Introduction
Physics Class 11 becomes an important leap over class 10 because students will learn about the mechanics of the universe in depth, ranging from particle movement to laws of thermodynamics and oscillation. It is essential to understand the concept, variable, and application of all those formulas as only memorizing them won’t be sufficient to solve numerical problems. Here is an all-inclusive compilation of physics formulas for class 11 chapter-wise for fast revision and CBSE exams.
Class 11 Physics Formulas Chapter Wise
Chapter 1: Units and Measurements
Important Topics
- System of Units (SI Units)
- Significant Figures
- Dimensional Analysis
- Error Propagation
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( Percentage Error = (\Delta a / a) \times 100 \) | Relative and percentage error | \(\Delta a\) = absolute error, \(a\) = measured value | No unit (%) |
| 2 | \( Error Addition: Z = A + B \Rightarrow \Delta Z = \Delta A + \Delta B \) | Error propagation in sum | \(\Delta Z, \Delta A, \Delta B\) = absolute errors | Same as base unit |
| 3 | \( Error Multiplication: Z = A \times B \Rightarrow \Delta Z / Z = \Delta A / A + \Delta B / B \) | Error propagation in product | \(\Delta Z / Z\) = relative error | No unit |
| 4 | \( Least Count = Pitch / Number \ of \ divisions \) | Screw gauge / Spherometer | Pitch = distance per rotation | mm or cm |
Explanation of Formula
Dimensional analysis plays a very important role in checking the validity of an equation and unit conversion from one system of units to another. The error formula gives us the possible maximum error in the derived value due to errors in the measured values.
Application of Formula
Frequently used in laboratory work for the calculation of least count and calculation of final error.
⭐ Must Remember
- \([M^a L^b T^c]\) is the standard dimensional formula representation.
- For error multiplication or division, relative errors are always added.
Quick Revision Points
- Number of significant figures determines the precision of the measurement.
- For addition/subtraction, the result should have the same number of decimal places as the number with the least decimal places.
- For multiplication/division, the result should have the same number of significant figures as the number with the least significant figures.
Exam Tips
- Always write the final answer with correct significant figures and proper SI units.
- In error questions, clearly state whether you are finding absolute error, relative error, or percentage error.
Chapter 2: Motion in a Straight Line
Important Topics
- Distance and Displacement
- Average and Instantaneous Velocity
- Uniformly Accelerated Motion
- Kinematic Equations
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( v = u + at \) | First kinematic equation | \(v\) = final vel, \(u\) = initial vel, \(a\) = accel, \(t\) = time | m/s |
| 2 | \( s = ut + (1/2)at^2 \) | Second kinematic equation | \(s\) = displacement | m |
| 3 | \( v^2 = u^2 + 2as \) | Third kinematic equation | (variables as above) | (m/s)^2 |
| 4 | \( s_{nth} = u + (a/2)(2n – 1) \) | Displacement in nth second | \(n\) = the specific second | m |
Formula Explanation
The three basic kinematic equations apply strictly to motion with uniform (constant) acceleration. The formula for the nth second gives the distance covered specifically during the nth second of motion, not the total distance in n seconds.
Formula Application
Used to calculate the trajectory of objects in free fall, vehicles accelerating on a straight road, or any 1D motion with constant acceleration.
⭐ Must Remember
- \(\vec{v}_{avg} = \Delta \vec{x} / \Delta t\). For instantaneous velocity, take the limit \(\Delta t \to 0\).
- The area under the velocity-time graph gives displacement, while the slope gives acceleration.
Quick Revision Points
- Slope of position-time (x-t) graph = velocity.
- If acceleration is zero, velocity is constant.
- Under free fall, \(a = g \approx 9.8 \ m/s^2\).
Exam Tips
- Always choose a clear origin and coordinate axis (positive/negative directions) before solving the problem.
- Remember that ‘s’ in the equation \(v^2 = u^2 + 2as\) is displacement, not total distance traveled.
