NCERT Solutions for Class 11 Physics

NCERT Solutions for Class 11 Physics has been formulated to help students understand difficult physics concepts with ease. Physics in 11th Class is a challenging subject that tests the skills and mental aptitude of the students. Therefore, scoring good marks in the subject requires you to follow a methodical approach and a proper preparation strategy.

NCERT Solutions prepared by Goprep’s expert teachers are focussed on addressing the challenges that students face while preparing complex Physics topics. These solutions are aimed at helping students understand course material properly and solve complex problems quite easily. So, if you are studying from our NCERT Physics Class 11 Solutions, you don't need to worry as these solutions are reliable and error-free.

NCERT Class 11 Physics Solutions - All Chapters

NCERT Solutions for Class 11 Physics that we provide include chapter-wise explanations for all the important topics. The topics such as Units, Measurements, Motion in a Straight Line & Plane, Rotational Motion, Work, Energy & Power, and Mechanical Properties are explained in detail. More importantly, the CBSE 11th Class Physics Solutions from us are free of cost and can be accessed without any hassle.

Students who have utilized our NCERT CBSE 11th Class Physics Solutions have had an impressive rise in their overall marks in the Physics exam. So, if you are looking forward to practicing chapter-wise NCERT Physics Book of Class 11 you can click on the given above. 

NCERT Class 11 Solutions for Physics (Part 1)

Chapter 1: Physical World

Introduction: As you are now a Science student, it is necessary that you must know about the scope of Physics, different branches of Physics in relation to other Sciences, and major contributions or discoveries in the field of Science. 

After going through NCERT Class 11 Physics Solutions for chapter-1, you will be aware of different branches of Physics such as Electromagnetism, Mechanics, Modern Physics, Thermodynamics, etc. Further, you will learn the following topics with the help of our NCERT solutions. 

Topics

• Science and Scientific Methods
• Physics and its Scope
• Physics in Relation to other Sciences
• Major Contributions and Discoveries by Physicists 

Chapter 2: Units and Measurements

Introduction: The second chapter of the NCERT Class 11 Physics textbook “Physical World” consists of topics that will allow you to learn this subject from scratch. In day-to-day life, we often discuss the measurement of different things. We can compare any physical quantity with its standard unit. 

As you delve deeper into this chapter, you will learn fundamental units of various fundamental quantities. Also, you will study four systems of units, among which the SI system is applicable universally. Dimensions is another crucial topic that is useful for knowing the amount of a physical quantity.

View the complete list of topics covered in Class 11 Physics chapter 2 below.

 Topics

• Measurement
• Physical Quantities 
• Units
• Fundamental Units
• Systems of Units
• Relationship between Some Mechanical SI Unit and Commonly Used Units
• Dimensions
• Homogeneity Principle
• Significant Figures
• Error

Important formulas/ values

1. 1 astronomical unit = 1.49 x 10¹¹ m (average distance between the sun and earth)
2. 1 fermi =10^-15 m
3. 1 light year = 9.46 x 10¹⁵ m
4. 1 parsec = 3.08 x 10¹⁶ m = 3.26 light year
5. 1 X-ray unit = 10^-13 m

Chapter 3: Motion in a Straight Line

Introduction: In chapter-3 “Motion in a Straight Line”, you will first revisit the basic terminologies and concepts that you learnt in NCERT Class 9 Science textbook chapter-8 “Motion”. You must be familiar with three types of motion, which are linear, circular and oscillatory. In class 9, you also learn to distinguish between distance/ displacement, speed/ velocity, and uniform/ non-uniform acceleration. 

In class 11, you will learn to plot kinematical graphs. Recall displacement-time and velocity-time graphs from class 9 textbook; we obtained the path of a particle moving in a linear motion. Finally, you will derive three equations of motion and deduce them to obtain some important formulas. 

Below is the list of topics that you will deal with in chapter-3.

