The SI unit of luminous intensity is candela.

One astronomical unit is the average distance between Earth and Sun.

Dimensional formula of force is [MLT⁻²].

Planck’s constant has dimensions of angular momentum.

The dimensional formula of power is [ML²T⁻³].

One parsec is equal to 3.26 light years.

Least count of a vernier callipers is 0.01 cm.

Systematic errors are constant in magnitude and sign.

Absolute error is the magnitude of difference between true and measured value.

Percentage error is (absolute error / true value) × 100.

Significant figures in 0.0025 are two.

Dimensional analysis cannot determine the value of dimensionless constants.

The SI unit of solid angle is steradian.

One fermi is equal to 10⁻¹⁵ m.

Avogadro’s number has dimensions of [mol⁻¹].

Surface tension has dimensions of force per unit length.

The dimensional formula of impulse is same as that of momentum.

Relative error is the ratio of absolute error to the true value.

One light year is the distance travelled by light in one year.

Precision refers to the closeness of repeated measurements.

Average velocity is total displacement divided by total time.

Instantaneous velocity is the limiting value of average velocity as time interval approaches zero.

Acceleration is the rate of change of velocity.

For a freely falling body, initial velocity is zero.

Distance is a scalar quantity while displacement is a vector.

The area under velocity-time graph gives displacement.

The slope of velocity-time graph gives acceleration.

In uniform circular motion, speed is constant but velocity changes.

Centripetal acceleration is directed towards the centre.

Relative velocity of A with respect to B is v_A − v_B.

Projectile motion is a combination of horizontal uniform motion and vertical accelerated motion.

Maximum range of a projectile on horizontal plane is u²/g.

Time of flight of a projectile is 2u sinθ / g.

The trajectory of a projectile is a parabola.

Horizontal component of velocity remains constant in projectile motion (neglecting air resistance).

Vertical component of velocity becomes zero at the highest point.

Acceleration due to gravity is independent of mass of the body.

Equations of motion are valid only for constant acceleration.

Average speed is total path length divided by total time.

A body moving with constant speed can have variable velocity.

Velocity is zero at the highest point of a vertically projected body.

The displacement in nth second is given by s_n = u + a(2n−1)/2.

Rain appears to fall vertically when observed from a moving vehicle if relative velocity is vertical.

Angular displacement is measured in radians.

Linear velocity v = rω in circular motion.

Tangential acceleration changes the speed in circular motion.

Radial acceleration changes the direction in circular motion.

A body projected vertically up returns with the same speed (neglecting air resistance).

The motion of a particle is said to be one-dimensional if it moves along a straight line.

Position vector locates the position of a particle with respect to origin.

Newton’s first law defines inertia.

Inertia is the property of a body to resist change in its state of rest or uniform motion.

Momentum is the product of mass and velocity.

Impulse is equal to change in momentum.

Newton’s second law states that force is rate of change of momentum.

Force and acceleration are in the same direction.

Newton’s third law states that every action has equal and opposite reaction.

Action and reaction act on different bodies.

Friction always opposes relative motion.

Static friction is a self-adjusting force.

Limiting friction is the maximum static friction.

Kinetic friction is less than limiting friction.

Coefficient of friction is independent of area of contact.

Rolling friction is less than sliding friction.

Pseudo force acts in non-inertial frames.

Apparent weight of a body in a lift accelerating upward is m(g+a).

Apparent weight of a body in a lift accelerating downward is m(g−a).

Apparent weight becomes zero in free fall.

Centripetal force is provided by tension, gravity or friction depending on the situation.

Banking of roads provides the necessary centripetal force.

Angle of banking is independent of mass of the vehicle.

Maximum speed on a banked road is √[rg(tanθ + μ)/(1 − μ tanθ)].

Conservation of linear momentum holds when net external force is zero.

Rocket propulsion works on the principle of conservation of momentum.

Recoil velocity of a gun is opposite to the velocity of bullet.

A body is in equilibrium if net force and net torque are zero.

Concurrent forces are in equilibrium if vector sum is zero.

Force of friction is independent of relative speed (to a good approximation).

Static friction can be greater than kinetic friction.

The coefficient of static friction is greater than coefficient of kinetic friction.

Tension is a pulling force transmitted through a string.

Normal reaction is perpendicular to the surface of contact.

