NCERT Solutions for Class 11 Physics - Free Latest PDF (2024-25)

Chapter 1- Units and Measurement

This chapter will clarify your concepts about what is a unit, base units, derived units, system of units, and much more. It will immensely help you to understand what is the need and value of the international system of units and how they are decided. Various methods such as the parallax method, parallax angle, and other methods to measure length and mass. This chapter also includes the Measurement of time, The precision of instruments and errors in measurement, Significant figures, Dimensions of physical quantities, Dimensional formulae, and dimensional equations.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of  Chapter 1 - Units and Measurement to crack your exams.

Dimensional Formula:

• Any physical quantity Q can be expressed as: $[Q] = M^a L^b T^c I^d$

Significant Figures:

• The number of digits in a measurement that is known reliably plus the first uncertain digit.

• Rules for Significant Figures:

• Non-zero digits are always significant.

• Any zeros between significant digits are significant.

• Leading zeros are not significant.

• Trailing zeros in a number containing a decimal point are significant.

Errors in Measurement:

• Absolute Error: $\Delta a = |a_{\text{mean}} - a_i|$

• Relative Error (or Fractional Error): $\delta a = \dfrac{\Delta a}{a_{\text{mean}}}$

• Percentage Error: $\text{Percentage Error} = \delta a \times 100\%$

• Sum or Difference: $\Delta Z = \Delta A + \Delta B$

• Product or Quotient: $\dfrac{\Delta Z}{Z} = \dfrac{\Delta A}{A} + \dfrac{\Delta B}{B}$

• Power: $\dfrac{\Delta Z}{Z} = n \dfrac{\Delta A}{A}$

Students can access extra study materials on the Units and Measurement, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 1

Chapter 2 - Motion in a Straight Line

This chapter is a part of the Kinematics and is a very interesting one. In the chapter, motion in a straight line, you will learn about the frame of reference, reference point, what is called path length, the magnitude of displacement, relative and velocity, instantaneous velocity, acceleration, retardation, etc. This chapter includes Position, path length, and displacement, Average velocity and average speed, Kinematic equations for uniformly accelerated motion, and Relative Velocity.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of Chapter 2 - Motion in a Straight Line to crack your exams.

• Displacement: A vector quantity representing the change in position of an object. It has both magnitude and direction.
  $\Delta x = x_2 - x_1$

• Average Velocity: $v_{\text{avg}} = \dfrac{\Delta x}{\Delta t}$

• Instantaneous Velocity: $v = \dfrac{dx}{dt}$

• Average Acceleration: $a_{\text{avg}} = \dfrac{\Delta v}{\Delta t}$

• Instantaneous Acceleration: $a = \dfrac{dv}{dt}$

• First Equation: $v = u + at$

• Second Equation: $s = ut + \dfrac{1}{2} at^2$

• Third Equation: $v^2 = u^2 + 2as$

• Uniform Motion: Motion with constant velocity (zero acceleration). The object covers equal distances in equal intervals of time.

• Non-uniform Motion: Motion with variable velocity (non-zero acceleration). The object covers unequal distances in equal intervals of time.

Students can access extra study materials on the Motion in a Straight Line, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 2

Chapter 3 - Motion in a Plane

In this chapter, you will learn how to measure motion in a plane and what are scalar and vector quantities. Topics like Position and displacement vectors, equality of vectors, and addition and subtraction of vectors through a graphical method are some of the primary topics explained in this chapter. This chapter includes the Multiplication of vectors by real numbers, the Resolution of vectors, Vector addition — analytical method, Motion in a plane, Relative velocity in two dimensions, Projectile motion, and Uniform circular motion.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of Chapter 3 - Motion in a Plane to crack your exams.