Topics

• Point Object and Reference Systems
• Distance and Displacement
• Types of Motion
• Velocity and Speed
• Uniform Speed and Uniform Velocity
• Variable Speed and Variable Velocity
• Average Speed and Average Velocity
• Acceleration and Uniform Acceleration
• Kinematical Graphs
• Equations of Motion
• Relative Velocity

Important formulas of “Motion in a Straight Line”

1. Velocity (V) = Displacement/ Time

2. Speed (S) = Distance/ Time

3. Average Speed (V_av) = Total distance/ Total time taken

4. Average Velocity = Total displacement/ Total time taken

5. Acceleration (a) = Change in velocity/ Time taken

6. Instantaneous Speed = lim _{(∆t → 0)} (∆x/ ∆t) 

7. Instantaneous Acceleration = lim _{(∆t → 0)} (∆v/ ∆t) 

8. Equations of Motion 

(a). v = u + at

Some more important formulas:

1. Equation for uniformly accelerated motion along a straight line, where displacement in a particular instant of time (nth second of the motion) is given by 
    s_nth = u + ½ a (2n - 1)

2. Suppose a body is thrown vertically upwards with an initial velocity (u), then
(a). The maximum height obtained by the body = H = u²/ 2g
(b). The total time to go up and return to the point of projection = 2u/ g

Chapter 4: Motion in a Plane

Introduction: In continuation to what you studied in chapter-3, chapter-4 “Motion in a Plane” contain topics based on motion in two dimensions. To analyse the motion of an object in two-dimensions, you must be well-versed with vectors. So far, you know about scalar and vector quantities. In this class, you will study characteristics of vectors, types of vectors, and various other topics given below. 

Topics

• Motion
• Scaler and Vector Quantities
• Characteristics of Vectors
• Types of Vectors
• Parallelogram Law of Vector Addition
• Triangle Law of Vector Addition
• Polygon Law of Vector Addition
• Properties of Vector Addition
• Resolution of Vectors
• Position Vector
• Multiplication of Vectors
• Properties of Scalar Product
• Properties of Cross Product
• Lami’s Theorem
• Projectile Motion
• Angular Displacement
• Angular Velocity
• Angular Acceleration
• Uniform Circular Motion
• Centripetal Acceleration

Important formulas of “Motion in a Plane”

Parallelogram Law of Vector Addition

1. If A and B are two adjacent sides of a parallelogram and making an angle 𝛉, then the resultant vector is given by R. 

    Where R = √(A2 + B2 + 2AB Cos𝛉)

2. Direction of Resultant = ɑ = tan^-1 {(BSin𝛉)/ (A + BCos𝛉)} 

Lami’s Theorem

(P/ Sin Ꞵ) = (Q/ Sin γ) = (R/ Sin ɑ)

Projectile Motion

1. Trajectory of a projectile = Y = [(tan 𝛉) x - {(g/ 2(u Cos 𝛉)²} x²]

2. Time of Flight = T = 2u Sin 𝛉/ g

3. Horizontal Range = R = u² Sin 2𝛉/ g

4. Maximum Height = H = u² Sin²𝛉/ 2g

Chapter 5: Laws of Motion

Introduction: Sir Isaac Newton, a great physicist, coined the term force. Force is responsible for bringing a body into motion or rest. It is of two types- balanced force and unbalanced force. Force can also change the direction, speed or shape of a body. 

In this chapter, you will study various familiar topics from earlier NCERT textbooks. These include Newton’s three laws of motion, linear momentum, the law of conservation of momentum etc. 

Check out the complete list of topics that will be covered in this chapter below. 

Topics

• Force
• Newton’s Laws of Motion
• Linear Momentum
• Impulse
• Law of Conservation of Momentum
• Concurrent Forces and Equilibrium
• Simple Pulley
• Apparent Weight and Actual Weight
• Friction
• Laws of Friction
• Angle of Friction & Angle of Repose
• Centripetal Force
• Centrifugal Force
• Motion in a Vertical Circle

Important formulas of “Laws of Motion”

1. Force = Mass x  Acceleration

2. Linear Momentum = Mass x Velocity

3. Impulse = I = ∫ F dt

4. Law of Conservation of Momentum = F_ext = 0, Σⁿ_{i= 1} P_i = constant

5. Tension in the string of a pulley can be obtained by T, Where T = (2 m₁ m₂ g)/ (m₁ + m₂)

6. Magnitude of kinetic frictional force = f_k = μ_k N

7. Coefficient of friction = μ = limiting frictional force (F)/ normal reaction R

8. Angle of Friction = 𝛉 = tan^-1 μ

9. Angle of Repose = ɑ = tan^-1 μ

10. Centrifugal Force = F = mv²/ r = mr⍵²

Chapter 6: Work, Energy and Power

Introduction: From earlier NCERT textbooks, you already have an idea about Work and Energy. In class 11, you will build up your knowledge based on your previous learning. For instance, you will derive the equation for ‘work done due to applied force that varies with time or position’. 