Weight of a body is the gravitational force acting on it.

Mass is a measure of inertia.

Inertial mass and gravitational mass are equivalent.

Work done by a constant force is F·s = Fs cosθ.

Work done is zero if force is perpendicular to displacement.

Kinetic energy is (1/2)mv².

Potential energy is mgh near the Earth’s surface.

Work-energy theorem states that work done equals change in kinetic energy.

Mechanical energy is conserved when only conservative forces act.

Power is the rate of doing work.

Instantaneous power is F·v.

Average power is total work divided by total time.

1 horse power = 746 watt.

Potential energy of a spring is (1/2)kx².

Elastic potential energy is stored in a stretched or compressed spring.

Conservative force is one for which work is path independent.

Non-conservative forces dissipate mechanical energy as heat.

Collision is elastic if both momentum and kinetic energy are conserved.

In inelastic collision, kinetic energy is not conserved.

Perfectly inelastic collision results in maximum loss of kinetic energy.

Coefficient of restitution e = 1 for elastic collision.

Coefficient of restitution e = 0 for perfectly inelastic collision.

Centre of mass of a system moves as if all mass is concentrated there.

Velocity of separation = e × velocity of approach (along line of impact).

Work done by gravity depends only on vertical displacement.

The SI unit of energy is joule.

1 calorie = 4.186 joule.

Power is a scalar quantity.

Centre of mass of a uniform rod lies at its geometric centre.

Torque is the moment of force: τ = r × F.

Angular momentum L = r × p.

Torque is equal to rate of change of angular momentum.

Moment of inertia of a body is Σmr².

Moment of inertia of a thin ring about its axis is MR².

Moment of inertia of a disc about its axis is (1/2)MR².

Parallel axis theorem: I = I_cm + Md².

Perpendicular axis theorem is valid for planar bodies.

Angular velocity ω = dθ/dt.

Angular acceleration α = dω/dt.

Linear acceleration a = rα for pure rotation.

Kinetic energy of rotation is (1/2)Iω².

Total kinetic energy = translational + rotational KE.

Conservation of angular momentum holds when external torque is zero.

A body rolling without slipping has v = rω.

Rolling friction is responsible for pure rolling on horizontal surface.

Radius of gyration k is defined by I = Mk².

Angular impulse is equal to change in angular momentum.

Couple produces pure rotation.

Moment of inertia is minimum about an axis through centre of mass.

For a rigid body, distance between any two points remains constant.

Instantaneous axis of rotation is the axis about which the body is purely rotating at an instant.

A disc rolling on a horizontal surface has KE = (3/4)Mv².

Torque is maximum when force is perpendicular to position vector.

Angular momentum is a vector quantity.

Precession occurs when torque is perpendicular to angular momentum.

The SI unit of torque is N·m.

Moment of inertia depends on the axis of rotation.

A system is in rotational equilibrium if net torque is zero.

Newton’s law of gravitation: F = Gm₁m₂/r².

Gravitational force is always attractive.

Acceleration due to gravity g = GM/R².

Value of g decreases with height as g_h = g(1 − 2h/R).

Value of g decreases with depth as g_d = g(1 − d/R).

Gravitational potential energy is −GMm/r.

Gravitational potential is −GM/r.

Escape velocity from Earth’s surface is √(2gR) ≈ 11.2 km/s.

Orbital velocity of a satellite is √(GM/r).

Time period of a satellite is 2π√(r³/GM).

Kepler’s first law: planets move in elliptical orbits with Sun at one focus.

Kepler’s second law: areal velocity is constant.

Kepler’s third law: T² ∝ r³.

Weightlessness is experienced in a freely falling elevator or satellite.

Geostationary satellites have time period of 24 hours.

Height of geostationary satellite is about 36,000 km.

Binding energy of a satellite is −GMm/2r.

Intensity of gravitational field is −GM/r².

Gravitational force is a conservative force.

The value of G is 6.67 × 10⁻¹¹ N m² kg⁻².

Acceleration due to gravity is maximum at poles.

Acceleration due to gravity is minimum at equator.

Variation of g with latitude is due to rotation of Earth.

Polar radius of Earth is less than equatorial radius.

Escape velocity is independent of the mass of the body.

A body projected with escape velocity never returns.

Total energy of a satellite is negative.