• Position Vector: $\mathbf{r} = x \hat{i} + y \hat{j} + z \hat{k}$

• Velocity Vector: $\mathbf{v} = \dfrac{d\mathbf{r}}{dt} = v_x \hat{i} + v_y \hat{j} + v_z \hat{k}$

• Acceleration Vector: $\mathbf{a} = \dfrac{d\mathbf{v}}{dt} = a_x \hat{i} + a_y \hat{j} + a_z \hat{k}$

• Projectile Motion:

• Horizontal Range: $R = \dfrac{v_0^2 \sin 2\theta}{g}$

• Time of Flight: $T = \dfrac{2 v_0 \sin \theta}{g}$

• Maximum Height: $H = \dfrac{v_0^2 \sin^2 \theta}{2g}$

• Equation of Trajectory: $y = x \tan \theta - \dfrac{g x^2}{2 v_0^2 \cos^2 \theta}$

• Uniform Circular Motion:

• Centripetal Acceleration: $a_c = \dfrac{v^2}{r}$

• Centripetal Force: $F_c = m \dfrac{v^2}{r}$

• Addition of Vectors:

• Resultant Vector: $\mathbf{R} = \mathbf{A} + \mathbf{B}$

• Magnitude of Resultant Vector: $R = \sqrt{A^2 + B^2 + 2AB \cos \theta}$

• Direction of Resultant Vector: $\tan \alpha = \dfrac{B \sin \theta}{A + B \cos \theta}$

Students can access extra study materials on the  Motion in a Plane, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 3

Chapter 4 - Law of Motion

This chapter includes Aristotle’s fallacy, The law of inertia, Newton’s first law of motion, Newton’s second law of motion, Newton’s third law of motion, Conservation of momentum, Equilibrium of a particle, Common forces in mechanics, and Circular motion. Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of  Chapter 4 - Law of Motion to crack your exams.

• Newton's First Law (Law of Inertia): An object will remain at rest or in uniform motion unless acted upon by an external force

• Newton's Second Law: $\mathbf{F} = m \mathbf{a}$

• Newton's Third Law: For every action, there is an equal and opposite reaction.
  $\mathbf{F}_{12} = -\mathbf{F}_{21}$

• Force due to Gravity: $F = mg$ 

• Frictional Force:

• Static Friction: $f_s \leq \mu_s N$

• Kinetic Friction: $f_k = \mu_k N$

• Tension in a String: For a string with a mass m hanging under gravity:
  $T = mg$

• Normal Force:

• On a horizontal surface: $N = mg$

• On an inclined plane: $N = mg \cos \theta$

• Centripetal Force: $F_c = \dfrac{mv^2}{r}$

Students can access extra study materials on the Law of Motion These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 4

Chapter 5 - Work, Energy and Power

You will also get to know the Scalar product and its distributive laws taught in this chapter which is the foundation for further complex concepts. This chapter includes  Notions of work and kinetic energy: The work-energy theorem, Kinetic energy, Work done by a variable force, The work-energy theorem for a variable force, The concept of potential energy, The conservation of mechanical energy, The potential energy of a spring, Various forms of energy, Power, and Collisions.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of Chapter 5 - Work, Energy and Power to crack your exams.

• Newton's First Law (Law of Inertia): An object will remain at rest or in uniform motion unless acted upon by an external force.

• Newton's Second Law: $\mathbf{F} = m \mathbf{a}$

• Newton's Third Law: For every action, there is an equal and opposite reaction.
  $\mathbf{F}_{12} = -\mathbf{F}_{21}$

• Force due to Gravity: $F = mg$

• Kinetic Friction: $f_k = \mu_k N$

• Tension in a String: $T = mg$

• Normal Force:

• On a horizontal surface: $N = mg$

• On an inclined plane: $N = mg \cos \theta$

• Centripetal Force: $F_c = \dfrac{mv^2}{r}$

• Work-Energy Theorem: $W = \Delta K = \dfrac{1}{2}mv_f^2 - \dfrac{1}{2}mv_i^2$

• Impulse: $J = \Delta p = F \Delta t$

Students can access extra study materials on Work, Energy and Power These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 5

Chapter 6 - Systems of Particles and Rotational Motion

This chapter explains the theoretical and mathematical parts of the concepts. The chapter includes concepts of the Centre of mass and its motion, Linear momentum of a system of particles, Vector product of two vectors, Angular velocity - Its relation with linear velocity, Torque, and angular momentum, Equilibrium of a rigid body, Moment of inertia

Theorems of perpendicular and parallel axes, Kinematics of rotational motion about a fixed axis, Angular momentum in case of rotation about a fixed axis, and Rolling motion.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of  Chapter 6 - Systems of Particles and Rotational Motion to crack your exams.

