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PRAGYAN 2026 - IAT PHYSICS + COMPLETE REVISION IAT Physics RAacister Revision Guicde High-Weightage Chapters - Key Concepts - Formulas - IAT PYQs - Exam Tips G . Mechanics ) @ » Waves & TD) G . Electrostatics ) G * Current Electricity ) G . Optics ) CG + Modern Physics ) G . Thermodynamics ) Ce + Magnetism & ENE ) RAechanics Kinematics - Newton's Laws - Work-Energy - Rotation - Gravitation G Very High Weightage ) C68 questions in TAT) 1.1- KINEMATICS Equations of Motion mp VELOCITY DISPLACEMENT v=u tat s = ut + tat? VELOCITY-DISP NTH SECOND v2 = u2 + 2as S, = u + a(2n-1)/2 S, formula (distance in nth second): extremely common in IAT MCQs — memorise it cold. Projectile Motion mp Relative Motion ¢ Time of flight: T = 2u sin@ / g ¢ Relative velocity: v_AB = v_A - v_B ¢ Max height: H = u? sin? / 2g ° Range: R = u? sin20 / g ¢ Max Range: 0 = 45° — R_max = u2/g * Complementary angles (8 and 90°-6) give same range. ¢ River-boat: 6_drift minimised when sin 8 =v_r/v_b ¢ For minimum time: boat points perpendicular to river. e For zero drift: boat aims upstream at angle a where sin a = v_r/v_b / ) IAT PYOs — Kinematics IAT 2022 A ball is thrown horizontally from a height of 20m. If it travels a horizontal distance of 40m before hitting the ground, what is the initial speed? (g = 10 m/s?) > t = v(2h/g) = v4 = 2s; u = 40/2 = 20 m/s IAT 2023 Two balls are projected from the same point with the same speed at angles 30° and 60° to the horizontal. The ratio of their ranges is: > Ri/R2 = sin6@° / sinl20° = 1 : 1 (complementary angles + same range) L S 1.2 - NEWTON'S LAWS & FRICTION ~ Newton's Laws Imp ¢ 1st Law: Inertia — body at rest/uniform motion unless acted upon by net external force. ¢ 2nd Law: F = ma (net force = rate of change of momentum). ¢ 8rd Law: Every action has equal and opposite reaction (on different bodies). Pseudo Force = -ma (in non-inertial frame). Applied in direction opposite to acceleration of the frame. S Friction mp ¢ Static: f_s PE = #x200x(0.1)? = 1 J 1.4 - ROTATIONAL MOTION Key Concepts & Formulae imp TORQUE ANG. MOMENTUM t=rxF=TIa L = Iw = mvr ROT. KE ROLLING KE KE = 4Iw? KE = 4mv? + 41Iw? Body Moment of Inertia Axis Solid Sphere 2MR2/5 Diameter Hollow Sphere 2MR2/3 Diameter Solid Cylinder/Disc MR2/2 Central axis Hollow Cylinder/Ring MR? Central axis Rod ML?/12 Centre Rod ML?2/3 End Rolling without slipping: v_cm = Rw. For inclined plane, solid sphere reaches bottom first (smallest I/MR?). 1.5 - GRAVITATION Key Formulae imp Kepler's Laws imp ¢ F=GMm/r? (Newtor's law) ¢ Ist: Planets move in elliptical orbits; Sun ¢ g=GM/R? (surface gravity) at one focus. ° gat height h: g' = g(R/R+h)? ¢ gat depth d: g' = g(1- d/R) © Orbital velocity: vo = \(GM/r) = V(gR?/r) * Escape velocity: v_e = \(2gR) = \(2GM/R) * 2nd: Equal areas in equal times (L is conserved). © 3rd: T? « r? — T?/r? = constant. Geostationary orbit: T = 24h, orbit = 36,000 km above Earth's surface. IAT PYO — Gravitation IAT 2021 The orbital period of a satellite at height h above Earth's surface is T. If h is doubled, what is the new period? > T « r4(3/2). ra = Rth, rz = R+2h. Tz = Tix(r2/r1)*(3/2). Substitute values. Wreves & SFEINRA Simple Harmonic Motion - Sound Wave Properties CG High Weightage ) C35 questions in TAT ) 2.1: SIMPLE HARMONIC MOTION SHM Fundamentals isp DISPLACEMENT x = A sin(wt + ) VELOCITY v = Aw cos(wt) ACCELERATION a= -w?x TIME PERIOD T = 2n/w | v = w(A2 - x?) + v is max at x=0, zero at x=+A ¢ KE: %Zmw?