Later in the chapter, you will find questions based on the law of conservation of energy, power, the law of conservation of momentum, to name some. NCERT Class 11 Physics exercise solutions will also include solved questions based on the following topics.

Topics

• Work done
• Energy
• Types of Energy
• Work- Energy Theorem
• Law of Conservation of Energy
• Power
• Elastic and Inelastic Collisions in Two Dimensions
• Coefficient of Restitution/ Resilience
• Conservative and Non-Conservative Forces

Important formulas of “Work, Energy and Power”

1. Work Done (W) = FS Cos 𝛉

2. Equation of work done when an applied force changes with time or position is given by

    W = ∫ F. ds

3. Work Energy Theorem

W = Change in K.E. of a body = ∆ K.E.

4. Equivalence of Mass and Energy = E = mc² where, c = 3 x 10⁸ ms^-1

5. Power = P = dW/ dt = F v Cos ɑ

Chapter 7: System of Particles and Rotational Motion

Introduction: Having learnt the core concepts such as vectors and inertia, chapter-7 “System of Particles and Rotational Motion” will not be much challenging. At the beginning of this chapter, you will learn to derive the equation for the centre of mass of a two-particle system. Using a similar approach, you can obtain equations for velocity and acceleration of the centre of mass. 

In the latter half of this chapter, you will come across important terminologies such as torque, angular momentum, the moment of inertia, the radius of gyration, and more. 

Our subject-matter experts have enlisted all the topics that are part of this chapter below.

Topics

• Centre of Mass
• Motion of Centre of Mass
• Vector Product or Cross Product of two vectors
• Torque
• Angular Momentum
• Axis of Rotation
• Moment of Inertia
• Radius of Gyration
• Theorem of Parallel and Perpendicular Axes
• Rolling Motion
• Law of Conservation of Angular Momentum

Important formulas of “System of Particles and Rotational Motion”

1. Centre of Mass

• The position vector of the centre of mass of a two-particle system can be represented as- r_cm = (m₁r₁ + m₂r₂)/ (m₁ + m₂)

• The velocity of the centre of mass of a two-particle system can be represented as- V_cm = (m₁v₁ + m₂v₂)/ (m₁ + m₂)

• The acceleration of the centre of mass of a two-particle system can be represented as- a_cm = (m₁a₁ + m₂a₂)/ (m₁ + m₂)

2. Torque or Moment of force (Ꞇ) = force x perpendicular distance = rF Sin 𝛉 n

3. Moment of Inertia (I) = m₁r₁² + m₂r₂² + ……… + m_nr_n² = Σⁿ_i=1 m_ir_i²

4. Radius of Gyration (K) = √{(r₁² + r₂² + ……… + r_n²)/ n}

Chapter 8: Gravitation

Introduction: One fine day, a physicist named Isaac Newton was sitting under a tree and was struck by an apple on his head. Following this incident, he began his research on finding the logic behind apple falling down and not going up. After careful analysis, he concluded that the gravitational force of Earth was responsible for attracting the apple towards itself. 

A free-falling object under the influence of gravitational force changes its velocity at different time periods. As a result, the free-falling object towards the Earth is said to have achieved ‘acceleration due to gravity’. 

Below is the complete list of topics that are part of NCERT Class 11 Physics book. 