• Center of Mass:

• For a system of particles: $\mathbf{R} = \dfrac{\sum m_i \mathbf{r}_i}{\sum m_i}$

• For a continuous body: $\mathbf{R} = \dfrac{1}{M} \int \mathbf{r} \, dm$

• Moment of Inertia: $I = \sum m_i r_i^2$

• Parallel Axis Theorem: $I = I_{\text{cm}} + Md^2$

• Perpendicular Axis Theorem: $I_z = I_x + I_y$

Students can access extra study materials on Systems of Particles and Rotational Motion, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 6

Chapter 7 - Gravitation

Chapter 7 of Class 11 Physics, Gravitation, takes you into the depths of the concept of Gravitation. In this chapter, you will get a good grip on the technical basis of gravitation, the Universal law of gravitation, Kepler’s laws, Acceleration due to gravity of the earth, Acceleration due to gravity below and above the surface of the earth, the gravitational constant, Gravitational potential energy, Earth satellites, Escape speed, Energy of an orbiting satellite, Geostationary, and polar satellites and Weightlessness.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of  Chapter 7 - Gravitation to crack your exams.

• Newton's Law of Universal Gravitation: $F = G \dfrac{m_1 m_2}{r^2}$

• Gravitational Field Strength: $g = \dfrac{F}{m} = G \dfrac{M}{r^2}$

• Gravitational Potential Energy: $U = -G \dfrac{m_1 m_2}{r}$

• Gravitational Potential: $V = -G \dfrac{M}{r}$

• Escape Velocity: $v_e = \sqrt{\dfrac{2GM}{R}}$

• Orbital Velocity: $v_o = \sqrt{\dfrac{GM}{r}}$

• Acceleration due to Gravity at a Height hhh above the Earth's Surface: $g_h = g \left( \dfrac{R}{R + h} \right)^2$

• Total Energy of a Satellite in Orbit: $E = -\dfrac{GMm}{2r}$

Students can access extra study materials on Gravitation, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 7

Chapter 8 - Mechanical Properties of Solids

In the Mechanical properties of solids, you will study the physical properties of solids, such as plasticity, elasticity, and others. The fundamental properties of solids are readily available to learn in this chapter. Stress, compressive stress, tensile stress, longitudinal stress, tangential or shearing stress, shearing strain hydraulic stress, and volume strain are some of the concepts that will build the foundation for learning the properties of solids.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of Chapter 8 - Mechanical Properties of Solids to crack your exams.

• Stress:

• Tensile Stress: $\sigma = \dfrac{F}{A}$

• Strain:

• Longitudinal Strain: $\epsilon = \dfrac{\Delta L}{L}$

• Hooke's Law: $\sigma = E \epsilon$

• Young's Modulus: $E = \dfrac{\sigma}{\epsilon} = \dfrac{FL}{A \Delta L}$

• Shear Stress: $\tau = \dfrac{F}{A}$

• Shear Modulus (Modulus of Rigidity): $G = \dfrac{\tau}{\gamma}$

• Bulk Modulus: $K = -\dfrac{P}{\Delta V / V}$

Students can access extra study materials on the Mechanical Properties of Solids, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 8

Chapter 9 - Mechanical Properties of Fluids

In this chapter, you will study some common physical properties of liquids and gases. This chapter includes concepts of Pressure, Streamline flow, Bernoulli’s principle, Viscosity, and Surface tension. Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of  Chapter 9 - Mechanical Properties of Fluids to crack your exams.

