Every formula you need for JEE Main Physics, chapter by chapter. JEE Main Physics is 25 questions and 100 marks — four marks for a right answer, one mark off for a wrong one. Keep this open on your phone and run through one chapter a day.
This sheet matches the trimmed syllabus.
Every line here has been checked against the current NTA syllabus, word by word. The topics taken out in 2024 are not on this sheet — no Doppler effect in sound, no radioactive decay law or half-life, no Carnot engine, no cyclotron, no transistor, no earth’s magnetism, no dispersive power, no potentiometer. If the formula sheet you are using still carries those, it was written before the change. Learning them costs you time you do not have.
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JEE Main Physics Formula Sheet
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Mathematical Tools · Units and Measurements · Motion in a Straight Line · Motion in a Plane · Laws of Motion · Work Energy and Power · Rotational Motion · Centre of Mass · Gravitation · Mechanical Properties of Solids · Mechanical Properties of Fluids · Thermal Properties of Matter · Thermodynamics · Kinetic Theory of Gases · Oscillations · Waves · Electric Charges and Fields · Electrostatic Potential and Capacitance · Current Electricity · Moving Charges and Magnetism · Magnetism and Matter · Electromagnetic Induction · Alternating Current · Electromagnetic Waves · Ray Optics · Wave Optics · Dual Nature of Radiation and Matter · Atoms · Nuclei · Semiconductor Electronics
Mathematical Tools
| Resultant of two vectors | R = √(A² + B² + 2AB cosθ) |
| Direction of the resultant | tanα = B sinθ / (A + B cosθ) |
| Dot product | A·B = AB cosθ |
| Cross product | |A × B| = AB sinθ |
| Slope of a graph | velocity = dx/dt, acceleration = dv/dt |
| Area under a graph | displacement = area under the v–t graph |
NTA took the vector block out of the Physics syllabus in 2024. Vectors still run through Kinematics, Laws of Motion and Electrostatics, and they are in the Maths paper, so do not drop them.
Practise: Mathematical Tools — JEE Main questions with answer key
Units and Measurements
| Dimensions worth memorising | [Force] = MLT⁻², [Energy] = ML²T⁻², [Power] = ML²T⁻³ |
| Error in a sum or difference | the absolute errors add |
| Error in a product or quotient | the percentage errors add |
| Error in a power | if Z = AᵖBᵠ, then ΔZ/Z = p(ΔA/A) + q(ΔB/B) |
| Vernier least count | 1 main scale division − 1 vernier scale division |
| Screw gauge least count | pitch ÷ number of divisions on the circular scale |
Practise: Units and Measurements — JEE Main questions with answer key
Motion in a Straight Line
| First equation | v = u + at |
| Second equation | s = ut + ½at² |
| Third equation | v² = u² + 2as |
| Distance in the nth second | sₙ = u + (a/2)(2n − 1) |
| Average velocity | total displacement ÷ total time |
Practise: Motion in a Straight Line — JEE Main questions with answer key
Motion in a Plane
| Time of flight | T = 2u sinθ / g |
| Maximum height | H = u² sin²θ / 2g |
| Range | R = u² sin2θ / g, largest at θ = 45° where R = u²/g |
| Equation of the path | a parabola, y = x tanθ − gx² / (2u²cos²θ) |
| Centripetal acceleration | a = v²/r = ω²r |
| Relative velocity | vᴀʙ = vᴀ − vʙ |
Practise: Motion in a Plane — JEE Main questions with answer key
Laws of Motion
| Newton’s second law | F = ma = dp/dt |
| Impulse | FΔt = Δp |
| Static and kinetic friction | fₛ(max) = μₛN, fₖ = μₖN |
| Body in a lift | apparent weight N = m(g ± a) |
| Banked road, no friction | v = √(rg tanθ) |
| Level circular road | vₘₐₓ = √(μrg) |