Chapter 3: Motion in a Plane
Important Topics
- Scalars and Vectors
- Projectile Motion
- Relative Velocity
- Uniform Circular Motion
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( R = (u^2 \sin 2\theta) / g \) | Horizontal Range of projectile | \(u\) = initial speed, \(\theta\) = angle, \(g\) = gravity | m |
| 2 | \( H = (u^2 \sin^2 \theta) / (2g) \) | Maximum Height of projectile | (variables as above) | m |
| 3 | \( T = (2u \sin \theta) / g \) | Time of Flight | (variables as above) | s |
| 4 | \( a_c = v^2 / r \) | Centripetal Acceleration | \(v\) = speed, \(r\) = radius | m/s^2 |
Formula Explanation
Projectile motion is a 2D motion where horizontal velocity (\(u_x\)) remains constant (no air resistance) and vertical velocity (\(u_y\)) changes due to gravity (\(g\)). Centripetal acceleration is always directed towards the center of the circular path.
Formula Application
Used to calculate the trajectory of a thrown cricket ball, a bullet fired from a gun, or an object tied to a string moving in a circle.
⭐ Must Remember
- For maximum range, the angle of projection \(\theta = 45^\circ\), and \(R_{max} = u^2 / g\).
- For complementary angles (\(\theta\) and \(90^\circ – \theta\)), Range is the same: \(R_\theta = R_{90-\theta}\).
Quick Revision Points
- The path of a projectile is a parabola.
- Vector addition follows the triangle law or parallelogram law of addition.
- \(\vec{v}_{rel} = \vec{v}_A – \vec{v}_B\) (velocity of A with respect to B).
Exam Tips
- In projectile motion, treat horizontal and vertical motions independently using kinematic equations.
- Never mix x-axis and y-axis components in the same equation.
Chapter 4: Laws of Motion
Important Topics
- Newton’s Laws of Motion
- Friction
- Dynamics of Circular Motion
- Conservation of Momentum
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( \vec{F} = m \vec{a} \) | Newton’s Second Law | \(F\) = force, \(m\) = mass, \(a\) = acceleration | N (Newton) |
| 2 | \( f_s = \mu_s N \) | Limiting Static Friction | \(\mu_s\) = coeff. of static friction, \(N\) = normal force | N |
| 3 | \( f_k = \mu_k N \) | Kinetic Friction | \(\mu_k\) = coeff. of kinetic friction | N |
| 4 | \( v_{max} = \sqrt{\mu_s r g} \) | Max velocity on unbanked road | \(r\) = radius of turn, \(g\) = gravity | m/s |
Formula Explanation
Newton’s Second Law establishes the direct proportionality between force and acceleration. Friction always opposes relative motion; static friction is self-adjusting up to a maximum limit, while kinetic friction is constant during motion.
Formula Application
Used to calculate stopping distances of vehicles, tension in elevator cables, and maximum safe speeds on curved roads.
⭐ Must Remember
- Impulse \(J = F \times \Delta t = \Delta p\) (Change in momentum).
- Banking angle for frictionless road: \(\tan \theta = v^2 / (rg)\).
Quick Revision Points
- Action and reaction forces act on different bodies, hence they do not cancel each other out.
- Momentum (\(p = mv\)) is conserved if the net external force on the system is zero.
Exam Tips
- Always draw a clear Free Body Diagram (FBD) before writing the equations of motion.
- Identify whether the friction is static or kinetic. If the object is moving, use kinetic friction.
Chapter 5: Work, Energy and Power
Important Topics
- Work-Energy Theorem
- Potential and Kinetic Energy
- Conservative and Non-Conservative Forces
- Power and Collisions
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( W = \vec{F} \cdot \vec{d} = Fd \cos \theta \) | Work done by constant force | \(d\) = displacement, \(\theta\) = angle between F and d | J (Joule) |
| 2 | \( K = (1/2)mv^2 \) | Kinetic Energy | \(m\) = mass, \(v\) = velocity | J |
| 3 | \( W_{net} = \Delta K = K_f – K_i \) | Work-Energy Theorem | \(K_f, K_i\) = final and initial KE | J |
| 4 | \( P_{avg} = W / t \) | Average Power | \(W\) = work, \(t\) = time | W (Watt) |
Formula Explanation
Work is a scalar quantity. If force and displacement are perpendicular (\(\theta = 90^\circ\)), work done is zero. The Work-Energy theorem states that the net work done on a particle equals the change in its kinetic energy.
