples of each.

Long Answer3M
Q4

Define specific heat capacity and latent heat. 200 g of water at 80°C is mixed with 100 g of water at 20°C. Find the final temperature.

Long Answer3M
Q5

What is the anomalous expansion of water? What is its significance in nature?

Short Answer2M
Ch 12

Thermodynamics

Introduces the zeroth, first, and second laws of thermodynamics. Students study various thermodynamic processes (isothermal, adiabatic, isochoric, isobaric), heat engines, refrigerators, and the concept of entropy. Carnot's cycle and its efficiency are essential board topics.

Key Topics

Zeroth law: thermal equilibrium and temperature definitionFirst law: ΔU = Q − W; sign convention for Q and WIsothermal process: ΔT = 0, ΔU = 0, Q = W; W = nRT ln(V₂/V₁)Adiabatic process: Q = 0, ΔU = −W; PVᵞ = constant; γ = C_p/C_vSecond law: Kelvin-Planck statement; Clausius statement; irreversibilityCarnot engine efficiency: η = 1 − T₂/T₁; Carnot theorem: no engine is more efficient than CarnotEntropy: ΔS = Q_rev/T; entropy increases in irreversible processes

Important Questions

Q1

State the first law of thermodynamics. Apply it to (i) isothermal and (ii) adiabatic processes.

Long Answer4M
Q2

Describe the Carnot cycle. Derive an expression for the efficiency of a Carnot engine.

Long Answer5M
Q3

State the second law of thermodynamics in two different ways. Show that they are equivalent.

Long Answer3M
Q4

A Carnot engine operates between 727°C and 27°C. Find its efficiency and the heat rejected to the sink for every 1000 J of heat absorbed.

Long Answer3M
Q5

What is the coefficient of performance (COP) of a refrigerator? How is it related to the efficiency of a heat engine?

Short Answer2M
Ch 13

Kinetic Theory

Develops the kinetic theory of gases to explain macroscopic properties (pressure, temperature, specific heat) in terms of molecular motion. Students derive the pressure of an ideal gas, the kinetic interpretation of temperature, and the law of equipartition of energy.

Key Topics

Assumptions of kinetic theory: elastic collisions, negligible volume, no intermolecular forcesPressure of ideal gas: P = ⅓ρv²_rms = ⅓(Nm/V)v²_rmsrms speed: v_rms = √(3RT/M) = √(3kT/m); mean speed: v̄ = √(8RT/πM); most probable: v_p = √(2RT/M)Kinetic interpretation of temperature: ½mv²_rms = (3/2)kTEquipartition of energy: each degree of freedom has energy ½kT; monatomic f = 3, diatomic f = 5 (rigid), 7 (non-rigid)Specific heats: C_v = (f/2)R; C_p = C_v + R; γ = C_p/C_v = (f+2)/fMean free path λ = 1/(√2 πd²n); Avogadro's number N_A = 6.023 × 10²³

Important Questions

Q1

Derive an expression for the pressure exerted by an ideal gas using kinetic theory. Hence obtain the kinetic interpretation of temperature.

Long Answer5M
Q2

State the law of equipartition of energy. Using it, find C_v and C_p for a diatomic gas and calculate γ.

Long Answer4M
Q3

Calculate the rms speed of nitrogen molecules at 27°C. (M = 28 g/mol, R = 8.31 J mol⁻¹ K⁻¹)

Short Answer2M
Q4

What is mean free path? On what factors does it depend?

Short Answer2M
Q5

At what temperature will the rms speed of oxygen molecules be equal to the rms speed of hydrogen molecules at 300 K?

Long Answer3M
Ch 14

Oscillations

Covers simple harmonic motion (SHM) as a fundamental type of periodic motion. Students derive equations for displacement, velocity, and acceleration in SHM, and study simple pendulums, spring-mass systems, and energy in SHM. Damped, free, forced oscillations, and resonance are also covered.

