Physics Formula Sheet for CUET UG 2025

📋 Comprehensive Collection of Essential Physics Formulas

This formula sheet covers all essential topics for CUET UG Physics. Keep this handy for quick revision and last-minute preparation.

⚡ Mechanics

Kinematics

• Average Velocity: v_avg = Δx/Δt
• Average Acceleration: a_avg = Δv/Δt
• Equations of Motion:
  • v = u + at
  • s = ut + ½at²
  • v² = u² + 2as
  • s = (v + u)/2 × t
• Relative Velocity: v_AB = v_A - v_B

Projectile Motion

• Horizontal Range: R = (u² sin 2θ)/g
• Maximum Height: H = (u² sin²θ)/(2g)
• Time of Flight: T = (2u sin θ)/g
• Trajectory Equation: y = x tan θ - (gx²)/(2u² cos²θ)

Newton’s Laws

• First Law: F = 0 (equilibrium)
• Second Law: F = ma
• Third Law: F_action = -F_reaction
• Weight: W = mg
• Friction: f ≤ μN (maximum), f = μN (kinetic)

Work, Energy, and Power

• Work: W = F · s = Fs cos θ
• Kinetic Energy: KE = ½mv²
• Potential Energy: PE = mgh
• Power: P = W/t = F · v
• Work-Energy Theorem: W_net = ΔKE
• Conservation of Energy: KE₁ + PE₁ = KE₂ + PE₂

Circular Motion

• Angular Velocity: ω = v/r = 2π/T = 2πf
• Angular Acceleration: α = Δω/Δt
• Centripetal Acceleration: a_c = v²/r = ω²r
• Centripetal Force: F_c = mv²/r = mω²r
• Linear Velocity: v = ωr
• Period: T = 2π/ω

Gravitation

• Newton’s Law of Gravitation: F = G(m₁m₂)/r²
• Gravitational Field: g = GM/r²
• Gravitational Potential: V = -GM/r
• Escape Velocity: v_e = √(2GM/R) = √(2gR)
• Orbital Velocity: v_o = √(GM/r)
• Kepler’s Third Law: T² ∝ r³

Simple Harmonic Motion

• Restoring Force: F = -kx
• Angular Frequency: ω = √(k/m)
• Period: T = 2π√(m/k)
• Frequency: f = 1/T = ω/(2π)
• Displacement: x = A sin(ωt + φ)
• Velocity: v = Aω cos(ωt + φ)
• Acceleration: a = -Aω² sin(ωt + φ)

🌊 Waves and Oscillations

Wave Properties

• Wave Speed: v = fλ
• Frequency: f = 1/T
• Angular Frequency: ω = 2πf
• Wave Number: k = 2π/λ
• Phase Velocity: v_p = ω/k
• Group Velocity: v_g = dω/dk

Sound Waves

• Speed of Sound: v = √(B/ρ) (solids), v = √(γRT/M) (gases)
• Doppler Effect: f’ = f(v ± v_o)/(v ∓ v_s)
• Beat Frequency: f_beat = |f₁ - f₂|
• Intensity Level: β = 10 log₁₀(I/I₀)
• Fundamental Frequency: f₁ = v/(2L) (closed pipe), f₁ = v/2L (open pipe)

String Waves

• Wave Speed: v = √(T/μ)
• Fundamental Frequency: f₁ = (1/2L)√(T/μ)
• Harmonics: f_n = nf₁

🔥 Thermodynamics

Heat and Temperature

• Heat Capacity: C = Q/ΔT
• Specific Heat: Q = mcΔT
• Latent Heat: Q = mL
• Heat Transfer:
  • Conduction: Q/t = kA(ΔT/Δx)
  • Convection: Q/t = hAΔT
  • Radiation: P = σeAT⁴

Laws of Thermodynamics

• First Law: ΔU = Q - W
• Work Done: W = PΔV
• Isothermal Process: PV = constant, W = nRT ln(V₂/V₁)
• Adiabatic Process: PV^γ = constant, TV^(γ-1) = constant
• Efficiency of Heat Engine: η = 1 - Q_c/Q_h
• Carnot Efficiency: η = 1 - T_c/T_h

Kinetic Theory

• Pressure: P = (1/3)ρv_rms²
• Root Mean Square Velocity: v_rms = √(3kT/m)
• Average Kinetic Energy: KE_avg = (3/2)kT
• Ideal Gas Law: PV = nRT

⚡ Electromagnetism

Electrostatics

• Coulomb’s Law: F = k(q₁q₂)/r², where k = 1/(4πε₀)
• Electric Field: E = F/q = kQ/r²
• Electric Potential: V = kQ/r
• Potential Energy: U = kq₁q₂/r
• Electric Flux: Φ = E·A = EA cos θ
• Gauss’s Law: Φ = Q_enc/ε₀

Capacitors

• Capacitance: C = Q/V
• Parallel Plate: C = ε₀A/d
• Energy Stored: U = ½CV² = ½QV = Q²/(2C)
• Series Combination: 1/C_eq = 1/C₁ + 1/C₂
• Parallel Combination: C_eq = C₁ + C₂