Topics

• Keplar’s Law of Planetary Motion
• Newton’s Law of Gravitation
• Principle of Superposition of Gravitation
• Acceleration due to Gravity
• Variation of Acceleration due to Gravity
• Gravitation Field and its Intensity
• Gravitational Potential
• Gravitational Potential Energy
• Satellite
• Orbital Velocity
• Geostationary Satellite

Important formulas of “Gravitation”

1. Newton’s Law of Gravitation
    F = G m₁m₂/ r²

2. Relation between ‘G’ and ‘g’
    g = GM/ R²

3. Variation of Acceleration Due to Gravity

(a). Effect of Altitude: Value of acceleration due to gravity at a height (h) from the surface of Earth is given by-

      gh = g/ {1 + (h/ R)}²

      If h << R, then g_h = g/ {1 - (2h/R)} (Using the Binomial Theorem)

(b). Effect of depth: The value of acceleration due to gravity at a depth (d) is given by-

      g_d = g {(1 - (d/R)}, where d → depth

(c). Effect due to the rotation of Earth: The acceleration due to gravity decreases with rotation and increases with the increase in latitude. It is given by- 

      g_𝛉 = g {1 - (R⍵²/g) cos²𝛉}, where, 𝛉 → latitude of the point

4. Gravitational Potential

The Gravitational Potential is represented by (V)

V = - GM/ r

5. Gravitational Potential Energy

The gravitational potential energy of a system is given by = -GMm/ r

6. Escape Velocity

    V_e = √2GM/ R = √2gR

NCERT Solutions for Class 11 Physics (Part 2)

Chapter 9: Mechanical Properties of Solids

Introduction: There are five states of matter- solid, liquid, gas, plasma and Bose-Einstein condensate. In chapter-9 of NCERT Class 11 Physics textbook, you will gain knowledge about various mechanical properties of solids, such as elasticity, plasticity, rigidity etc. Next, you will learn to obtain expressions for Young’s modulus, Shear modulus, and Bulk modulus. 

There are a total of 21 questions in chapter-9 exercise from the following topics:

Topics

• Elasticity
• Plasticity
• Stress
• Strain
• Hooke’s Law
• Stress-Strain Curve
• Young’s Modulus
• Bulk Modulus
• Shear Modulus
• Poisson’s Ratio
• Elastic Fatigue
• Breaking Stress

Important formulas of “Mechanical Properties of Solids”

1. Stress = Force (F)/ Area (A)
2. Strain = Change in length/ original length
3. Hooke’s law (Modulus of elasticity) = Stress/ Strain
4. Young’s Modulus (Y) = (F/A) / (∆l/ l) = Fl/ A.∆l = mgl/ πr².∆l
5. Bulk modulus (B) = (F/A) / (∆V/ V) = =p/ ∆V/ V
6. Shear Modulus (ɳ) = Tangential Stress/ Shear Strain = (F/A)/ 𝛉
7. Poisson’s Ratio = Lateral Strain/ Longitudinal Strain = -(∆D/ D) / (∆l/ l)

Chapter 10: Mechanical Properties of Fluids

Introduction: Recall the first chapter of NCERT Class 9 Science textbook, where you studied the differences between solid, liquid and gas. In class 11, you will study the mechanical properties of fluids, i.e., liquid and gas. A fluid substance has a tendency to flow due to large intermolecular spaces in comparison to solids. Fluids have a weak molecular force of attraction due to which they do not have a definite shape. 

As you move further in this chapter, you will develop an understanding of the following topics. In this NCERT chapter, there are a total of 41 questions. 

Topics

• Pressure
• Pascal’s Law
• Archimedes Principle
• Law of Flotation
• Equation of Continuity
• Energy of a Liquid
• Bernoulli’s Theorem
• Viscosity
• Coefficient of Viscosity
• Stoke’s Law
• Terminal Velocity
• Poiseuille’s Equation
• Reynold’s Number
• Critical Velocity
• Surface Tension and Surface Energy
• Angle of Contact
• Torricelli’s Theorem
• Magnus Effect

Important formulas of “Mechanical Properties of Fluids”

1. Pressure = Force/ Area

2. Pascal’s Law

    F₁/ a₁ = F₂/ a₂

3. Energy of a liquid = Pressure energy/ Mass of liquid = P/ Ⲣ

4. Bernoulli’s Theorem

    (P/ Ⲣ) + (v²/2) + gh = constant

5. Viscosity

    F = -(ɳA) dv/dx

6. Terminal Velocity (v)

    v = 2r² (ⲣ - 𝛔) g/ 9ɳ
    Where ⲣ → the density of the material of the body
              r  → radius

7. Poiseuille’s Equation (V)

    V = πⲣr⁴/ 8ɳ!