Kinetic energy of a satellite is positive.

Potential energy of a satellite is negative and twice the kinetic energy in magnitude.

Parking orbit is the geostationary orbit.

Polar satellites are used for remote sensing.

The gravitational force provides the centripetal force for planetary motion.

Moon’s gravity is about 1/6th of Earth’s gravity.

Weight of a body is zero at the centre of Earth.

Gravitational mass and inertial mass are proportional.

Stress is restoring force per unit area.

Strain is change in dimension divided by original dimension.

Hooke’s law states that stress is proportional to strain within elastic limit.

Young’s modulus Y = longitudinal stress / longitudinal strain.

Bulk modulus B = −ΔP / (ΔV/V).

Shear modulus η = shear stress / shear strain.

Poisson’s ratio σ = lateral strain / longitudinal strain.

Elastic energy density is (1/2) × stress × strain.

Breaking stress is the maximum stress a material can withstand.

Plasticity is the property of permanent deformation.

Ductility is the ability to be drawn into wires.

Malleability is the ability to be hammered into sheets.

Viscosity is the internal friction of fluids.

Stokes’ law: viscous force F = 6πηrv.

Terminal velocity is reached when viscous force + buoyancy = weight.

Bernoulli’s theorem is based on conservation of energy.

According to Bernoulli, P + ρgh + (1/2)ρv² = constant.

Venturimeter works on Bernoulli’s principle.

Torricelli’s theorem: speed of efflux = √(2gh).

Surface tension is force per unit length.

Excess pressure inside a soap bubble is 4T/r.

Excess pressure inside a liquid drop is 2T/r.

Capillary rise h = 2T cosθ / (ρgr).

Angle of contact is acute for water and glass.

Angle of contact is obtuse for mercury and glass.

Archimedes’ principle: buoyant force equals weight of displaced fluid.

A body floats if density is less than that of liquid.

Centre of buoyancy is the centre of mass of displaced fluid.

Streamline flow is steady and laminar.

Turbulent flow occurs at high Reynolds number.

Critical velocity is the velocity above which flow becomes turbulent.

Reynolds number Re = ρvd/η.

Hydraulic press works on Pascal’s law.

Pascal’s law: pressure applied is transmitted equally in all directions.

Atmospheric pressure is equal to 76 cm of mercury column.

Temperature is a measure of hotness or coldness.

Absolute zero is 0 K or −273.15 °C.

Heat is a form of energy in transit.

Specific heat capacity is heat required to raise temperature of unit mass by 1 °C.

Latent heat is heat required for change of state without change in temperature.

First law of thermodynamics: ΔQ = ΔU + ΔW.

Internal energy is a state function.

Work done in isobaric process is PΔV.

Work done in isochoric process is zero.

Work done in isothermal process is nRT ln(V₂/V₁).

Adiabatic process: Q = 0.

In adiabatic process, TV^γ−1 = constant.

Carnot engine is the most efficient heat engine.

Efficiency of Carnot engine = 1 − T₂/T₁.

Second law of thermodynamics: heat cannot flow from cold to hot body without external work.

Entropy is a measure of disorder.

Entropy of the universe always increases.

Triple point of water is 273.16 K at 0.006 atm.

Ideal gas equation is PV = nRT.

Boyle’s law: PV = constant at constant temperature.

Charles’ law: V/T = constant at constant pressure.

Gay-Lussac’s law: P/T = constant at constant volume.

Kinetic interpretation of temperature: (1/2)m⟨v²⟩ = (3/2)kT.

Root mean square speed v_rms = √(3RT/M).

Average kinetic energy per molecule is (3/2)kT.

Pressure of ideal gas P = (1/3)ρv_rms².

Degrees of freedom for monoatomic gas is 3.

Degrees of freedom for diatomic gas is 5 at room temperature.

Specific heat at constant volume C_v = fR/2.

Specific heat at constant pressure C_p = C_v + R.

Ratio of specific heats γ = C_p/C_v.

For monoatomic gas γ = 5/3.

For diatomic gas γ = 7/5.

Mean free path is the average distance travelled between collisions.

Brownian motion provides evidence for molecular motion.

Absolute temperature is proportional to average kinetic energy.

Real gases obey van der Waals equation.

Critical temperature is the temperature above which gas cannot be liquefied.

Isothermal process occurs at constant temperature.