Formula Application
Used to calculate the work done by friction to stop a moving car, the power output of an engine, and analyzing elastic and inelastic collisions.
⭐ Must Remember
- For elastic collisions: Momentum is conserved AND Kinetic Energy is conserved.
- \(e = (v_2 – v_1) / (u_1 – u_2)\) (Coefficient of restitution).
- \(e = 1\) (Elastic), \(e = 0\) (Perfectly Inelastic).
Quick Revision Points
- Gravitational Potential Energy \(U = mgh\) (where \(h\) is height from reference point).
- Power \(P = \vec{F} \cdot \vec{v}\) (Instantaneous power).
- 1 kWh = \(3.6 \times 10^6 \ J\).
Exam Tips
- In work calculation \(W = Fd \cos \theta\), ‘d’ is the displacement, not the total distance traveled.
- In collision problems, always apply conservation of momentum first before considering energy.
Chapter 6: System of Particles and Rotational Motion
Important Topics
- Center of Mass
- Torque and Angular Momentum
- Moment of Inertia
- Rolling Motion
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( \vec{\tau} = \vec{r} \times \vec{F} \) | Torque | \(r\) = position vector, \(F\) = force | N m |
| 2 | \( \vec{L} = \vec{r} \times \vec{p} \) | Angular Momentum | \(p\) = linear momentum | kg m^2 / s |
| 3 | \( \vec{\tau} = I \vec{\alpha} \) | Rotational analogue of F=ma | \(I\) = moment of inertia, \(\alpha\) = angular accel | N m |
| 4 | \( I_{uniform \ rod} = (ML^2) / 12 \) | MI of rod about center | \(M\) = mass, \(L\) = length | kg m^2 |
Formula Explanation
Torque is the rotational equivalent of force, and Moment of Inertia is the rotational equivalent of mass. Angular momentum remains conserved if net external torque is zero.
Formula Application
Used to analyze rotating wheels, spinning tops, balancing of acrobats, and planetary rotations.
⭐ Must Remember
- Parallel Axis Theorem: \(I_z = I_{cm} + Md^2\).
- Perpendicular Axis Theorem (for 2D bodies): \(I_z = I_x + I_y\).
- Rolling without slipping: \(v_{cm} = R\omega\).
Quick Revision Points
- \(L = I\omega\) is analogous to \(p = mv\).
- Kinetic Energy of rolling = \(KE_{trans} + KE_{rot} = (1/2)mv_{cm}^2 + (1/2)I\omega^2\).
- \(I_{solid \ sphere} = (2/5)MR^2\), \(I_{hollow \ sphere} = (2/3)MR^2\).
Exam Tips
- Memorize the Moment of Inertia for standard shapes (rod, ring, disc, solid/hollow spheres) about center of mass.
- When applying conservation of angular momentum, check for external torque first.
Chapter 7: Gravitation
Important Topics
- Kepler’s Laws
- Newton’s Law of Gravitation
- Gravitational Potential Energy
- Escape Velocity and Satellites
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( F = (G m_1 m_2) / r^2 \) | Universal Gravitational Force | \(G\) = grav. constant, \(m_1, m_2\) = masses, \(r\) = distance | N |
| 2 | \( g = GM / R^2 \) | Acc. due to gravity at surface | \(M\) = planet mass, \(R\) = planet radius | m/s^2 |
| 3 | \( v_{esc} = \sqrt{2GM / R} \) | Escape Velocity | (variables as above) | m/s |
| 4 | \( T^2 = (4\pi^2 r^3) / (GM) \) | Time period of satellite | \(r\) = orbital radius | s^2 |
Formula Explanation
Gravitational force is an attractive, central, and conservative force. Escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body.
Formula Application
Used to calculate satellite orbits (geostationary and polar), escape velocity of rockets, and variation of ‘g’ with altitude and depth.