(A?-x?) — max at equilibrium e PE: “%mw?x? — max at extremes ¢ Total Energy: E = “mw?A? = constant * Sound speed increases with temperature: v « \T \ Standing Waves & Resonance Doppler Effect tmp IMP f' = f « (v + v_observer) / (v ¥ ¢ String (both ends fixed): f, = nv/2L v_source) * Closed pipe (one end): f, = (2n-1)v/4L (odd harmonics only) *¢ Observer moves toward source: use + in * Open pipe (both ends): f, = nv/2L (all numerator, harmonics) ¢ Source moves toward observer: use - in ¢ Node: zero displacement; Antinode: max denominator. displacement. e Frequency increases when approaching, decreases when receding. Beats Imp ¢ Beat frequency: f_beat = |fi - fal ¢ Beats are heard when two slightly different frequencies interfere. ¢ Max beats perceptible by human ear: ~10 Hz. IAT Tip: If a tuning fork of 512 Hz produces 4 beats/sec with another, the second fork is 508 or 516 Hz. Use additional info to decide which. Electrostatics Coulomb's Law - Electric Field - Potential - Capacitors CG Very High Weightage ) (5-7 questions in TAT ) 3-1: COULOMB'S LAW & ELECTRIC FIELD Coulomb's Law & Field mp COULOMB K VALUE F = kqiq2/r? k = 9x10° Nm2/C2 E FIELD (POINT) E FIELD (PLATE) E = kq/r? E = o/€o Configuration E field Inside conductor E=0 Infinite line charge E = A/(2n€or) Infinite plane sheet E = o/(2€0) Between parallel plates E = o/€o0 Inside uniformly charged sphere E = pr/(3e0) « 5 Outside sphere E = kQ/r2 « 1/r2 E inside hollow conductor = O. Charges reside on surface only (Faraday cage principle). 3.2 - ELECTRIC POTENTIAL & POTENTIAL ENERGY Potential imp POTENTIAL (POINT) PE OF SYSTEM V = kq/r U = kqaqa/r E-V RELATION WORK DONE E = -dV/dr W = q(V_A - V_B) ¢ Equipotential surface: No work done moving charge along it. e Eis always perpendicular to equipotential surfaces. ¢ Vinside hollow sphere = V on surface = kQ/R (constant inside). E can be zero where V # O, and V can be zero where E # O. Don't confuse them! 3.3 - GAUSS'S LAW & FLUX Gauss's Law mp § E+ dA = Qenc / € IAT 2021 An electric dipole of moment p is placed in uniform field E at angle 30°. Find the torque. > t = pE sin® = pE sin30° = pE/2 Current Electricity Ohm's Law - Kirchhoff's Laws - Cells - Wheatstone Bridge (% High Weightage ) (~3-5 questions in IAT ) 4.1- OHM'S LAW & RESISTANCE Core Formulae imp OHM'S LAW RESISTANCE v=IR R = pL/A POWER R WITH TEMP P = VI = I?R = V2/R R = Ro(1 + aAT) Series: R_eff = Ri + Ra t+... | | Parallel: 1/R_eff = 1/R1 + 1/R2 ¢ Same current; voltage divides. ¢ Same voltage; current divides. Colour code for resistors: B B ROY Great Britain Very Good Wife = Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, White = O-9 4.2 -KIRCHHOFF'S LAWS & CELLS Kirchhoff's Laws mp ¢ KCL (Junction Rule): =I_in = =|_out (charge conservation). ¢ KVL (Loop Rule): Sum of all EMFs and voltage drops in a closed loop = O. Sign Convention for KVL: Go in direction of current > voltage drop is negative (-IR). Go against current — +IR. EMF: if