Adiabatic walls do not allow heat transfer.

Heat capacity is extensive while specific heat is intensive.

Calorie is the heat required to raise 1 g water by 1 °C.

Mechanical equivalent of heat J = 4.186 J/cal.

Zeroth law of thermodynamics defines temperature.

Thermal equilibrium means no net heat flow.

Conduction is heat transfer through molecular collisions.

Convection is heat transfer by bulk motion of fluid.

Radiation is heat transfer by electromagnetic waves.

Black body is a perfect absorber and emitter.

Stefan’s law: E = σT⁴.

Wien’s displacement law: λ_m T = constant.

Newton’s law of cooling: rate of cooling ∝ temperature difference.

Thermal conductivity is high for metals.

Perfect gas has zero intermolecular forces.

Internal energy of ideal gas depends only on temperature.

Simple harmonic motion is the projection of uniform circular motion.

Restoring force in SHM is F = −kx.

Time period of a simple pendulum T = 2π√(l/g).

Time period of a spring-mass system T = 2π√(m/k).

Frequency of SHM is independent of amplitude.

Phase difference of π/2 exists between displacement and velocity in SHM.

Acceleration is maximum at extreme positions in SHM.

Total energy in SHM is (1/2)kA².

Potential energy is maximum at extreme positions.

Kinetic energy is maximum at mean position.

Forced oscillations occur under periodic external force.

Resonance occurs when driving frequency equals natural frequency.

Damped oscillations have decreasing amplitude.

Wave is a disturbance that transfers energy.

Transverse waves have particles oscillating perpendicular to propagation.

Longitudinal waves have particles oscillating parallel to propagation.

Speed of wave on a string v = √(T/μ).

Speed of sound in air is approximately 340 m/s at 25 °C.

Speed of sound increases with temperature.

Wavelength is the distance between two consecutive crests.

Frequency is the number of oscillations per second.

Wave equation: y = A sin(ωt − kx).

Phase velocity is ω/k.

Superposition principle: net displacement is vector sum of individual displacements.

Interference is the redistribution of energy due to superposition.

Constructive interference occurs when path difference is nλ.

Destructive interference occurs when path difference is (2n+1)λ/2.

Beats are produced by superposition of two close frequencies.

Beat frequency is |f₁ − f₂|.

Standing waves are formed by superposition of two identical waves travelling in opposite directions.

Nodes are points of zero displacement in standing waves.

Antinodes are points of maximum displacement.

Fundamental frequency of a closed pipe is v/4L.

Fundamental frequency of an open pipe is v/2L.

Doppler effect is the apparent change in frequency due to relative motion.

Apparent frequency increases when source approaches observer.

Intensity of sound is proportional to square of amplitude.

Decibel is the unit of intensity level.

Ultrasonic waves have frequency greater than 20 kHz.

Infrasonic waves have frequency less than 20 Hz.

Shock waves are produced when source speed exceeds wave speed.

Mach number is the ratio of source speed to wave speed.

Reflection of sound produces echo.

Refraction of sound occurs due to temperature gradient.

Diffraction is more prominent when wavelength is comparable to obstacle size.

Laws of reflection: angle of incidence = angle of reflection.

Image formed by a plane mirror is virtual, erect and of same size.

Focal length of a plane mirror is infinity.

Mirror formula: 1/v + 1/u = 1/f.

Magnification of mirror m = −v/u.

Concave mirror can form real and virtual images.

Convex mirror always forms virtual, erect and diminished image.

Focal length of a spherical mirror is R/2.

Power of a lens is 1/f (in metres) and measured in dioptre.

Lens formula: 1/v − 1/u = 1/f.

Magnification of lens m = v/u.

Convex lens converges light and is called converging lens.

Concave lens diverges light and is called diverging lens.

Combination of thin lenses in contact: 1/F = 1/f₁ + 1/f₂.

Total internal reflection occurs when light travels from denser to rarer medium at i > c.

Critical angle c = sin⁻¹(1/μ).

Optical fibre works on total internal reflection.

Refraction at plane surface: μ = real depth / apparent depth.

Snell’s law: μ₁ sin i = μ₂ sin r.

Absolute refractive index of a medium is c/v.

Relative refractive index is the ratio of absolute refractive indices.