⭐ Must Remember
- Orbital velocity \(v_o = \sqrt{GM / r}\).
- Gravitational Potential Energy \(U = -GMm / r\).
- \(v_{esc} = \sqrt{2} v_o\).
Quick Revision Points
- \(g\) decreases with altitude (\(g_h = g(R / (R+h))^2\)) and depth (\(g_d = g(1 – d/R)\)).
- Time period of a geostationary satellite is exactly 24 hours.
- Gravitational potential \(V = -GM / r\).
Exam Tips
- Always distinguish between orbital radius ‘r’ and altitude ‘h’ (\(r = R + h\)).
- Gravitational PE is always negative, assuming zero at infinity.
Chapter 8: Mechanical Properties of Solids
Important Topics
- Stress and Strain
- Hooke’s Law
- Young’s Modulus, Bulk Modulus, Shear Modulus
- Elastic Potential Energy
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( Stress = F / A \) | Restoring force per unit area | \(F\) = force, \(A\) = cross-section area | Pa or N/m^2 |
| 2 | \( Strain = \Delta L / L \) | Relative change in dimension | \(\Delta L\) = change in length, \(L\) = original length | Unitless |
| 3 | \( Y = Stress / Strain = (F L) / (A \Delta L) \) | Young’s Modulus | (variables as above) | Pa |
| 4 | \( U = (1/2) \times Stress \times Strain \) | Elastic Potential Energy density | \(U\) = energy per unit volume | J/m^3 |
Formula Explanation
Hooke’s Law states that within the elastic limit, stress is directly proportional to strain. Young’s Modulus measures the resistance of a solid to elongation or compression.
Formula Application
Used in structural engineering to design beams, bridges, and cables, ensuring they can withstand specific loads without breaking.
⭐ Must Remember
- Within elastic limit: \(Y = (F L) / (A \Delta L)\).
- Poisson’s ratio \(\sigma = -(\Delta D / D) / (\Delta L / L)\) (theoretical limits: -1 to 0.5).
Quick Revision Points
- \(K = -V (\Delta P / \Delta V)\) (Bulk modulus, reciprocal of compressibility).
- \(\eta = F / (A \theta)\) (Shear modulus).
- Stress-strain curve: Proportional limit > Elastic limit > Yield point > Ultimate stress > Breaking point.
Exam Tips
- Strain is dimensionless, so the units of all moduli (Y, K, \(\eta\)) are the same as stress (N/m^2 or Pascal).
- Read the question carefully to identify whether tension, compression, or shear is acting on the body.
Chapter 9: Mechanical Properties of Fluids
Important Topics
- Pressure and Pascal’s Law
- Bernoulli’s Principle
- Viscosity and Stokes’ Law
- Surface Tension and Capillarity
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( P + (1/2)\rho v^2 + \rho g h = constant \) | Bernoulli’s Principle | \(P\) = pressure, \(\rho\) = density, \(v\) = velocity, \(h\) = height | N/m^2 |
| 2 | \( F = 6 \pi \eta r v \) | Stokes’ Law (Viscous drag) | \(\eta\) = coeff. of viscosity, \(r\) = radius, \(v\) = velocity | N |
| 3 | \( v_T = 2 r^2 (\rho – \sigma) g / (9 \eta) \) | Terminal Velocity | \(\rho, \sigma\) = densities of sphere and fluid | m/s |
| 4 | \( h = (2 S \cos \theta) / (\rho g r) \) | Capillary Rise | \(S\) = surface tension, \(\theta\) = contact angle, \(r\) = tube radius | m |
Formula Explanation
Bernoulli’s principle is the conservation of mechanical energy per unit volume for an ideal fluid in streamline flow. Viscosity acts like internal friction, opposing relative motion between fluid layers.
Formula Application
Used in designing airplane wings (aerodynamics), calculating flow speed in pipes, analyzing raindrop velocities, and understanding blood flow in arteries.
⭐ Must Remember
- Continuity Equation: \(A_1 v_1 = A_2 v_2\) (Volume flow rate is constant).
- Reynolds number \(R_e = (\rho v D) / \eta\). If \(R_e < 2000\), flow is streamline; if \(R_e > 3000\), flow is turbulent.
