⚙️

JEE Main · Cheatsheet

Physics Quick Revision

All NCERT + JEE-typical formula bank across mechanics, EM, waves, modern.

Units, dimensions & error

SI base 7; derived: N, J, Pa, W, C, V, Ω, T, Wb.
Homogeneity: dimension of every term equal.
Error: product/quotient → %errors add; power → multiplied.
Screw gauge LC = pitch/CSD; Vernier LC = 1 MSD − 1 VSD.

Kinematics

Eqns

v=u+at, s=ut+½at², v²=u²+2as

Projectile R

u² sin2θ/g

u² sin²θ/2g

2u sinθ/g

Rel velocity

v_AB = v_A − v_B

Laws of motion

F = dp/dt = ma; impulse J = FΔt = Δp.
Friction limiting μₛN, kinetic μₖN.
Circular: a_c = v²/r; banking tanθ = v²/rg (frictionless).
Pseudo-force in non-inertial frame.

Work, energy, power & collisions

∫F·dx

½mv² = p²/2m

Spring U

½kx²

Elastic v₁'

((m₁−m₂)u₁ + 2m₂u₂)/(m₁+m₂)

COR e

(v₂'−v₁')/(u₁−u₂)

Tip: Perfectly elastic e=1; perfectly inelastic e=0.

Rotational motion

Iα

Iω

KE_rot

½Iω²

Rolling KE

½mv²(1+I/mr²)

Parallel axis

I = I_cm + md²

Tip: I: solid sphere 2/5 mR², hollow 2/3 mR², disc ½mR², ring mR², rod (centre) mL²/12.

Gravitation

GMm/r²

g_h

g(1−2h/R)

g_d

g(1−d/R)

v_esc

√(2gR)

v_orb

√(gR)

T² ∝

r³ (Kepler)

Elasticity & fluid mechanics

stress/strain = (F/A)/(ΔL/L)

Bulk K

−V dP/dV

Bernoulli

P + ½ρv² + ρgh = const

Stokes

F = 6πηrv

Excess P (drop)

2T/r; bubble 4T/r

Thermal, kinetic & thermodynamics

mcΔT; mL for phase change

Conduction

kAΔT/L

Stefan

P = εσAT⁴

Isothermal W

nRT ln(V₂/V₁)

Adiabatic

PVᵞ = const

Carnot η

1 − T_c/T_h

v_rms

√(3RT/M)

SHM & waves

SHM

x=A sin(ωt+φ); T=2π√(m/k)

Pendulum

T=2π√(L/g)

String v

√(T/μ)

Sound v

√(γP/ρ)

Doppler

f'=f(v±v_o)/(v∓v_s)

Tip: Open pipe: all harmonics. Closed pipe: only odd. Beat freq = |f₁−f₂|.

Electrostatics

kq₁q₂/r²

E (point)

kq/r²

E (sheet)

σ/2ε₀

E (dipole axial)

2kp/r³

kq/r

Cap (∥)

ε₀A/d; with κ: κC

U (cap)

½CV² = Q²/2C

Current, magnetism & AC

Ohm

V = IR

Drift

v_d = I/nAe

B (wire)

μ₀I/2πr

B (solenoid)

μ₀nI

Force wire

IL×B

EMF

−dΦ/dt

√(R²+(X_L−X_C)²)

Resonance

ω=1/√(LC)

Q-factor

(1/R)√(L/C)

EM waves

c = 1/√(μ₀ε₀); E ⟂ B ⟂ dir.
Momentum p = U/c; radiation pressure I/c.
Spectrum: radio < micro < IR < visible < UV < X < γ.

Ray & wave optics

Lens

1/v − 1/u = 1/f

Lensmaker

(n−1)(1/R₁−1/R₂)

Prism

n=sin((A+D)/2)/sin(A/2)

YDSE β

λD/d

Single slit min

a sinθ = nλ

Brewster

tanθ_p = n

Malus

I = I₀ cos²θ

Modern physics

Photon E

hν = hc/λ

KE_max

hν − φ

de Broglie

λ = h/p

Bohr rₙ

0.529 n²/Z Å

Eₙ (H)

−13.6/n² eV

Decay

N=N₀ e⁻λt; t½=0.693/λ

E=Δmc²

1 u ≈ 931.5 MeV

Semiconductors & communication

n-type (pentavalent), p-type (trivalent).
Diode: forward conducts; Zener for regulation.
Half-wave (1 diode), full-wave (2 diodes / bridge 4).
Transistor CE: β = I_C/I_B; gain = R_out/R_in × β.
Logic gates: NAND, NOR are universal.
AM, FM, PM modulation.