Prism formula: μ = sin[(A+δ_m)/2] / sin(A/2).

Dispersion is the splitting of white light into constituent colours.

Rainbow is formed due to dispersion and total internal reflection in water droplets.

Chromatic aberration is due to different focal lengths for different colours.

Achromatic combination removes chromatic aberration.

Simple microscope has magnification 1 + D/f.

Compound microscope has objective of short focal length and eyepiece of larger focal length.

Astronomical telescope has objective of large focal length and eyepiece of short focal length.

Magnifying power of telescope in normal adjustment is f_o/f_e.

Resolving power of microscope is 2μ sinθ / λ.

Resolving power of telescope is d/1.22λ.

Scattering of light is responsible for blue colour of sky.

Rayleigh scattering intensity ∝ 1/λ⁴.

Red light is scattered least and is used in danger signals.

Primary rainbow is brighter and has red on the outer side.

Secondary rainbow has inverted colour sequence.

Apparent depth is less than real depth in denser medium.

A swimming pool appears shallower due to refraction.

Power of accommodation of eye is the ability to change focal length.

Near point of normal eye is 25 cm.

Far point of normal eye is infinity.

Myopia is corrected by concave lens.

Hypermetropia is corrected by convex lens.

Presbyopia is corrected by bifocal lens.

Astigmatism is corrected by cylindrical lens.

Cataract is the clouding of eye lens.

The human eye has a convex lens.

Least distance of distinct vision is 25 cm.

Magnifying power is the ratio of angle subtended with instrument to that without instrument.

Huygens’ principle: every point on a wavefront acts as a source of secondary wavelets.

Wavefront is the locus of points having the same phase.

Interference of light was first demonstrated by Young.

Condition for constructive interference: path difference = nλ.

Condition for destructive interference: path difference = (2n+1)λ/2.

Fringe width β = λD/d.

Intensity in interference is proportional to square of amplitude.

Coherent sources have constant phase difference.

Diffraction is the bending of light around obstacles.

Fresnel diffraction occurs with finite distance sources.

Fraunhofer diffraction occurs with parallel rays.

Single slit diffraction minima: a sinθ = nλ.

Resolving power increases with decrease in wavelength.

Polarisation proves the transverse nature of light.

Brewster’s law: tan i_p = μ.

Polaroid is used to produce plane polarised light.

Malus’ law: I = I₀ cos²θ.

Double refraction occurs in anisotropic crystals.

Optic axis is the direction of no double refraction.

Quarter wave plate introduces a path difference of λ/4.

Coulomb’s law: F = kq₁q₂/r².

Electric field intensity E = F/q₀.

Electric field due to a point charge is kq/r².

Electric field lines start from positive charge and end on negative charge.

Electric flux Φ = E·A.

Gauss’s law: Φ = q_enclosed / ε₀.

Electric field inside a charged conductor is zero.

Electric field just outside a charged conductor is σ/ε₀.

Electric potential V = work done per unit charge.

Potential due to a point charge is kq/r.

Potential difference is work done in moving unit charge.

Equipotential surface is perpendicular to electric field lines.

Work done in moving a charge on equipotential surface is zero.

Capacitance C = Q/V.

Capacitance of a parallel plate capacitor is ε₀A/d.

Energy stored in a capacitor is (1/2)CV².

Capacitance increases when dielectric is inserted.

Dielectric constant K = C_medium / C_vacuum.

Series combination of capacitors: 1/C = 1/C₁ + 1/C₂.

Parallel combination of capacitors: C = C₁ + C₂.

Electric dipole moment p = q × 2a.

Torque on a dipole in uniform field τ = p × E.

Potential energy of a dipole is −p·E.

Electric field due to a dipole on axial line is 2kp/r³.

Electric field due to a dipole on equatorial line is −kp/r³.

Faraday’s ice pail experiment demonstrates induction.

Charging by induction does not require contact.

Conservation of charge: total charge is conserved.

Quantisation of charge: q = ±ne.

Millikan’s oil drop experiment measured charge of electron.

Dielectric strength is the maximum electric field a material can withstand.

Polarisation of dielectric produces bound charges.

Van de Graaff generator produces high voltages.

Corona discharge occurs at sharp points.

Lightning conductor works on the principle of corona discharge.

The SI unit of capacitance is farad.

1 farad = 1 coulomb/volt.