8. Reynold’s Number (R_e)

    R_e = ⲣvd/ ɳ

9. Critical Velocity
 
    v_c = Kɳ/ ⲣr

10. Surface Energy 
 
     h = 2T Cos𝛉/ rⲣg  

Chapter 11: Thermal Properties of Matter

Introduction: In the previous two chapters, you studied the mechanical properties of solids and fluids. This chapter will introduce you to the thermal properties of matter. To start from the basics, heat is a form of energy which is transferred from one object to another by virtue of its temperature difference. In grade 9 NCERT Science book, you learnt two ways for changing the state of matter- by pressure and temperature. 

You must remember when we supply heat to a body, its molecules attain kinetic energy due to which their intermolecular force of attraction is reduced. Further, in this chapter, you will read the following topics.

Topics

• Thermal Expansion
• Thermal Stress
• Thermal Capacity
• Specific Heat Capacity
• Calorimeter
• Basic Heat Formula
• Latent Heat
• Heat Transfer
• Thermal Resistance
• Newton’s Law of Cooling
• Black Body Radiation

Important formulas of “Thermal Properties of Matter”

1. Thermal Stress = Force (F)/ Area (A) = Yɑ ∆t
2. Thermal Capacity (S) = Q/ ∆t
3. Specific Heat Capacity (S) = Q/ m ∆t
4. Basic Heat Formula (Q) = m x S x t
5. Heat Transfer (H) = Q/ t = KA (T₁ - T₂)/ l
6. Newton’s Law of Cooling = dT/ dt = -K (T-T_S) 

Chapter 12: Thermodynamics

Introduction: Thermodynamics is a branch of Physics in which heat transforms into other forms of energy and vice-versa. So far, you were dealing with microscopic Science, but thermodynamic system involves the study of bulk systems, i.e., at the macroscopic level. There are three laws of thermodynamics- zeroth law, first law and second law. 

At the end of this chapter, you will find a total of 13 questions in the back-exercise based on topics given below. 

Topics

• Thermal Equilibrium
• Zeroth Law of Thermodynamics
• Heat, Work, and Internal Energy
• First Law of Thermodynamics
• Relation between Cp and Cu
• Thermodynamic State Variables
• Equation of State
• Thermodynamic Processes
• Quasi-Static Processes
• Isothermal Process
• Adiabatic Process
• Reversible Process
• Second Law of Thermodynamics
• Refrigerator

Chapter 13: Kinetic Theory

Introduction: From previous Science lessons, you can recall that the gas particles possess the highest rate of kinetic energy due to large intermolecular spaces. In class 11, you will first read about an ideal gas, which strictly adheres to gas laws such as Boyle’s law, Charle’s law, Gay Lussac’s law etc. 

In total, this chapter consists of 14 back-exercise questions based on the list of concepts given below.

Topics

• Ideal Gas
• Kinetic Theory and Gas Pressure
• Boyle’s Law
• Charles's Law
• Gay Lussac’s Law
• Avagadro’s Law
• Graham’s Law of Diffusion of Gases
• Dalton’s Law of Partial Pressures
• Kinetic Interpretation of Temperature
• Degrees of Freedom
• Law of Equipartition of Energy
• Mean Free Path

Important formulas of “Kinetic Theory”

1. Kinetic Theory and Gas Pressure
    P = ⅓ ⲣc^-2
    where, ⲣ is the density of the gas & c-2 is the mean square speed of the gas molecules

2. Boyle’s Law

    V ∝ 1/P 

    where V is the volume of a fixed mass of a gas

             P is the pressure of the gas

3. Charles’s Law

    V ∝ T 

    where, V is the volume of a fixed mass of a gas

              T is the temperature of the gas

4. Gay Lussac’s Law

    P ∝ T

5. Mean speed of molecules of a gas (v_mean)

    v_mean = (v₁ + v₂ + ….. + v_n)/ n = √8K_BT/ πm

6. Mean Free Path

    ƛ = (ƛ₁ + ƛ₂ + ƛ₃ + …...ƛ_N)/ N = |1/ √2πd²n = kT/ √2πd²p

    where d is molecular diameter

             N is number of molecules per unit volume

             T is absolute temperature

             P is pressure

Chapter 14: Oscillations

Introduction: Oscillation is defined as to and fro motion of a body about a fixed point after regular intervals of time. You first came across this topic when you studied the motion of a pendulum. In this class, you will be introduced to a special type of periodic oscillatory motion known as ‘simple harmonic motion’. 

