NEET Physics Formulas (36 Yrs)

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### Kinematics - **Displacement:** $\Delta x = x_f - x_i$ - **Average Velocity:** $v_{avg} = \frac{\Delta x}{\Delta t}$ - **Average Acceleration:** $a_{avg} = \frac{\Delta v}{\Delta t}$ - **Equations of Motion (Constant Acceleration):** - $v = u + at$ - $s = ut + \frac{1}{2}at^2$ - $v^2 = u^2 + 2as$ - $s_n = u + \frac{a}{2}(2n - 1)$ (Displacement in $n^{th}$ second) - **Relative Velocity:** $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$ ### Laws of Motion - **Newton's Second Law:** $\vec{F} = m\vec{a}$ - **Impulse:** $\vec{J} = \vec{F}\Delta t = \Delta\vec{p}$ - **Momentum:** $\vec{p} = m\vec{v}$ - **Conservation of Momentum:** $\sum \vec{p}_{initial} = \sum \vec{p}_{final}$ - **Friction Force:** $f_s \le \mu_s N$, $f_k = \mu_k N$ - **Centripetal Force:** $F_c = \frac{mv^2}{r} = m\omega^2 r$ ### Work, Energy & Power - **Work Done:** $W = \vec{F} \cdot \vec{d} = Fd\cos\theta$ - **Kinetic Energy:** $K = \frac{1}{2}mv^2$ - **Potential Energy (Gravitational):** $U_g = mgh$ - **Potential Energy (Spring):** $U_s = \frac{1}{2}kx^2$ - **Work-Energy Theorem:** $W_{net} = \Delta K$ - **Power:** $P = \frac{W}{t} = \vec{F} \cdot \vec{v}$ - **Conservation of Mechanical Energy:** $K_i + U_i = K_f + U_f$ (for conservative forces) ### Rotational Motion - **Angular Displacement:** $\Delta\theta$ - **Angular Velocity:** $\omega = \frac{d\theta}{dt}$ - **Angular Acceleration:** $\alpha = \frac{d\omega}{dt}$ - **Equations of Rotational Motion:** - $\omega = \omega_0 + \alpha t$ - $\theta = \omega_0 t + \frac{1}{2}\alpha t^2$ - $\omega^2 = \omega_0^2 + 2\alpha\theta$ - **Torque:** $\vec{\tau} = \vec{r} \times \vec{F} = I\vec{\alpha}$ - **Moment of Inertia:** $I = \sum mr^2$ - **Angular Momentum:** $\vec{L} = I\vec{\omega} = \vec{r} \times \vec{p}$ - **Rotational Kinetic Energy:** $K_{rot} = \frac{1}{2}I\omega^2$ - **Radius of Gyration:** $K = \sqrt{\frac{I}{M}}$ ### Gravitation - **Newton's Law of Gravitation:** $F = G\frac{m_1 m_2}{r^2}$ - **Gravitational Acceleration:** $g = G\frac{M}{R^2}$ - **Variation of g with Altitude:** $g' = g(1 - \frac{2h}{R})$ (for $h \ll R$) - **Variation of g with Depth:** $g' = g(1 - \frac{d}{R})$ - **Gravitational Potential Energy:** $U = -\frac{GMm}{r}$ - **Gravitational Potential:** $V = -\frac{GM}{r}$ - **Escape Velocity:** $v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}$ - **Orbital Velocity:** $v_o = \sqrt{\frac{GM}{r}}$ - **Time Period of Satellite:** $T = 2\pi\sqrt{\frac{r^3}{GM}}$ (Kepler's Third Law: $T^2 \propto r^3$) ### Properties of Matter - **Stress:** $\sigma = \frac{F}{A}$ - **Strain:** $\epsilon = \frac{\Delta L}{L}$ (Longitudinal), $\epsilon_V = \frac{\Delta V}{V}$ (Volumetric), $\phi$ (Shear) - **Young's Modulus:** $Y = \frac{\text{Stress}}{\text{Longitudinal Strain}} = \frac{FL}{A\Delta L}$ - **Bulk Modulus:** $B = \frac{\text{Stress}}{\text{Volumetric Strain}} = \frac{-P}{\Delta V/V}$ - **Shear Modulus (Rigidity):** $G = \frac{\text{Shear Stress}}{\text{Shear Strain}} = \frac{F/A}{\phi}$ - **Poisson's Ratio:** $\nu = -\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}$ - **Surface Tension:** $T = \frac{F}{L}$ - **Excess Pressure in Liquid Drop:** $\Delta P = \frac{2T}{R}$ - **Excess Pressure in Soap Bubble:** $\Delta P = \frac{4T}{R}$ - **Capillary Rise:** $h = \frac{2T\cos\theta}{r\rho g}$ - **Viscous Force (Stokes' Law):** $F = 6\pi\eta rv$ - **Terminal Velocity:** $v_t = \frac{2r^2(\rho - \sigma)g}{9\eta}$ - **Bernoulli's Principle:** $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$ - **Equation of Continuity:** $A_1v_1 = A_2v_2$ ### Thermodynamics - **Thermal Expansion:** - Linear: $\Delta L = L_0\alpha\Delta T$ - Area: $\Delta A = A_0\beta\Delta T = A_0(2\alpha)\Delta T$ - Volume: $\Delta V = V_0\gamma\Delta T = V_0(3\alpha)\Delta T$ - **Heat Capacity:** $C = \frac{\Delta Q}{\Delta T}$ - **Specific Heat Capacity:** $c = \frac{\Delta Q}{m\Delta T}$ - **Latent Heat:** $Q = mL$ - **Calorimetry Principle:** $Q_{gain} = Q_{lost}$ - **Work Done by Gas:** $W = P\Delta V$ - **First Law of Thermodynamics:** $\Delta U = Q - W$ - **Mayer's Formula:** $C_P - C_V = R$ - **Efficiency of Heat Engine:** $\eta = 1 - \frac{Q_C}{Q_H} = 1 - \frac{T_C}{T_H}$ - **Coefficient of Performance (Refrigerator):** $COP = \frac{Q_C}{W} = \frac{T_C}{T_H - T_C}$ - **Stefan-Boltzmann Law:** $P = \epsilon\sigma A T^4$ - **Wien's Displacement Law:** $\lambda_m T = b$ - **Newton's Law of Cooling:** $\frac{dQ}{dt} = -k(T - T_0)$ ### Kinetic Theory of Gases - **Ideal Gas Equation:** $PV = nRT = Nk_BT$ - **Average Kinetic Energy per molecule:** $E_{avg} = \frac{3}{2}k_BT$ - **RMS Speed:** $v_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3k_BT}{m}}$ - **Pressure of an Ideal Gas:** $P = \frac{1}{3}\frac{nm}{V}v_{rms}^2$ - **Degrees of Freedom:** $f$ - Monatomic: $f=3$ - Diatomic: $f=5$ (at moderate temps) - Polyatomic: $f=6$ - **Internal Energy:** $U = \frac{f}{2}nRT$ - **Molar Specific Heat:** - $C_V = \frac{f}{2}R$ - $C_P = (\frac{f}{2} + 1)R$ - **Adiabatic Process:** $PV^\gamma = \text{constant}$, $T V^{\gamma-1} = \text{constant}$, $P^{1-\gamma} T^\gamma = \text{constant}$ - $\gamma = \frac{C_P}{C_V} = 1 + \frac{2}{f}$ ### Oscillations and Waves - **Simple Harmonic Motion (SHM):** - Displacement: $x = A\sin(\omega t + \phi)$ - Velocity: $v = A\omega\cos(\omega t + \phi) = \omega\sqrt{A^2 - x^2}$ - Acceleration: $a = -A\omega^2\sin(\omega t + \phi) = -\omega^2 x$ - Angular Frequency: $\omega = \sqrt{\frac{k}{m}}$ (spring), $\omega = \sqrt{\frac{g}{L}}$ (simple pendulum) - Time Period: $T = \frac{2\pi}{\omega}$ - Total Energy: $E = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2 A^2$ - **Wave Equation:** $y = A\sin(kx - \omega t + \phi)$ - **Wave Speed:** $v = f\lambda = \frac{\omega}{k}$ - **Speed of Sound in Gas:** $v = \sqrt{\frac{\gamma P}{\rho}} = \sqrt{\frac{\gamma RT}{M}}$ - **Speed of Transverse Wave on String:** $v = \sqrt{\frac{T}{\mu}}$ - **Intensity:** $I = \frac{P}{A} \propto A^2 f^2$ - **Beat Frequency:** $f_{beat} = |f_1 - f_2|$ - **Doppler Effect:** $f' = f \left(\frac{v \pm v_o}{v \mp v_s}\right)$ (Upper signs for approach, lower for recession) - **Organ Pipes:** - Open pipe: $f_n = \frac{nv}{2L}$, $n=1,2,3...$ (all harmonics) - Closed pipe: $f_n = \frac{(2n-1)v}{4L}$, $n=1,2,3...$ (odd harmonics) ### Electrostatics - **Coulomb's Law:** $F = k\frac{|q_1 q_2|}{r^2}$ where $k = \frac{1}{4\pi\epsilon_0}$ - **Electric Field:** $\vec{E} = \frac{\vec{F}}{q_0} = k\frac{q}{r^2}\hat{r}$ - **Electric Potential:** $V = k\frac{q}{r}$ - **Relationship between E and V:** $\vec{E} = -\nabla V = -\frac{dV}{dr}$ - **Electric Potential Energy:** $U = k\frac{q_1 q_2}{r}$ - **Electric Dipole Moment:** $\vec{p} = q\vec{d}$ - **Torque on Dipole in E-field:** $\vec{\tau} = \vec{p} \times \vec{E}$ - **Electric Flux:** $\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0}$ (Gauss's Law) - **Capacitance:** $C = \frac{Q}{V}$ - **Parallel Plate Capacitor:** $C = \frac{\epsilon_0 A}{d}$ - **Capacitors in Series:** $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + ...$ - **Capacitors in Parallel:** $C_{eq} = C_1 + C_2 + ...$ - **Energy Stored in Capacitor:** $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}QV$ - **Energy Density in E-field:** $u_E = \frac{1}{2}\epsilon_0 E^2$ ### Current Electricity - **Current:** $I = \frac{dQ}{dt} = nAve$ - **Ohm's Law:** $V = IR$ - **Resistance:** $R = \rho\frac{L}{A}$ - **Resistivity:** $\rho_T = \rho_0(1 + \alpha(T - T_0))$ - **Resistors in Series:** $R_{eq} = R_1 + R_2 + ...$ - **Resistors in Parallel:** $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$ - **Electric Power:** $P = VI = I^2R = \frac{V^2}{R}$ - **Joule's Law of Heating:** $H = I^2Rt$ - **Kirchhoff's Laws:** - Junction Rule: $\sum I_{in} = \sum I_{out}$ - Loop Rule: $\sum \Delta V = 0$ - **Wheatstone Bridge (balanced):** $\frac{R_1}{R_2} = \frac{R_3}{R_4}$ - **Meter Bridge:** $R_1/R_2 = l_1/(100-l_1)$ - **Potentiometer:** $V \propto l$, $E_1/E_2 = l_1/l_2$ - **Internal Resistance of Cell:** $r = R(\frac{E}{V} - 1)$ ### Magnetic Effects of Current & Magnetism - **Biot-Savart Law:** $d\vec{B} = \frac{\mu_0}{4\pi}\frac{I d\vec{l} \times \vec{r}}{r^3}$ - **Magnetic Field due to Long Straight Wire:** $B = \frac{\mu_0 I}{2\pi r}$ - **Magnetic Field at Center of Circular Loop:** $B = \frac{\mu_0 I}{2R}$ - **Magnetic Field at Axis of Circular Loop:** $B = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}$ - **Magnetic Field inside Solenoid:** $B = \mu_0 nI$ - **Ampere's Circuital Law:** $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$ - **Lorentz Force:** $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$ - **Magnetic