The 74 formulas MHT-CET Physics actually tests

Coulomb force, field and potential

F = kq₁q₂/r² E = kq/r² V = kq/r k = 1/4πε₀ = 9 × 10⁹ N m² C⁻²

q = charge

r = distance

E is a vector; V is a scalar

Note:Add fields as vectors and potentials as signed numbers. At the midpoint of two equal like charges E = 0 but V does not.

Gauss's law

Φ = q_enclosed / ε₀

Φ = flux through a CLOSED surface

Note:Shape does not matter. A charge at a cube's centre sends Φ/6 through each face.

Electric dipole

p = q × 2a E_axis = 2kp/r³ E_equator = kp/r³ τ = pE sin θ U = −pE cos θ

p = dipole moment

θ = angle between p and E

Capacitance and combinations

C = ε₀A/d (with dielectric: KC) parallel: C = C₁ + C₂ series: 1/C = 1/C₁ + 1/C₂

A = plate area

d = separation

K = dielectric constant

Energy stored in a capacitor

U = ½CV² = Q²/2C = ½QV

Battery connected: V fixed

Battery removed: Q fixed

Note:Slab inserted with the battery on: C, Q and U rise by K. With the battery off: V and U fall by K.

Standard moments of inertia

ring MR² disc ½MR² solid sphere ⅖MR² hollow sphere ⅔MR² rod (centre) ML²/12 rod (end) ML²/3

M = mass

R = radius

L = length

Parallel and perpendicular axis theorems

I = I_cm + Md² I_z = I_x + I_y (flat bodies only)

d = distance between the parallel axes

Note:The perpendicular-axis theorem does not apply to a 3-D body.

Angular momentum and torque

L = Iω τ = dL/dt = Iα no external torque: I₁ω₁ = I₂ω₂

ω = angular speed

α = angular acceleration

Rolling without slipping

KE = ½mv²(1 + K²/R²) a = g sin θ / (1 + K²/R²)

K = radius of gyration

K²/R²: sphere 2/5, disc 1/2, ring 1

Note:Smallest K²/R² reaches the bottom first: sphere, then disc, then ring.

Banking and the vertical circle

banking: tan θ = v²/rg vertical circle: v_top ≥ √(gr), v_bottom ≥ √(5gr)

r = radius

θ = banking angle

Progressive wave

y = A sin(ωt − kx) v = ω/k = fλ k = 2π/λ

A = amplitude

ω = angular frequency

k = wave number

Vibrating string

v = √(T/μ) fₙ = (n/2L)√(T/μ)

T = tension

μ = mass per unit LENGTH

n = 1, 2, 3 …

Pipes

open: fₙ = nv/2L (all n) closed: fₙ = nv/4L (odd n only) end correction e = 0.6r per open end

L = length

r = radius of the pipe

Note:A closed pipe's first overtone is its THIRD harmonic.

Beats

beat frequency = |f₁ − f₂|

Loading a fork lowers its frequency; filing raises it

Capillary rise

h = 2T cos θ / rρg

T = surface tension

θ = contact angle

r = tube radius

Note:h ∝ 1/r: halve the radius, double the rise.

Excess pressure

drop: ΔP = 2T/r soap bubble: ΔP = 4T/r

A soap film has two surfaces

Surface energy

W = T × ΔA soap bubble of radius r: W = 8πr²T

ΔA = increase in surface area

Note:n drops merging: R = n^(1/3) r; area falls, energy is released.

Stokes' law and terminal velocity

F = 6πηrv v_t = 2r²(ρ − σ)g / 9η

η = viscosity

ρ = density of the sphere

σ = density of the fluid

Note:v_t ∝ r².

Continuity and Bernoulli

A₁v₁ = A₂v₂ P + ½ρv² + ρgh = constant Torricelli: v = √(2gh)

A = cross-section

v = flow speed

Young's double slit

β = λD/d in a liquid: β/μ film shift = (μ − 1)tD/d

D = slit–screen distance

d = slit separation

t = film thickness

Interference intensity

I = I₁ + I₂ + 2√(I₁I₂) cos φ I_max/I_min = ((√I₁ + √I₂)/(√I₁ − √I₂))²

φ = phase difference

Note:Two equal sources: maximum 4I, minimum 0.