positive terminal first — +e. EMF & Internal Resistance Imp Wheatstone Bridge imp ¢ Terminal voltage: V = € - Ir (discharging) ¢ Balanced condition: P/Q = R/S (no current © V=e+ Ir (charging) through galvanometer). * Max power to external: R_ext =r * Metre Bridge: R/S = I/(100-1) © Cells in series: ¢_total = €1+€2; r_total = ¢ Potentiometer: Used to compare EMFs or ritte find internal resistance. * Cells in parallel: ¢_eq = £(ei/ri)/Z(1/ri) ° EMF ratio: €:/€2 = h/le X IAT PYQ — Current Electricity IAT 2022 Three resistors of 2Q, 3Q, and 6Q are connected in parallel. A 12V battery is connected. Find the total current drawn. > 1/R_eff = 1/2+1/3+1/6 = 3/6+2/6+1/6 = 6/6 = 1 » R_eff = 10. I = 12/1 = 12A IAT 2023 A cell of EMF 2V and internal resistance 0.50 delivers current to external resistance 1.50. Find terminal voltage. > I = 2/(@.5+1.5) = 1A. V_terminal = e-Ir = 2-1x0.5 = 1.5V Optics Ray Optics - Wave Optics - Interference - Diffraction Ce Very High Weightage ) (5-6 questions in TAT ) 5.1- RAY OPTICS — MIRRORS & REFRACTION [ A = (2n-1)A/2 | | Yn = nAD/d ¢ Constructive interference: Path diff = nA — bright. ¢ Destructive interference: Path diff = (n+%2)A — dark. ¢ If white light used: central fringe is white; others are coloured. ¢ Fringe width B « A (violet fringes narrower than red). Coherent sources: same frequency, constant phase difference. Essential for interference pattern. Single Slit Diffraction & Polarization ve ¢ 1st dark fringe: a sin® = A y = AD/a * Central maximum width = 2AD/a ¢ Brewster's angle: tan i_B = n — at this angle, reflected light is fully polarized. ¢ Malus's Law: | = lo cos?6 (polarized light through analyser) IAT PYOs — Optics IAT 2022 In YDSE, slits are separated by 0.5mm and screen is 1m away. If wavelength is 500nm, find fringe width. > B = AD/d = (500x10-°x1)/(0.5x10-3) = 1x10-3 m = 1 mm IAT 2023 A convex lens of focal length 20cm forms a real image at 60cm from the lens. Find object distance. > 1/v-1/u = 1/f + 1/60-1/u = 1/20 + 1/u = 1/60-1/20 = (1-3)/60 = -1/30. u = -30cm IAT 2021 Critical angle for glass-air interface is 30°. Find refractive index of glass. > sin C = 1/n + n = 1/sin30° = 1/0.5 = 2 NAoclern Physics Photoelectric Effect - Atomic Models - Nuclear Physics - Radioactivity G Very High Weightage ) C57 questions in TAT ) 6.1. PHOTOELECTRIC EFFECT & DUAL NATURE Einstein's Photoelectric Equation vp PHOTON ENERGY PHOTOELECTRIC E = hf = he/A hf = Wo + KE_max STOPPING POT. eVs = KE_max DE BROGLIE A = h/mv = h/p ° h=6626 x 10-* J-s (Planck's constant) ¢ Threshold frequency: fo = Wo/h e No emission below fo regardless of intensity. * Intensity 4: more electrons emitted (current 7), KE unchanged. e Frequency 7: KE_max increases, current unchanged. Stopping potential depends only on frequency, NOT intensity. This is a classic IAT trap! 6.2 - BOHR'S MODEL & HYDROGEN SPECTRUM Bohr's Model imp RADIUS In = 0.529xn2/Z A VELOCITY Vn = 2.18x10®xZ/n m/s ENERGY ANG. MOMENTUM E, = -13.6 Z?