| Vertical circle, top of the loop | vₘᵢₙ = √(gr) |
Practise: Laws of Motion — JEE Main questions with answer key
Work Energy and Power
| Work | W = Fs cosθ |
| Kinetic energy | KE = ½mv² = p²/2m |
| Work–energy theorem | Wₙₑₜ = ΔKE |
| Potential energy of a spring | U = ½kx² |
| Power | P = W/t = F·v |
| Elastic collision, equal masses | the two velocities are exchanged |
| Coefficient of restitution | e = relative speed of separation ÷ relative speed of approach |
Practise: Work Energy and Power — JEE Main questions with answer key
Rotational Motion
| Torque and angular momentum | τ = Iα, L = Iω |
| Moments of inertia | ring MR², disc ½MR², solid sphere (2/5)MR², hollow sphere (2/3)MR², rod about its centre ML²/12 |
| Parallel axis theorem | I = Icm + Md² |
| Perpendicular axis theorem | Iz = Ix + Iy, for a flat body |
| Rolling body, total KE | KE = ½mv²(1 + k²/R²) |
| Rolling down an incline | a = g sinθ / (1 + k²/R²) |
| Conservation of angular momentum | I₁ω₁ = I₂ω₂ when no external torque acts |
Practise: Rotational Motion — JEE Main questions with answer key
Centre of Mass
| Position of the centre of mass | xcm = (m₁x₁ + m₂x₂) / (m₁ + m₂) |
| Velocity of the centre of mass | vcm = (m₁v₁ + m₂v₂) / (m₁ + m₂) |
| With no external force | vcm does not change, whatever happens inside |
Practise: Centre of Mass — JEE Main questions with answer key
Gravitation
| Law of gravitation | F = Gm₁m₂ / r², G = 6.67 × 10⁻¹¹ |
| g at a height | g′ = g(1 − 2h/R) for h much smaller than R |
| g at a depth | g′ = g(1 − d/R) |
| Orbital velocity | vₒ = √(GM/r) |
| Escape velocity | vₑ = √(2GM/R) = √2 × vₒ, about 11.2 km/s for the earth |
| Time period of a satellite | T² = 4π²r³ / GM |
| Energy of a satellite | E = −GMm / 2r |
Practise: Gravitation — JEE Main questions with answer key
Mechanical Properties of Solids
| Stress and strain | stress = F/A, strain = Δl/l |
| Young’s modulus | Y = FL / Al |
| Extension under a load | l = FL / AY |
| Bulk modulus | B = −ΔP / (ΔV/V), and compressibility = 1/B |
| Modulus of rigidity | η = shear stress ÷ shear strain |
| Breaking load | breaking stress × area of cross section |
Practise: Mechanical Properties of Solids — JEE Main questions with answer key
Mechanical Properties of Fluids
| Pressure in a liquid | P = P₀ + hρg |
| Pascal’s law | pressure applied to an enclosed fluid is passed on undiminished |
| Buoyant force | = Vρg, the weight of the fluid displaced |
| Equation of continuity | A₁v₁ = A₂v₂ |
| Bernoulli’s principle | P + ½ρv² + ρgh = constant |
| Stokes’ law | F = 6πηrv |
| Terminal velocity | v = 2r²(ρ − σ)g / 9η |
| Excess pressure | drop 2T/r, soap bubble 4T/r |
| Capillary rise | h = 2T cosθ / rρg |
Practise: Mechanical Properties of Fluids — JEE Main questions with answer key
Thermal Properties of Matter
| Linear, areal and volume expansion | ΔL = LαΔT, β = 2α, γ = 3α |
| Heat gained or lost | Q = mcΔT |
| Latent heat | Q = mL; ice 80 cal/g, water 540 cal/g |
| Principle of calorimetry | heat lost by the hot body = heat gained by the cold body |
| Conduction | Q/t = kA(T₁ − T₂) / L |
| Thermal resistance | R = L / kA; rods end to end add, rods side by side add as conductances |
Practise: Thermal Properties of Matter — JEE Main questions with answer key
Thermodynamics
| First law | ΔQ = ΔU + ΔW |
| Isothermal process | T constant, ΔU = 0, W = nRT ln(V₂/V₁) |
| Adiabatic process | Q = 0, PVᵞ = constant, TVᵞ⁻¹ = constant, W = (P₁V₁ − P₂V₂)/(γ − 1) |
| Isochoric process | V constant, W = 0, ΔQ = ΔU = nCᵥΔT |
| Isobaric process | P constant, W = PΔV, ΔQ = nCₚΔT |
| Mayer’s relation | Cₚ − Cᵥ = R |