Electric field is conservative in nature.

Potential is a scalar quantity while field is a vector.

The work done by electrostatic force is independent of path.

Electric current I = dq/dt.

Ohm’s law: V = IR.

Resistance R = ρl/A.

Resistivity depends on the nature of material.

Conductance is the reciprocal of resistance.

Series combination: R = R₁ + R₂ + …

Parallel combination: 1/R = 1/R₁ + 1/R₂ + …

Kirchhoff’s current law: algebraic sum of currents at a junction is zero.

Kirchhoff’s voltage law: algebraic sum of potential differences in a loop is zero.

Wheatstone bridge is balanced when P/Q = R/S.

Meter bridge is based on Wheatstone bridge principle.

Potentiometer measures emf without drawing current.

Internal resistance of a cell r = (E/V − 1)R.

Emf is the maximum potential difference when no current is drawn.

Terminal voltage V = E − Ir.

Joule’s law of heating: H = I²Rt.

Electric power P = VI = I²R = V²/R.

1 kilowatt hour = 3.6 × 10⁶ J.

Temperature coefficient of resistance is positive for metals.

Superconductivity occurs below critical temperature.

Drift velocity v_d = eEτ/m.

Current density J = σE.

Mobility μ = v_d/E.

Colour code of resistors helps in identifying resistance value.

Shunt is a low resistance connected in parallel with galvanometer.

Ammeter is a galvanometer with low resistance shunt.

Voltmeter is a galvanometer with high series resistance.

Ideal ammeter has zero resistance.

Ideal voltmeter has infinite resistance.

The SI unit of current is ampere.

Magnetic field lines form closed loops.

Earth’s magnetic field has both horizontal and vertical components.

Magnetic meridian is the vertical plane containing magnetic axis.

Angle of declination is the angle between geographic and magnetic meridian.

Angle of dip is the angle between total magnetic field and horizontal.

Magnetic moment of a current loop m = IA.

Torque on a current loop τ = m × B.

Biot-Savart law gives magnetic field due to a current element.

Magnetic field due to a long straight wire B = μ₀I/2πr.

Magnetic field at the centre of a circular loop B = μ₀I/2R.

Ampere’s circuital law: ∮ B·dl = μ₀I_enclosed.

Solenoid produces uniform magnetic field inside.

Magnetic field inside a long solenoid B = μ₀nI.

Force on a moving charge F = q(v × B).

Lorentz force is the force on a charged particle in electromagnetic field.

Force between two parallel currents is attractive if currents are in same direction.

Cyclotron accelerates charged particles using magnetic field.

Magnetic flux Φ = B·A.

Faraday’s law: induced emf = −dΦ/dt.

Lenz’s law gives the direction of induced current.

Self inductance L = Φ/I.

Mutual inductance M = Φ₂/I₁.

Energy stored in an inductor is (1/2)LI².

Eddy currents are induced currents in bulk conductors.

Eddy currents cause heating and are minimised by laminations.

Transformer works on mutual induction.

Step-up transformer increases voltage and decreases current.

Step-down transformer decreases voltage and increases current.

Efficiency of an ideal transformer is 100%.

Alternating current changes direction periodically.

Peak value, rms value and average value are related for AC.

rms value of AC is I₀/√2.

Capacitive reactance X_C = 1/ωC.

Inductive reactance X_L = ωL.

Impedance Z = √[R² + (X_L − X_C)²].

Power in AC circuit is VI cosφ.

Power factor cosφ = R/Z.

Resonance in LCR circuit occurs when X_L = X_C.

Quality factor Q = ω₀L/R.

LC oscillations are analogous to SHM.

Photoelectric effect: emission of electrons by light.

Einstein’s photoelectric equation: hν = φ + (1/2)mv²_max.

Work function is the minimum energy to eject electron.

de Broglie wavelength λ = h/p.

Heisenberg uncertainty principle: Δx·Δp ≥ h/4π.

Bohr’s model: angular momentum is quantised as mvr = nh/2π.

Energy of electron in nth orbit of hydrogen E_n = −13.6/n² eV.

Binding energy of nucleus is the energy required to break it into nucleons.

Mass defect Δm is converted into binding energy via E = Δmc².

Intrinsic semiconductor has equal number of electrons and holes; doping creates p-type or n-type semiconductors.