/n? eV L = nh/2n Series na Region Lyman 1 UV Balmer 2 Visible ¢ Fusion: Light nuclei combine — heavier + more energy (H — He in Sun) Radioactivity mp DECAY LAW HALF-LIFE N = Noe*(-At) Tt = 0.693/A ACTIVITY MEAN LIFE A = AN = Aoe*(-At) t = 1/A = T4/0.693 Decay Change in Z Change in A a decay Z-2 A-4 B- decay Z4+1 A unchanged B* decay Z-1 A unchanged y decay No change No change After n half-lives: N = No/2°. If T¥% = 20min and t = Thr: n = 3 half-lives > N = No/8. IAT PYQ — Nuclear Physics IAT 2022 A radioactive substance has half-life of 5 years. What fraction remains after 20 years? > n = 20/5 = 4 half-lives. Fraction = (1/2)* = 1/16 Thermodynamics Laws of Thermodynamics - Processes - Kinetic Theory - Heat Transfer (% High Weightage ) (3-4 questions in IAT ) 7-1: LAWS OF THERMODYNAMICS Four Laws imp e Zeroth Law: Thermal equilibrium and temperature concept. A=B and B=C — A=C. ¢ First Law: AU = Q - W (energy conservation; Q = heat added, W = work done by system) ¢ Second Law: Entropy of universe always increases; heat flows from hot to cold spontaneously. ¢ Third Law: Entropy — O as T > OK (absolute zero unattainable). Thermodynamic Processes Imp Process Condition Work done W AU Isothermal T = const nRT 1n(V2/Vi) ) Adiabatic Q=0 -AU = nC AT nC AT Isochoric V = const tv) nC AT Isobaric P = const PAV = nRAT nCyAT Adiabatic: PVAy = const; TVA(y-1) = const; TPA((I-y)/y) = const. y = Cp/Cv. 7.2 -KINETIC THEORY OF GASES Key Results imp IDEAL GAS KE AVG PV = nRT KE = (3/2)kT per molecule RMS SPEED MEAN SPEED v_rms = V(3RT/M) v_mean = v(8RT/nM) ¢ Most probable speed: v_mp = ¥(2RT/M) ¢ v_mp:v_mean:v_rms = 1: 1.128 : 1.225 ¢ Degrees of freedom: Monatomic = 3; Diatomic = 5; Triatomic = 6. © Cy= (f/2)R; C, = (f/2+1)R; y = 1+ 2/f y values: Monatomic = 5/3; Diatomic = 7/5; Triatomic linear = 7/6. Long straight wire B = pol/2nr Centre of circular loop (radius R) B = pol/2R Inside solenoid B = ponl Inside toroid B = poNI/2nr Outside solenoid/toroid Bz=0 8.2 - ELECTROMAGNETIC INDUCTION Faraday's & Lenz's Law mp EMF INDUCED FLUX € = -d0/dt © = BA cos@ MOTIONAL EMF SELF -INDUCTANCE e€ = Bvl e€ = -L dI/dt ¢ Lenz's Law: Induced current opposes the change in flux (follows from energy conservation). ¢ L for solenoid: L = pon?Al = UoN?A/I e Energy stored in inductor: U = “LI? Transformer: Vi/V2 = Ni/N2 = L/h (for ideal transformer, 100% efficiency). AC Circuits iP INDUCTIVE REACTANCE CAPACITIVE REACTANCE X_L = wh = nfl X_C = 1/wC IMPEDANCE (LCR) RESONANCE Z = v(R2+(X_L-X_C)2) f_x = 1/(2nvLC) e At resonance: X_L = X_C, Z = R (minimum), | = V/R (maximum). ¢ Power factor: cos @ = R/Z e Average power: P = V_rms x I_rms x cos @ © Virms = Vo/V2; |_rms = lo/V2 IAT PYQs — EMI & Magnetism c IAT 2023 A conducting rod of length 0.5m moves with velocity 2 m/s perpendicular to a field B = O.4T. Find induced EMF. 2 € = Bvl = 0.4x2x0.5 = 0.4V IAT 2022 In an LCR series circuit, L=1H, C=10OuF, R=200. Find the resonant frequency. >» fox = 1/(2nvLC) = 1/(2nv(1x10-4)) = 1/(2nx0.01) = 15.9 Hz IAT 2022 A proton moves with speed v in magnetic field B. Radius of circular path is r. If speed is doubled, new radius is: > xr = mv/qB. New r = m(2v)/qB = 2r NAcister Formula Sheet All must-memorise formulae at a glance Mechanics mp Formula Meaning v =u + at; v? = u? + 2as; s = ut + tat? Equations of motion R = u?sin20/g; H = u2sin?0/2g; T = 2usin®/g Projectile F = ma; p = mv; J = Ap = Fat Newton / Impulse W = Fd cos0; KE = +mv?; PE = mgh Work / Energy t = Ia; L = Iw; KE_rot = +Iw? Rotational 