Quick Revision Points
- Pressure at depth \(h\): \(P = P_0 + \rho g h\).
- Excess pressure inside a drop: \(\Delta P = 2S / r\).
- Excess pressure inside a soap bubble: \(\Delta P = 4S / r\).
Exam Tips
- In Bernoulli’s equation, ensure all terms have consistent units (usually convert everything to SI).
- If the capillary tube is immersed in a liquid that depresses (like mercury), \(\theta > 90^\circ\), making ‘h’ negative.
Chapter 10: Thermal Properties of Matter
Important Topics
- Heat Transfer and Calorimetry
- Thermal Expansion
- Specific Heat Capacity
- Heat Conduction
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( Q = m s \Delta T \) | Heat Transfer | \(m\) = mass, \(s\) = specific heat, \(\Delta T\) = temp change | J |
| 2 | \( \Delta L = L \alpha \Delta T \) | Linear Expansion | \(L\) = original length, \(\alpha\) = coeff. of linear expansion | m |
| 3 | \( H = k A (T_1 – T_2) / d \) | Rate of Heat Conduction | \(k\) = thermal cond., \(A\) = area, \(d\) = thickness | W or J/s |
| 4 | \( Q = m L \) | Latent Heat (Phase change) | \(L\) = latent heat | J |
Formula Explanation
Heat transfer during temperature change depends on specific heat, while phase change depends on latent heat. Thermal expansion describes how the dimensions of a body change with temperature.
Formula Application
Used in calorimetry problems, designing railway tracks (expansion gaps), and calculating heat loss through walls of buildings.
⭐ Must Remember
- Relation between coefficients: \(\beta = 2\alpha\) (Areal), \(\gamma = 3\alpha\) (Volume).
- \(T_C = T_K – 273.15\).
Quick Revision Points
- Specific heat of water \(s = 4186 \ J/kg-K\).
- Stefan-Boltzmann Law: \(E = \sigma T^4\) (Blackbody radiation).
- Newton’s Law of Cooling: Rate of cooling \(\propto\) temp difference.
Exam Tips
- In calorimetry, always ensure heat lost by the hot body equals heat gained by the cold body (assuming no loss to surroundings).
- Remember to convert Celsius to Kelvin for gas and radiation laws.
Chapter 11: Thermodynamics
Important Topics
- Zeroth, First, and Second Laws
- Isothermal and Adiabatic Processes
- Work done in various processes
- Carnot Engine
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( \Delta U = Q – W \) | First Law of Thermodynamics | \(\Delta U\) = internal energy, \(Q\) = heat added, \(W\) = work by gas | J |
| 2 | \( W_{iso} = n R T \ln(V_2 / V_1) \) | Work in Isothermal process | \(n\) = moles, \(R\) = gas const, \(V_1, V_2\) = volumes | J |
| 3 | \( W_{adia} = n R (T_1 – T_2) / (\gamma – 1) \) | Work in Adiabatic process | \(\gamma = C_p / C_v\), \(T_1, T_2\) = temps | J |
| 4 | \( \eta = 1 – (T_2 / T_1) \) | Carnot Engine Efficiency | \(T_1\) = source temp (K), \(T_2\) = sink temp (K) | Unitless (%) |
Formula Explanation
The First Law is essentially the conservation of energy. In isothermal processes, \(\Delta T = 0 \Rightarrow \Delta U = 0\), so \(Q = W\). In adiabatic processes, \(Q = 0\), so \(\Delta U = -W\).
Formula Application
Used to calculate the efficiency of heat engines, refrigerators, and understanding energy transfers in thermal systems.
⭐ Must Remember
- Mayer’s Formula: \(C_p – C_v = R\).
- Adiabatic relation: \(P V^\gamma = constant\).
- Isothermal relation: \(P V = constant\).
Quick Revision Points
- Work done BY the gas is positive (\(+W\)), work done ON the gas is negative (\(-W\)).
- For a refrigerator, Coefficient of Performance \(\alpha = T_2 / (T_1 – T_2)\).