Force on Current-carrying Wire:** $\vec{F} = I(\vec{L} \times \vec{B})$ - **Torque on Current Loop in B-field:** $\vec{\tau} = \vec{M} \times \vec{B}$ where $\vec{M} = NI\vec{A}$ - **Magnetic Potential Energy of Dipole:** $U = -\vec{M} \cdot \vec{B}$ - **Hall Effect:** $V_H = \frac{IB}{net}$ - **Gauss's Law for Magnetism:** $\oint \vec{B} \cdot d\vec{A} = 0$ - **Magnetic Permeability:** $\mu = \mu_0(1 + \chi_m)$ - **Magnetic Field Intensity:** $H = \frac{B}{\mu_0} - M$ ### Electromagnetic Induction & AC - **Magnetic Flux:** $\Phi_B = \int \vec{B} \cdot d\vec{A}$ - **Faraday's Law of EMI:** $\mathcal{E} = -\frac{d\Phi_B}{dt}$ - **Motional EMF:** $\mathcal{E} = Blv$ - **Self-Inductance:** $\Phi_B = LI$, $\mathcal{E} = -L\frac{dI}{dt}$ - **Mutual Inductance:** $\Phi_{B2} = MI_1$, $\mathcal{E}_2 = -M\frac{dI_1}{dt}$ - **Energy Stored in Inductor:** $U = \frac{1}{2}LI^2$ - **Energy Density in B-field:** $u_B = \frac{B^2}{2\mu_0}$ - **AC Voltage/Current:** $V = V_0\sin(\omega t)$, $I = I_0\sin(\omega t + \phi)$ - **RMS Values:** $V_{rms} = \frac{V_0}{\sqrt{2}}$, $I_{rms} = \frac{I_0}{\sqrt{2}}$ - **Inductive Reactance:** $X_L = \omega L$ - **Capacitive Reactance:** $X_C = \frac{1}{\omega C}$ - **Impedance (RLC Series):** $Z = \sqrt{R^2 + (X_L - X_C)^2}$ - **Phase Angle:** $\tan\phi = \frac{X_L - X_C}{R}$ - **Power in AC Circuit:** $P_{avg} = V_{rms}I_{rms}\cos\phi$ (Power Factor: $\cos\phi = R/Z$) - **Resonance Frequency:** $\omega_0 = \frac{1}{\sqrt{LC}}$ - **Transformer:** $\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}$ (for ideal transformer) ### Electromagnetic Waves - **Speed of EM Wave in Vacuum:** $c = \frac{1}{\sqrt{\mu_0\epsilon_0}}$ - **Speed of EM Wave in Medium:** $v = \frac{1}{\sqrt{\mu\epsilon}}$ - **Relationship between E and B:** $E = cB$ - **Energy Density:** $u = \frac{1}{2}\epsilon_0 E^2 + \frac{1}{2\mu_0} B^2 = \epsilon_0 E^2 = \frac{B^2}{\mu_0}$ - **Poynting Vector:** $\vec{S} = \frac{1}{\mu_0}(\vec{E} \times \vec{B})$ (Magnitude $S = \frac{E B}{\mu_0}$) ### Ray Optics & Optical Instruments - **Reflection:** Angle of incidence = Angle of reflection ($\angle i = \angle r$) - **Mirror Formula:** $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ - **Magnification:** $m = -\frac{v}{u} = \frac{h_i}{h_o}$ - **Refraction (Snell's Law):** $n_1\sin i = n_2\sin r$ - **Refractive Index:** $n = \frac{c}{v}$ - **Lens Maker's Formula:** $\frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$ - **Lens Formula:** $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ - **Power of Lens:** $P = \frac{1}{f}$ (in dioptres, $f$ in meters) - **Lenses in Contact:** $P_{eq} = P_1 + P_2 + ...$, $\frac{1}{f_{eq}} = \frac{1}{f_1} + \frac{1}{f_2} + ...