| Cyclic process | ΔU = 0 over a full cycle, so Q = W |
| Second law | heat does not flow on its own from a colder body to a hotter one |
Practise: Thermodynamics — JEE Main questions with answer key
Kinetic Theory of Gases
| Ideal gas equation | PV = nRT |
| Pressure of a gas | P = ⅓ρv²_rms |
| Three speeds | vrms = √(3RT/M), vmean = √(8RT/πM), vmp = √(2RT/M) |
| Average kinetic energy per molecule | = (3/2)kT |
| Degrees of freedom | monatomic 3, diatomic 5, and energy per mole = (f/2)RT |
| Specific heats | Cᵥ = (f/2)R, Cₚ = Cᵥ + R, γ = 1 + 2/f |
| Mean free path | λ = 1 / (√2 πd²n) |
Practise: Kinetic Theory of Gases — JEE Main questions with answer key
Oscillations
| Displacement in SHM | x = A sin(ωt + φ) |
| Velocity and acceleration | v = ω√(A² − x²), a = −ω²x |
| Spring–mass system | T = 2π√(m/k) |
| Simple pendulum | T = 2π√(l/g) |
| Springs in combination | parallel k = k₁ + k₂, series 1/k = 1/k₁ + 1/k₂ |
| Energy in SHM | total = ½mω²A², kinetic at x is ½mω²(A² − x²) |
Practise: Oscillations — JEE Main questions with answer key
Waves
| Wave speed | v = fλ |
| Progressive wave | y = A sin(ωt − kx), with k = 2π/λ |
| Wave on a stretched string | v = √(T/μ) |
| Sound in a gas | v = √(γP/ρ), and v ∝ √T |
| Stationary wave | node to node = λ/2 |
| Open pipe | fₙ = nv/2L, every harmonic present |
| Closed pipe | fₙ = (2n − 1)v/4L, odd harmonics only |
| Beats | f = |f₁ − f₂| |
Practise: Waves — JEE Main questions with answer key
Electric Charges and Fields
| Coulomb’s law | F = kq₁q₂ / r², with k = 9 × 10⁹ |
| Electric field of a point charge | E = kq / r² |
| Dipole moment | p = q × 2a |
| Field of a short dipole | axial 2kp/r³, equatorial kp/r³ |
| Torque on a dipole | τ = pE sinθ |
| Gauss’s law | φ = qin / ε₀ |
| Standard fields | infinite sheet σ/2ε₀, long wire λ/2πε₀r, inside a conductor zero |
Practise: Electric Charges and Fields — JEE Main questions with answer key
Electrostatic Potential and Capacitance
| Potential of a point charge | V = kq / r |
| Field from potential | E = −dV/dr |
| Potential of a dipole | V = kp cosθ / r² |
| Capacitance | C = Q/V; parallel plate C = ε₀A/d |
| With a dielectric | C = Kε₀A/d |
| Combinations | series 1/C = Σ1/Cᵢ, parallel C = ΣCᵢ |
| Energy stored | U = ½CV² = Q²/2C |
| Energy density | u = ½ε₀E² |
Practise: Electrostatic Potential and Capacitance — JEE Main questions with answer key
Current Electricity
| Current and drift velocity | I = nAevd, and mobility μ = vd / E |
| Resistance | R = ρL / A, conductivity σ = 1/ρ |
| Ohm’s law | V = IR |
| Resistance and temperature | R = R₀(1 + αΔT), and α is positive for a metal, negative for a semiconductor |
| I–V graph | a straight line through the origin for an ohmic conductor, curved for a non-ohmic one |
| Combinations | series R = ΣRᵢ, parallel 1/R = Σ1/Rᵢ |
| Cell with internal resistance | E = I(R + r), terminal voltage V = E − Ir |
| Kirchhoff’s laws | at a junction ΣI = 0; around a loop ΣV = 0 |
| Wheatstone bridge | balanced when P/Q = R/S |
| Metre bridge | R/S = l / (100 − l) |
| Power | P = VI = I²R = V²/R |
Practise: Current Electricity — JEE Main questions with answer key
Moving Charges and Magnetism
| Force on a moving charge | F = qvB sinθ |
| Force on a current-carrying wire | F = BIL sinθ |
| Biot–Savart law | dB = (μ₀/4π) I dl sinθ / r² |
| Long straight wire | B = μ₀I / 2πr |
| Centre of a circular coil | B = μ₀NI / 2r |
| Inside a long solenoid | B = μ₀nI |
| Circular path in a magnetic field | r = mv/qB, T = 2πm/qB, and the period does not depend on the speed |
| Force between parallel wires | F/L = μ₀I₁I₂ / 2πd |
| Torque on a current loop | τ = NIAB sinθ |