• Density: $\rho = \dfrac{m}{V}$

• Pressure: $P = \dfrac{F}{A}$

• Pascal's Law: The pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of its container.
  $P = P_0 + \rho gh$

• Archimedes' Principle: The buoyant force FbF_bFb​ on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

• Equation of Continuity: $A_1 v_1 = A_2 v_2$

• Bernoulli's Equation: $P + \dfrac{1}{2} \rho v^2 + \rho gh = \text{constant}$

Students can access extra study materials on the Mechanical Properties of Fluids, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 9

Chapter 10 - Thermal Properties of Matter

In this chapter, you will learn the actual definition of heat and how it is measured. You will study the various processes by which heat flows. As you go further, you will find out the reason why blacksmiths heat the iron ring before fitting on the rim of a wooden wheel of a horse cart and why the wind at a sea beach often reverses its direction after the sun goes down. You will learn why its temperature does not change during these processes even though a great deal of heat is flowing into or out of it.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of  Chapter 10 - Thermal Properties of Matter to crack your exams.

• Heat (Q): $Q = mc\Delta T$

• Specific Heat Capacity (c): $c = \dfrac{Q}{m\Delta T}$

• Heat Capacity (C): $C = mc$

• Latent Heat (L):

• Heat required for a phase change: $Q = mL$

• Thermal Expansion:

• Linear Expansion: $\Delta L = L_0 \alpha \Delta T$

• Area Expansion: $\Delta A = A_0 \beta \Delta T$

• Volume Expansion: $\Delta V = V_0 \gamma \Delta T$

• Thermal Conductivity (k):

• Heat transfer through conduction: $Q = \dfrac{kA\Delta T}{d} t$

• Stefan-Boltzmann Law: $P = \sigma A T^4$

• Newton's Law of Cooling: $\dfrac{dT}{dt} = -k (T - T_{\text{env}})$

Students can access extra study materials on the Thermal Properties of Matter, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 10

Chapter 11 - Thermodynamics

Thermodynamics is a branch of physics that deals with the ideas of heat and temperature and the interconversion of heat and other forms of energy. In this chapter, you will study the concepts of Thermal equilibrium, Zeroth law of Thermodynamics, First law of thermodynamics, Specific heat capacity, Thermodynamic state variables and equation of state, Thermodynamic processes, Heat engines, Second law of thermodynamics, and Carnot engine.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of Chapter 11 - Thermodynamics to crack your exams.

• First Law of Thermodynamics: $\Delta U = Q - W$

• Work Done in Isothermal Processes:

• For an ideal gas: $W = nRT \ln \dfrac{V_f}{V_i}$

• Work Done in Adiabatic Processes: $W = \dfrac{P_i V_i - P_f V_f}{\gamma - 1}$

• Relation Between Pressure and Volume in Adiabatic Processes: $P V^\gamma = \text{constant}$

• Enthalpy (H): $H = U + PV$

• Second Law of Thermodynamics:

• Kelvin-Planck Statement:

• It is impossible to construct a heat engine that operates on a cyclic process and converts all the heat into work.

• Clausius Statement:

• It is impossible to construct a device that operates on a cyclic process and transfers heat from a colder body to a hotter body without any external work.

• Efficiency of a Heat Engine: $\eta = \dfrac{W}{Q_1} = 1 - \dfrac{Q_2}{Q_1}$

• Carnot Cycle Efficiency: $\eta = 1 - \dfrac{T_C}{T_H}$

• Gibbs Free Energy (G):$G = H - TS$

Students can access extra study materials on Thermodynamics, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 11

Chapter 12 - Kinetic Theory

You will learn the behaviour of gases based on the idea that gas consists of fast-moving atoms or molecules. This chapter also introduces kinetic theory. Concepts include the Molecular nature of matter, the Behaviour of gases, the Kinetic theory of an ideal gas, the Law of equipartition of energy , Specific heat capacity, and Mean free path.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of  Chapter 12 - Kinetic Theory to crack your exams.