- Entropy of the universe always increases in an irreversible process.
Exam Tips
- Always use absolute temperature (Kelvin) in thermodynamics formulas, especially for Carnot efficiency.
- Carefully track the sign convention for \(Q\) and \(W\) in the First Law.
Chapter 12: Kinetic Theory of Gases
Important Topics
- Ideal Gas Law
- Kinetic Interpretation of Temperature
- Degrees of Freedom and Equipartition of Energy
- Mean Free Path
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( P V = n R T \) | Ideal Gas Equation | \(P\) = pressure, \(V\) = volume, \(n\) = moles | Pa m^3 |
| 2 | \( P = (1/3) \rho v_{rms}^2 \) | Kinetic Pressure | \(\rho\) = density, \(v_{rms}\) = root mean square speed | Pa |
| 3 | \( v_{rms} = \sqrt{3 R T / M} \) | RMS Speed of gas | \(R\) = gas const, \(T\) = temp, \(M\) = molar mass | m/s |
| 4 | \( E = (3/2) k_B T \) | Average KE per molecule | \(k_B\) = Boltzmann constant | J |
Formula Explanation
Pressure exerted by a gas is due to the continuous bombardment of molecules on the walls of the container. The average kinetic energy of a gas molecule depends only on its absolute temperature, not on its mass.
Formula Application
Used to derive gas laws, calculate speeds of gas molecules at different temperatures, and understand specific heats of gases.
⭐ Must Remember
- \(v_{rms} = \sqrt{3} v_{avg}\). Also, \(v_{mp} = \sqrt{2RT / M}\) (Most probable speed).
- Total internal energy of n moles of monoatomic gas: \(U = (3/2) nRT\).
Quick Revision Points
- \(R = N_A k_B\) (where \(N_A\) is Avogadro’s number).
- Mean free path \(l = 1 / (\sqrt{2} \pi n d^2)\) (where \(n\) = number density, \(d\) = molecular diameter).
- For monoatomic gas: \(C_v = (3/2)R\), \(C_p = (5/2)R\).
Exam Tips
- Ensure M is the MOLAR MASS (in kg/mol), not the mass of one molecule, when using \(v_{rms}\).
- Convert Celsius to Kelvin before applying gas laws.
Chapter 13: Oscillations
Important Topics
- Simple Harmonic Motion (SHM)
- Displacement, Velocity, and Acceleration in SHM
- Energy in SHM
- Pendulums
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( a = -\omega^2 x \) | Defining equation of SHM | \(a\) = accel, \(\omega\) = angular freq, \(x\) = displacement | m/s^2 |
| 2 | \( T = 2\pi \sqrt{m / k} \) | Time period of spring-mass system | \(m\) = mass, \(k\) = spring constant | s |
| 3 | \( T = 2\pi \sqrt{L / g} \) | Time period of Simple Pendulum | \(L\) = length, \(g\) = gravity | s |
| 4 | \( E = (1/2) m \omega^2 A^2 \) | Total Energy in SHM | \(A\) = amplitude | J |
Formula Explanation
In SHM, the acceleration is always directed opposite to the displacement and is proportional to it. The total energy (KE + PE) remains constant throughout the oscillation.
Formula Application
Used in analyzing spring systems, clock pendulums, and molecular vibrations.
⭐ Must Remember
- \(x(t) = A \sin(\omega t + \phi)\).
- Maximum velocity \(v_{max} = A \omega\). Maximum acceleration \(a_{max} = A \omega^2\).
- \(\omega = 2\pi f = 2\pi / T\).
Quick Revision Points
- At mean position: KE is max, PE is zero. At extreme positions: PE is max, KE is zero.
- For a liquid in a U-tube: \(T = 2\pi \sqrt{h / g}\) (where h is the height of liquid column in one arm).
Exam Tips
- If a spring is cut into pieces, the spring constant changes inversely with length.
- Remember that the time period of a pendulum is independent of its mass.