| Galvanometer conversions | ammeter S = IᵍG/(I − Iᵍ), voltmeter R = V/Iᵍ − G |
Practise: Moving Charges and Magnetism — JEE Main questions with answer key
Magnetism and Matter
| Magnetic moment | M = NIA for a current loop |
| Axial field of a short magnet | B = (μ₀/4π)(2M/d³) |
| Equatorial field | B = (μ₀/4π)(M/d³) |
| Torque and potential energy | τ = MB sinθ, U = −MB cosθ |
| Work done in turning a magnet | W = MB(cosθ₁ − cosθ₂) |
| Oscillating magnet | T = 2π√(I/MB) |
| Gauss’s law in magnetism | the net magnetic flux through any closed surface is zero |
| Three classes | diamagnetic, paramagnetic, ferromagnetic; above its Curie temperature a ferromagnetic substance turns paramagnetic |
Practise: Magnetism and Matter — JEE Main questions with answer key
Electromagnetic Induction
| Magnetic flux | φ = BA cosθ |
| Faraday’s law | e = − dφ/dt |
| Motional emf | e = Bvl |
| Self inductance | e = −L dI/dt, energy stored = ½LI² |
| Inductance of a solenoid | L = μ₀n²Al |
| Mutual inductance | e = −M dI₁/dt |
| Lenz’s law | the induced current opposes the change that caused it |
Practise: Electromagnetic Induction — JEE Main questions with answer key
Alternating Current
| Instantaneous current | I = I₀ sinωt |
| Root mean square values | Irms = I₀/√2, Vrms = V₀/√2 |
| Average over a half cycle | 2I₀/π |
| Reactances | XL = ωL, XC = 1/ωC |
| Impedance and phase | Z = √(R² + (XL − XC)²), tanφ = (XL − XC)/R |
| Resonance | f = 1 / 2π√(LC); at resonance Z = R and the current is largest |
| Average power | P = Vrms Irms cosφ, with power factor cosφ = R/Z |
| Transformer | Vₛ/Vₚ = Nₛ/Nₚ |
Practise: Alternating Current — JEE Main questions with answer key
Electromagnetic Waves
| Speed in vacuum | c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s |
| Speed in a medium | v = 1/√(με) |
| Field ratio | E₀ / B₀ = c |
| Direction | E, B and the direction of travel are mutually perpendicular |
| Intensity | I = ½ε₀E₀²c |
| Radiation pressure | I/c when fully absorbed, 2I/c when fully reflected |
| Displacement current | Id = ε₀ dφE/dt |
| Spectrum, longest wavelength first | radio, microwave, infrared, visible, ultraviolet, X-ray, gamma; visible is about 400 to 700 nm |
Practise: Electromagnetic Waves — JEE Main questions with answer key
Ray Optics
| Mirror formula | 1/v + 1/u = 1/f, with f = R/2 |
| Magnification by a mirror | m = −v/u |
| Lens formula | 1/v − 1/u = 1/f, and m = v/u |
| Lens maker’s formula | 1/f = (μ − 1)(1/R₁ − 1/R₂) |
| Power of a lens | P = 1/f in metres; lenses in contact P = P₁ + P₂ |
| Refraction | μ = sin i / sin r, and μ = c/v |
| Critical angle | sin C = 1/μ |
| Prism at minimum deviation | μ = sin((A + δₘ)/2) ÷ sin(A/2); for a thin prism δ = (μ − 1)A |
| Simple microscope | M = 1 + D/f, with D = 25 cm |
| Compound microscope | M = (v₀/u₀)(1 + D/fₑ), tube length L = v₀ + fₑ |
| Astronomical telescope | M = f₀/fₑ in normal adjustment, tube length L = f₀ + fₑ |
Practise: Ray Optics — JEE Main questions with answer key
Wave Optics
| Fringe width | β = λD/d |
| Maxima and minima | path difference nλ for a bright fringe, (2n − 1)λ/2 for a dark one |
| Intensity in interference | I = 4I₀cos²(φ/2) |
| Ratio of maximum to minimum | Imax/Imin = (√I₁ + √I₂)² ÷ (√I₁ − √I₂)² |
| Single slit diffraction | first minimum at sinθ = λ/a; width of the central maximum = 2λD/a |
| Brewster’s law | tan iₚ = μ |
| Malus’s law | I = I₀cos²θ |
Practise: Wave Optics — JEE Main questions with answer key
Dual Nature of Radiation and Matter
| Energy of a photon | E = hf = hc/λ; hc = 1240 eV·nm |
| Photoelectric equation | hf = φ + KEmax |