Current Electricity

• Current: I = Q/t
• Resistance: R = ρL/A
• Ohm’s Law: V = IR
• Power: P = IV = I²R = V²/R
• Electrical Energy: E = Pt = VIt
• Drift Velocity: v_d = I/(nAe)
• Resistivity: ρ = RA/L

Kirchhoff’s Laws

• Current Law: ΣI_in = ΣI_out
• Voltage Law: ΣV = 0 (around closed loop)
• Series Resistance: R_eq = R₁ + R₂ + …
• Parallel Resistance: 1/R_eq = 1/R₁ + 1/R₂ + …

Magnetism

• Magnetic Field: B = F/(qv sin θ)
• Force on Current: F = BIL sin θ
• Magnetic Flux: Φ = B·A = BA cos θ
• Faraday’s Law: ε = -dΦ/dt
• Lenz’s Law: Induced current opposes change
• Magnetic Force: F = q(v × B)

Electromagnetic Induction

• Induced EMF: ε = -N(dΦ/dt)
• Self-Inductance: ε = -L(dI/dt)
• Mutual Inductance: ε₂ = -M(dI₁/dt)
• Energy in Inductor: U = ½LI²
• Transformer: V₂/V₁ = N₂/N₁

🔦 Optics

Reflection and Refraction

• Law of Reflection: θ_i = θ_r
• Law of Refraction (Snell’s Law): n₁ sin θ₁ = n₂ sin θ₂
• Critical Angle: sin θ_c = n₂/n₁ (n₂ < n₁)
• Total Internal Reflection: θ_i > θ_c
• Refractive Index: n = c/v

Lenses

• Lens Maker’s Formula: 1/f = (n-1)(1/R₁ - 1/R₂)
• Thin Lens Equation: 1/f = 1/u + 1/v
• Magnification: m = v/u = h_i/h_o
• Power: P = 1/f (in meters)
• Lens Formula: 1/f = 1/v - 1/u (sign convention)

Mirrors

• Mirror Equation: 1/f = 1/u + 1/v
• Magnification: m = -v/u
• Focal Length: f = R/2 (spherical mirror)

Wave Optics

• Young’s Double Slit: y = (λD)/d (fringe width)
• Path Difference: Δx = d sin θ
• Constructive Interference: Δx = nλ
• Destructive Interference: Δx = (2n+1)λ/2
• Diffraction: sin θ = nλ/a (single slit)

Optical Instruments

• Simple Magnifier: M = D/f
• Compound Microscope: M = (D × v₀)/(f₀fₑ)
• Astronomical Telescope: M = f₀/fₑ

⚛️ Modern Physics

Atomic Structure

• Bohr Model: E_n = -13.6/n² eV (hydrogen)
• Radius: r_n = n² × 0.529 Å
• Frequency: f = (E₂ - E₁)/h
• Wavelength: λ = hc/(E₂ - E₁)

Photoelectric Effect

• Einstein’s Equation: KE_max = hf - φ₀
• Threshold Frequency: f₀ = φ₀/h
• Threshold Wavelength: λ₀ = hc/φ₀
• Stopping Potential: eV₀ = KE_max

X-rays

• Moseley’s Law: √f ∝ Z - σ
• Continuous X-ray: λ_min = hc/eV
• Characteristic X-ray: 1/λ = R(Z-σ)²(1/n₁² - 1/n₂²)

Nuclear Physics

• Mass-Energy Relation: E = mc²
• Binding Energy: BE = (Zm_p + Nm_n - M_nucleus)c²
• Radioactive Decay: N = N₀e^(-λt)
• Half-Life: t_½ = ln 2/λ
• Mean Life: τ = 1/λ
• Activity: A = λN = A₀e^(-λt)

Semiconductors

• Energy Gap: Si = 1.1 eV, Ge = 0.7 eV
• Intrinsic Carrier Concentration: n_i = n₀e^(-E_g/2kT)
• Forward Bias: V = V_bi - V_applied
• Reverse Bias: Depletion width increases

📊 Quick Reference Tables

Physical Constants

Prefixes

Unit Conversions

🎯 Exam Tips

Quick Revision Strategy

1. Memorize fundamental constants - frequently used
2. Understand formula applications - know when to use each
3. Practice dimensional analysis - check formula correctness
4. Review sign conventions - important for vectors and thermodynamics
5. Master problem-solving techniques - systematic approach

Common Mistakes to Avoid

1. Unit errors - ensure consistent units
2. Sign mistakes in vector quantities
3. Incorrect formula selection for given situations
4. Calculation errors in multi-step problems
5. Graph interpretation errors in data analysis

Problem-Solving Approach

1. Identify given quantities and what’s required
2. Select appropriate formula based on the situation
3. Check units and convert if necessary
4. Substitute values and calculate carefully
5. Verify answer is reasonable

🔗 Additional Resources

Practice Materials

• Physics Practice Questions
• Previous Year Questions
• Mock Tests

Study Support

• Expert Guidance
• Study Groups

📌 Remember: Understanding the concepts behind formulas is as important as memorizing them for CUET UG Physics!

Last Updated: October 2024 | CUET UG 2025 Physics Formula Sheet