• Ideal Gas Equation: $PV = nRT$

• Boltzmann Constant: $k_B = \dfrac{R}{N_A}$

• Root Mean Square Speed: $v_{\text{rms}} = \sqrt{\dfrac{3k_B T}{m}} = \sqrt{\dfrac{3RT}{M}}$

• Kinetic Energy of a Gas Molecule: $E_k = \dfrac{3}{2} k_B T$

• Pressure in Terms of Kinetic Theory: $P = \dfrac{1}{3} \rho v_{\text{rms}}^2$

• Law of Equipartition of Energy:

• The average energy associated with each degree of freedom: $\dfrac{1}{2} k_B T$

• Relation Between $C_p$ and $C_v$: $C_p - C_v = R$

Students can access extra study materials on the Kinetic Theory, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 12

Chapter 13 - Oscillations

Chapter 13, Oscillations, is an important and very interesting one. The chapter includes Periodic and oscillatory motions, Simple harmonic motion, Simple harmonic motion and uniform circular motion, Velocity and acceleration in simple harmonic motion, Force law for simple harmonic motion, Energy in simple harmonic motion, Damped simple harmonic motion, and Forced oscillations and resonance.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of  Chapter 13 - Oscillations to crack your exams.

• Simple Harmonic Motion (SHM):

• Equation of Motion: $x(t) = A \cos(\omega t + \phi)$

• Angular Frequency: $\omega = 2\pi f = \sqrt{\dfrac{k}{m}}$

• Frequency: $f = \dfrac{1}{T}$

• Period of SHM:

• For a Mass-spring System: $T = 2\pi \sqrt{\dfrac{m}{k}}$

• For a Simple Pendulum: $T = 2\pi \sqrt{\dfrac{L}{g}}$

• Displacement in SHM: $x(t) = A \cos(\omega t + \phi)$

• Velocity in SHM: $v(t) = -A \omega \sin(\omega t + \phi)$

• Potential Energy in SHM: $U = \dfrac{1}{2} k x^2 = \dfrac{1}{2} m \omega^2 x^2$

• Total Energy in SHM: $E = K + U = \dfrac{1}{2} k A^2 = \dfrac{1}{2} m \omega^2 A^2$

Students can access extra study materials on the Oscillations, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 13

Chapter 14 - Waves

This chapter will help you with concepts of waves and different types. This chapter will immensely help you in the conceptual study of Transverse and longitudinal waves, Displacement Relation in a Progressive Wave, Wavelength and Angular Wave Number, Amplitude and Phase, Period, Angular Frequency and Frequency, Speed of a Transverse Wave on Stretched String, The Speed of a Travelling Wave, Speed of a Longitudinal Wave (Speed of Sound), The Principle of Superposition of Waves, Reflection of Waves, and much more.

Class 11 NCERT solutions help the students to go through the formulas and concepts easily. Here find the Important formulas of  Chapter 14 - Waves to crack your exams.

• Wave Equation: $y(x,t) = A \sin(kx - \omega t + \phi)$

• Wave Number: $k = \dfrac{2\pi}{\lambda}$

• Angular Frequency: $\omega = 2\pi f$

• Speed of a Wave: $v = f \lambda = \dfrac{\omega}{k}$

• Principle of Superposition: When two or more waves overlap, the resultant displacement is the sum of the displacements of the individual waves.

• Standing Waves:

• Equation for Standing Wave: $y(x,t) = 2A \sin(kx) \cos(\omega t)$

• Wavelength and Frequency of Standing Waves on a String:

• Wavelength: $\lambda = \dfrac{2L}{n} \quad (n = 1, 2, 3, \ldots)$

• Frequency: $f = \dfrac{nv}{2L} \quad (n = 1, 2, 3, \ldots)$

• Sound Waves:

• Speed of Sound in a Medium: $v = \sqrt{\dfrac{B}{\rho}}$

Students can access extra study materials on the Waves, These resources are available for download, offering additional support for your studies.

Important Study Material Links for Class 11 Physics Chapter 14

CBSE Class 11 Physics Study Materials