Chapter 14: Waves
Important Topics
- Transverse and Longitudinal Waves
- Speed of Sound in Air and Solids
- Superposition of Waves and Interference
- Beats and Standing Waves
Important Formulas
| No. | Formula | Concept | Variables / Symbols | SI Unit |
|---|---|---|---|---|
| 1 | \( v = f \lambda \) | Wave Speed | \(f\) = frequency, \(\lambda\) = wavelength | m/s |
| 2 | \( v = \sqrt{T / \mu} \) | Speed of transverse wave on string | \(T\) = tension, \(\mu\) = linear mass density | m/s |
| 3 | \( v = \sqrt{E / \rho} \) | Speed of longitudinal wave | \(E\) = Bulk/Young’s modulus, \(\rho\) = density | m/s |
| 4 | \( f_{beat} = |f_1 – f_2| \) | Beat Frequency | \(f_1, f_2\) = frequencies of two waves | Hz |
Formula Explanation
The speed of a mechanical wave depends on the medium’s elastic and inertial properties. Beats occur when two waves of slightly different frequencies superimpose, creating a periodic variation in loudness.
Formula Application
Used in stringed musical instruments (guitars, sitars), calculating the speed of sound, Doppler effect in radar/sonar, and acoustics.
⭐ Must Remember
- Newton’s formula for sound in air: \(v = \sqrt{P / \rho}\).
- Laplace’s correction: \(v = \sqrt{\gamma P / \rho}\) (where \(\gamma = C_p / C_v\)).
- Doppler Effect: \(f’ = f (v \pm v_o) / (v \mp v_s)\).
Quick Revision Points
- For a closed organ pipe, fundamental frequency \(f = v / 4L\). Harmonics are odd multiples (\(f, 3f, 5f\dots\)).
- For an open organ pipe, fundamental frequency \(f = v / 2L\). Harmonics are all multiples (\(f, 2f, 3f\dots\)).
- Distance between adjacent nodes (or antinodes) in a standing wave is \(\lambda/2\).
Exam Tips
- Carefully determine if the wave is longitudinal or transverse before calculating its speed.
- In Doppler effect problems, assign signs to velocities based on the standard convention (source moving towards observer is negative in the denominator, observer moving towards source is positive in the numerator).
Most Important Class 11 Physics Formulas
- Kinematic Equations: \( v = u + at \), \( s = ut + (1/2)at^2 \), \( v^2 = u^2 + 2as \) (Foundation of Mechanics)
- Newton’s Second Law: \( F = ma \) and Impulse \( J = \Delta p \) (Crucial for dynamics)
- Work-Energy Theorem: \( W_{net} = \Delta K \) (Links force and motion to energy)
- Projectile Range: \( R = (u^2 \sin 2\theta) / g \) (Vital for 2D motion)
- Gravitational Potential Energy: \( U = -GMm / r \) (Foundation for astrophysics)
- Bernoulli’s Principle: \( P + (1/2)\rho v^2 + \rho g h = constant \) (Core fluid dynamics)
- First Law of Thermodynamics: \( \Delta U = Q – W \) (Energy conservation in thermal systems)
- SHM Time Period (Spring): \( T = 2\pi \sqrt{m / k} \) (Essential for oscillatory motion)
Formula Symbols and SI Units
| Quantity | Symbol | SI Unit |
|---|---|---|
| Displacement | \(s\) or \(x\) | m (meter) |
| Velocity | \(v\) or \(u\) | m/s (meter per second) |
| Acceleration | \(a\) | m/s^2 (meter per second squared) |
| Force | \(F\) | N (Newton) |
| Work / Energy | \(W\), \(U\), \(K\) | J (Joule) |
| Power | \(P\) | W (Watt) |
| Angle / Angular Displacement | \(\theta\) | rad (radian) |
| Angular Velocity | \(\omega\) | rad/s |
| Torque | \(\tau\) | N m |
| Moment of Inertia | \(I\) | kg m^2 |
| Pressure | \(P\) | Pa (Pascal) |
| Heat | \(Q\) | J (Joule) |
| Specific Heat | \(s\) or \(c\) | J/(kg K) |
| Temperature | \(T\) | K (Kelvin) |
Quick Revision Formula Sheet
| Chapter | Key Formula | Concept |
|---|---|---|
| Motion | \( v^2 = u^2 + 2as \) | Final velocity squared |
| Projectile | \( H = (u^2 \sin^2 \theta) / (2g) \) | Maximum height |
| Circular Motion | \( a_c = v^2 / r \) | Centripetal acceleration |
| Rotation | \( \vec{\tau} = I \vec{\alpha} \) | Rotational F=ma |
| Gravitation | \( v_{esc} = \sqrt{2GM / R} \) | Escape speed |