Key Topics

SHM: x = A sin(ωt + φ); v = Aω cos(ωt + φ); a = −ω²x (restoring acceleration)Angular frequency ω = 2π/T = 2πf; ω = √(k/m) for spring-massSimple pendulum: T = 2π√(L/g); valid for small anglesSpring-mass system: T = 2π√(m/k); springs in parallel k_eff = k₁ + k₂; series 1/k_eff = 1/k₁ + 1/k₂Energy in SHM: KE = ½mω²(A²−x²); PE = ½mω²x²; total E = ½mω²A² = constantDamped oscillations: amplitude decays as A e^(−bt/2m)Resonance: maximum amplitude when driving frequency = natural frequency

Important Questions

Q1

Derive expressions for displacement, velocity, and acceleration of a particle in SHM. Show that acceleration is proportional to displacement and directed towards the mean position.

Long Answer5M
Q2

Show that total energy of a particle in SHM is constant. How does it vary with displacement?

Long Answer4M
Q3

Find the period of a spring-mass system with spring constant 200 N/m and mass 0.5 kg.

Short Answer2M
Q4

What is resonance? Give two examples of resonance — one beneficial and one harmful.

Long Answer3M
Q5

The time period of a simple pendulum is 2 s on Earth's surface. What will be its period on a planet where g is half of Earth's g?

Short Answer2M
Ch 15

Waves

Covers transverse and longitudinal waves, their properties, and the wave equation. Students study the superposition principle, stationary waves, normal modes in strings and pipes, and the Doppler effect. Newton's formula for speed of sound and Laplace's correction are important exam topics.

Key Topics

Wave equation: y = A sin(kx − ωt); wave speed v = ω/k = λ/T = fλSpeed of transverse wave in string: v = √(T/μ); where μ = linear mass densitySpeed of longitudinal wave (sound): v = √(B/ρ); Newton's formula v = √(P/ρ); Laplace correction: v = √(γP/ρ)Principle of superposition: y = y₁ + y₂Standing waves in string: nodes and antinodes; λₙ = 2L/n; fₙ = nv/2LBeats: beat frequency = |f₁ − f₂|; used for tuning instrumentsDoppler effect: f' = f(v ± v_o)/(v ∓ v_s); cases for approach and recession

Important Questions

Q1

Derive Newton's formula for speed of sound in a gas. What correction did Laplace make and why?

Long Answer4M
Q2

Explain the formation of standing waves. Derive the frequencies of normal modes for a string fixed at both ends.

Long Answer5M
Q3

State the Doppler effect. Derive the general formula for apparent frequency when both source and observer are moving.

Long Answer5M
Q4

Two sound waves of frequencies 512 Hz and 516 Hz are superimposed. Find the beat frequency.

MCQ / 1 Mark1M
Q5

A string of length 0.5 m and linear mass density 10⁻³ kg/m is under tension 8 N. Find the fundamental frequency.

Long Answer3M

Frequently Asked Questions

Is NCERT enough for CBSE Class 11 Physics board exam?

Yes. CBSE board exams are designed entirely around NCERT. 80–90% of questions in the Class 11 Physics paper are directly based on NCERT concepts — sometimes reworded, never from outside NCERT. Completing all 76 important questions listed here is the minimum you need.

How to study NCERT Class 11 Physics for board exams?

Go chapter-by-chapter. Read the chapter first, then attempt the important questions without looking at answers. Check your answer structure — CBSE gives marks per point, so structure matters as much as content. For 5-mark answers: brief intro + 4–5 numbered points with keywords + conclusion.

Which chapters are most important in Class 11 Physics for CBSE boards?

Chapters with the most long-answer (5-mark) important questions carry the most marks in the board paper. Look at which chapters here have the highest question count — those are the ones CBSE has historically focused on. Don't skip any chapter, but spend extra time on these.

How many questions come from NCERT in CBSE Class 11 Physics exam?

Nearly all 76 questions in the Class 11 Physics board paper are rooted in NCERT. The exact question may be reworded, but the concept, definition, or formula always comes from the NCERT textbook. Practicing these 76 important questions covers the vast majority of what can be asked.