| Stopping potential | KEmax = eV₀ |
| Threshold | φ = hf₀ = hc/λ₀ |
| Momentum of a photon | p = h/λ = E/c |
| de Broglie wavelength | λ = h/p = h/mv |
| Electron accelerated through V | λ = 12.27/√V Å |
Practise: Dual Nature of Radiation and Matter — JEE Main questions with answer key
Atoms
| Bohr’s quantisation | mvr = nh/2π |
| Radius of the nth orbit | rₙ = 0.529 n²/Z Å |
| Energy of the nth level | Eₙ = − 13.6 Z²/n² eV |
| Energy of a transition | E = 13.6 Z²(1/n₁² − 1/n₂²) eV |
| Rydberg formula | 1/λ = RZ²(1/n₁² − 1/n₂²), R = 1.097 × 10⁷ m⁻¹ |
| Series | Lyman ultraviolet (n₁ = 1), Balmer visible (n₁ = 2), Paschen infrared (n₁ = 3) |
| Speed in the nth orbit | vₙ ∝ Z/n, and v₁ = c/137 |
Practise: Atoms — JEE Main questions with answer key
Nuclei
| Nuclear radius | R = R₀A^(1/3), R₀ = 1.2 fm |
| Nuclear density | about 2.3 × 10¹⁷ kg/m³, the same for every nucleus |
| Mass defect | Δm = [Zmₚ + (A − Z)mₙ] − M |
| Binding energy | BE = Δm × 931.5 MeV |
| Mass–energy equivalence | 1 u = 931.5 MeV |
| Peak of the binding energy curve | about 8.8 MeV per nucleon, near A = 56 |
| Q value of a reaction | Q = (mass of reactants − mass of products) × 931.5 MeV |
| Energy released | about 200 MeV per fission of uranium-235; about 26 MeV when four hydrogen nuclei build one helium nucleus |
Practise: Nuclei — JEE Main questions with answer key
Semiconductor Electronics
| Diode | conducts in forward bias, blocks in reverse bias |
| Rectifier output frequency | half wave = input frequency, full wave = twice the input frequency |
| Zener diode | works in reverse breakdown and holds the voltage steady |
| Other diodes | LED gives out light, photodiode works in reverse bias, solar cell makes an emf with no bias |
| Logic gates | AND = A·B, OR = A + B, NOT = Ā; NAND and NOR are the universal gates |
| De Morgan | the complement of a sum is the product of the complements, and the other way round |
Practise: Semiconductor Electronics — JEE Main questions with answer key
How to use a formula sheet
- Reading it is not revision. Cover the right column, say the formula aloud, then check.
- A formula you cannot write in five seconds is a formula you do not have in the exam.
- After each chapter, go and do the ten questions linked under it. That is where you find out what you actually know.
Where the marks sit, chapter by chapter: JEE Main Physics chapter-wise weightage.
The official syllabus, unit by unit: JEE Main Physics syllabus 2027, with what was taken out in 2024.
Knowing a formula is not the same as using it in time(फ़ॉर्मूला याद होना और समय पर लगा पाना — दो अलग चीज़ें हैं)
You can read this sheet and feel ready. In the paper the question is never whether you know the formula. It is whether the right one comes to you in two minutes, with the clock running. Only a timed paper shows you that.(यह शीट पढ़कर लगता है कि तैयारी हो गई। पेपर में सवाल यह नहीं होता कि फ़ॉर्मूला आता है या नहीं। सवाल यह होता है कि घड़ी चलते हुए, दो मिनट में सही फ़ॉर्मूला याद आता है या नहीं। यह सिर्फ़ टाइम लगाकर दिया गया पेपर दिखाता है।)
Dhurandhar has three timed papers for every chapter, each with a target score, an answer key and a hint for every question. Revise a chapter from this sheet, then sit its paper the same day.(धुरंधर में हर चैप्टर के तीन टाइम्ड पेपर हैं — टारगेट स्कोर, आंसर की, और हर सवाल का हिंट। इस शीट से एक चैप्टर दोहराइए, और उसी दिन उसका पेपर दीजिए।)
हर सवाल पर वार करो,
धुरंधर बनकर JEE पार करो!
One JEE Main Physics question every morning
It comes at 7 AM on Telegram. Tap the option you think is right and you will know at once whether it was. The worked hint follows the next morning.