| Elasticity | \( Y = (F L) / (A \Delta L) \) | Young’s modulus |
| Fluids | \( h = (2 S \cos \theta) / (\rho g r) \) | Capillary rise |
| Thermodynamics | \( W_{iso} = n R T \ln(V_2 / V_1) \) | Work in isothermal |
| Kinetic Theory | \( P = (1/3) \rho v_{rms}^2 \) | Pressure of gas |
| Oscillations | \( T = 2\pi \sqrt{L / g} \) | Simple pendulum period |
| Waves | \( v = \sqrt{T / \mu} \) | String wave speed |
Common Mistakes While Using Physics Formulas
- Mixing Units: Using \(g\) in cm/s^2 while mass is in kg. Always convert everything to SI units before substituting into formulas.
- Ignoring Vector Nature: Adding forces or velocities as simple numbers without considering their directions. Always use vector addition or resolve into components.
- Sign Convention Errors in Thermodynamics: Getting confused with \(+W\) and \(-W\). Remember: Work done BY the gas is positive (expansion), work done ON the gas is negative (compression).
- Using Kinematic Equations for Non-Uniform Acceleration: Applying \(v = u + at\) when acceleration ‘a’ is changing with time.
Numerical Problem-Solving Tips
- Read the question carefully and identify what is given and what needs to be found.
- Write the given values with their symbols and standard units.
- Draw a diagram (FBD, ray diagram, circuit, etc.) wherever applicable.
- Select the correct formula that relates the given quantities to the required quantity.
- Convert all given quantities into consistent SI units (e.g., convert km/hr to m/s).
- Substitute values carefully, ensuring scalar and vector components are handled correctly.
- Check the final answer: Does the unit match the expected physical quantity? Is the magnitude physically realistic?
Final Revision Strategy
Step 1: Learn the Concept
Understand the derivation of the formula. If you know how a formula is derived, you are less likely to forget it during the exam.
Step 2: Memorize Important Formulas
Create a formula sheet (like the one above) and read it daily. Active recall is the best method—cover the right side of the sheet and try to write the formula from memory.
Step 3: Practise Numericals
Solve a variety of numerical problems for each formula. Focus on quality and understanding rather than rote calculation.
Step 4: Revise Mistakes
Keep a log of mistakes you make in tests and practice. Before the final exam, review this log to ensure you don’t repeat the same conceptual or calculation errors.
Step 5: Take a Formula Test
Have a friend or teacher dictate formulas from different chapters, and you write them down with their conditions (e.g., \(W = Fd \cos \theta\) is for a constant force).
FAQs
Q1. How can I memorize Class 11 Physics formulas?
The best way to memorize formulas is to understand their derivations and meanings. Write them down repeatedly, create flashcards, and practice applying them to numerical problems immediately. Teaching a formula to a peer also solidifies your memory.
Q2. Which Class 11 Physics formulas are most important for exams?
Formulas from Laws of Motion (\(F=ma\)), Work-Energy Theorem (\(W_{net} = \Delta K\)), Projectile Motion (\(R = (u^2 \sin 2\theta) / g\)), and Thermodynamics (\(\Delta U = Q – W\)) are highly critical for school exams and carry significant weight.
Q3. Should I learn formulas without understanding the concepts?
No. Learning formulas without understanding concepts limits your ability to tackle application-based or twisted questions. Concepts tell you when and why to use a specific formula.
Q4. How can I use Physics formulas correctly in numerical problems?
Always start by writing given values in standard SI units. Check if the formula requires scalar or vector quantities. Substitute values with units to ensure dimensional consistency, and verify that the final answer has the correct unit.