Further, you will revisit common terminologies from earlier NCERT textbooks such as frequency, phase, and more. This chapter has a total of 31 exercise questions. 

Topics

• Periodic Motion
• Oscillatory Motion
• Simple Harmonic Motion
• Characteristics of Simple Harmonic Motion
• Frequency 
• Phase
• Springs in Series/ Parallel 
• Simple Pendulum
• Damped and Undamped SHM

Important formulas of "Oscillations"

1. Frequency = 1/ Time Period

2. Displacement of a particle executing SHM is given by 

    v = ⍵A √1- Sin² (⍵t ± ɸ) = ⍵A √1- (x²/A²) = ⍵√A² -x²

3. Acceleration of the particle executing SHM is given by

    a = -⍵A sin (⍵t ± ɸ) = -⍵²A

4. Kinetic energy in SHM = ½ mv² = ½ m⍵² (A² - x²)

5. Potential energy in SHM = ½ kx² = ½ m⍵²x²

6. Springs in Series = 1/k = 1/k₁ + 1/k₂

7. Springs in Parallel = k = k₁ + k₂

8. Simple Pendulum  

(a). Time period of a simple pendulum is given by- 

      T = 2π √l/g
(b). Frequency of a simple pendulum is given by-

      v = 1/2π (√2g/L)

Chapter 15: Waves

Introduction: You must be familiar with the term ‘Wave’ as we often talk about waves in the sea. Waves are caused by disturbances which travel through a particular medium due to repeated periodic motion of the particles about their mean position. In class 11, you will study characteristics of waves, types of waves, basic terminologies related to a wave etc. 

In total, 31 questions are given in the back-exercise of chapter-15 NCERT Class 11 Physics.  

Topics

• Waves
• Characteristics of a Wave
• Types of Waves
• Terminologies related to Wave
• Newton’s formula for the Velocity of Sound in Air
• General Equation of Progressive Waves
• Relation between Phase and Path Difference
• Principle of Superposition of Wave
• Stationary Waves
• Progressive Waves
• Law of Length
• Law of Tension 
• Law of Mass
• Doppler Effect

Important formulas of "Waves"

1. Relation between phase and path difference

   Φ = (2π/ ƛ) x path difference

2. Equation of a standing wave is given by

    y = 2A Sin Kx Cos (⍵t)

3. Doppler Effect

    v’ = {(v + v₀)/(v + v_S)} v 

CBSE Class 11 Physics Syllabus

CBSE Syllabus for Class 11 Physics consists of 10 units, carrying a total weightage of 70 marks. Check out the list of units and Class 11 Physics marking scheme in the tabular data shown below. 

CBSE Class 11 Physics Paper Pattern 

As stated above, the question paper of CBSE Class 11 Physics carries a total weightage of 70 marks. Here you can go through the exam pattern of CBSE Class 11 Physics Paper. 

Benefits of NCERT Class 11 Physics Solutions

• Prepared by expert teachers in compliance with the recent syllabus of CBSE
• Error free and effective solutions helpful in exam preparation
• Detailed and step-by-solutions for promoting a better understanding of the subject
• Cover all the important topics within each chapter
• Comprise of practice questions to help students prepare effectively
• Useful in learning harder topics and excel in the exam
• Cover explanations on the most important questions
• Easy to access and can be availed for free of cost

Final Words

So, preparing for the 11th Class Physics is now easier than ever before. You just need to browse through our NCERT Solutions for Class 11 Physics and you will be able to explore qualitative solutions that can give your exam preparation a solid boost. These solutions are error-free, reliable and give you an opportunity to cover the entire syllabus and prepare each topic meticulously.