$ - **Total Internal Reflection (TIR):** $\sin C = \frac{n_2}{n_1}$ (for $n_1 > n_2$) - **Prism Formula:** $n = \frac{\sin((A+\delta_m)/2)}{\sin(A/2)}$ - **Dispersion:** Angular dispersion $\theta = (\mu_v - \mu_r)A$ - **Microscope:** - Magnifying Power (normal adjustment): $M = \frac{L}{f_o}\frac{D}{f_e}$ - **Telescope:** - Magnifying Power (normal adjustment): $M = -\frac{f_o}{f_e}$ ### Wave Optics - **Young's Double Slit Experiment (YDSE):** - Path Difference: $\Delta x = d\sin\theta = \frac{yd}{D}$ - Bright Fringes (constructive): $\Delta x = n\lambda$ - Dark Fringes (destructive): $\Delta x = (n + \frac{1}{2})\lambda$ - Fringe Width: $\beta = \frac{\lambda D}{d}$ - **Intensity in Interference:** $I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi$ (For $I_1=I_2=I_0$, $I = 4I_0\cos^2(\phi/2)$) - **Diffraction (Single Slit):** - Minima: $a\sin\theta = n\lambda$ - Maxima (approx): $a\sin\theta = (2n+1)\frac{\lambda}{2}$ - **Rayleigh Criterion (Resolution):** - Microscope: $d_{min} = \frac{1.22\lambda}{2n\sin\theta}$ - Telescope: $\theta_{min} = \frac{1.22\lambda}{D}$ - **Malus's Law:** $I = I_0\cos^2\theta$ - **Brewster's Law:** $\mu = \tan i_p$ ### Dual Nature of Radiation & Matter - **Photon Energy:** $E = hf = \frac{hc}{\lambda}$ - **Momentum of Photon:** $p = \frac{h}{\lambda} = \frac{E}{c}$ - **Work Function:** $\phi_0 = hf_0$ - **Einstein's Photoelectric Equation:** $K_{max} = hf - \phi_0$ - **De Broglie Wavelength:** $\lambda = \frac{h}{p} = \frac{h}{mv} = \frac{h}{\sqrt{2mK}} = \frac{h}{\sqrt{2mqV}}$ ### Atoms & Nuclei - **Bohr's Model:** - Radius of $n^{th}$ orbit: $r_n = 0.529 \frac{n^2}{Z}$ Å - Energy of $n^{th}$ orbit: $E_n = -13.6 \frac{Z^2}{n^2}$ eV - Wavelength of emitted photon: $\frac{1}{\lambda} = RZ^2\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$ (Rydberg Formula) - **Nuclear Radius:** $R = R_0 A^{1/3}$ - **Mass Defect:** $\Delta m = (Zm_p + (A-Z)m_n) - M_{nucleus}$ - **Binding Energy:** $BE = \Delta m c^2$ - **Radioactive Decay Law:** $N = N_0 e^{-\lambda t}$ - **Half-life:** $T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$ - **Mean Life:** $\tau = \frac{1}{\lambda}$ - **Activity:** $A = -\frac{dN}{dt} = \lambda N$ ### Semiconductor Electronics - **Conduction in Semiconductors:** - $n_i^2 = n_e n_h$ (for intrinsic semiconductor) - **Diode (PN Junction):** - Forward Bias: Low resistance - Reverse Bias: High resistance - **Rectifiers:** Convert AC to DC - **Transistor (BJT):** - Current Gain: $\alpha = \frac{I_C}{I_E}$, $\beta = \frac{I_C}{I_B}$ - Relationship: $\beta = \frac{\alpha}{1-\alpha}$ - **Logic Gates:** AND, OR, NOT, NAND, NOR, XOR, XNOR - Truth Tables ### Communication Systems - **Antenna Length:** $L \approx \lambda/4$ - **Modulation Index (AM):** $\mu = \frac{A_m}{A_c}$ - **Bandwidth:** - AM: $2f_m$ - FM: $2(\Delta f + f_m)$ - **Power in AM Wave:** $P_t = P_c(1 + \frac{\mu^2}{2})$ - **Ground Wave Propagation:** Up to a few MHz - **Sky Wave Propagation:** Ionospheric reflection (3-30 MHz) - **Space Wave Propagation:** Line of Sight (LoS), TV, Satellite - Max LoS distance: $d = \sqrt{2Rh_T} + \sqrt{2Rh_R}$