Single slit

minima: a sin θ = nλ central maximum width = 2λD/a

a = slit width

Malus and Brewster

I = I₀ cos²θ tan θ_B = μ

Unpolarised light through one polariser: I₀/2

SHM kinematics

x = A sin(ωt + φ) v = ω√(A² − x²) a = −ω²x

v_max = ωA

a_max = ω²A

SHM energy

E = ½kA² PE = ½kx² KE = ½k(A² − x²)

KE = PE at x = A/√2

Spring-mass and combinations

T = 2π√(m/k) parallel: k = k₁ + k₂ series: 1/k = 1/k₁ + 1/k₂

A spring cut to 1/n of its length has n × k

Simple pendulum

T = 2π√(l/g_eff) lift up: g + a lift down: g − a

l = length

Transistor relations

I_E = I_B + I_C α = I_C/I_E β = I_C/I_B β = α/(1 − α)

CE amplifier: voltage gain = β R_out/R_in

power gain = β × voltage gain

Logic gates

AND A·B OR A+B NOT Ā NAND (A·B)‾ NOR (A+B)‾ XOR A⊕B

NAND and NOR are universal gates

Note:Trace a gate circuit row by row through its truth table; do not guess from the shapes.

Rectifier frequency

half-wave: output ripple f full-wave: 2f

f = input frequency

RMS values

V_rms = V₀/√2 I_rms = I₀/√2

Meters read RMS

Reactance

X_L = ωL X_C = 1/ωC

ω = 2πf

Series LCR

Z = √(R² + (X_L − X_C)²) tan φ = (X_L − X_C)/R V = √(V_R² + (V_L − V_C)²)

φ = phase of voltage ahead of current

Resonance

ω₀ = 1/√(LC) Z = R Q = ω₀L/R

Current is largest at resonance

Power and transformer

P = V_rms I_rms cos φ cos φ = R/Z V_s/V_p = N_s/N_p = I_p/I_s

cos φ = power factor

Faraday's law

e = −N dΦ/dt charge through the circuit q = NΔΦ/R

Φ = BA cos θ

Note:The charge does not depend on how fast the flux changed.

Motional EMF

sliding rod: e = Blv rod rotating about an end: e = ½Bωl² rotating coil: e₀ = NBAω

l = length

ω = angular speed

Self and mutual inductance

e = −L dI/dt U = ½LI² e₂ = −M dI₁/dt

L = self-inductance

M = mutual inductance

LR circuit

I = I₀(1 − e^(−t/τ)) τ = L/R

τ = time constant

Molecular speeds

v_rms = √(3RT/M) v_mean = √(8RT/πM) v_mp = √(2RT/M)

M = molar mass (kg/mol)

T in kelvin

Note:All three ∝ √(T/M). Quadruple T to double the speed.

Pressure and kinetic energy

P = ⅓ρv²_rms average KE per molecule = (3/2)kT

ρ = density of the gas

Equipartition and specific heats

C_v = (f/2)R C_p = C_v + R γ = 1 + 2/f

f = 3 (monatomic), 5 (diatomic)

Equations of motion

v = u + at s = ut + ½at² v² = u² + 2as s_nth = u + a(n − ½)

s_nth = distance in the nth second

Projectile

R = u² sin 2θ / g H = u² sin²θ / 2g T = 2u sin θ / g

θ measured above the horizontal

Note:Same range for θ and 90° − θ.

Uniform circular motion

a = v²/r = ω²r v = ωr

r = radius

Newton's second law and the lift

F = ma apparent weight: m(g + a) up, m(g − a) down, 0 in free fall

a = acceleration of the lift

Impulse and collisions

J = Δp = FΔt e = (v₂ − v₁)/(u₁ − u₂) rebound height = e²h

e = coefficient of restitution

Note:Momentum is conserved in every collision; kinetic energy only in an elastic one.

Standard fields

long wire: μ₀I/2πr loop centre: μ₀I/2R arc of angle θ: μ₀Iθ/4πR solenoid: μ₀nI

n = turns per unit length

θ in radians

Note:Add the parts with their directions — into and out of the page subtract.

Force on a moving charge

F = qvB sin θ r = mv/qB T = 2πm/qB

The period does not depend on the speed

Parallel wires and the galvanometer

F/l = μ₀I₁I₂/2πd m = NIA τ = mB sin θ current sensitivity = nBA/k

Like currents attract

k = torsion constant

Stefan–Boltzmann law

P = σAeT⁴ net: P = σAe(T⁴ − T₀⁴)

T in kelvin

e = emissivity

Note:Double T (kelvin): power × 16.

Wien's displacement law

λ_max T = b ≈ 2.9 × 10⁻³ m K

λ_max = peak wavelength

Newton's law of cooling

(T₁ − T₂)/t = k[(T₁ + T₂)/2 − T₀]

T₀ = surroundings

Thermal expansion

ΔL = LαΔT β = 2α γ = 3α

β = area, γ = volume coefficient

Einstein's photoelectric equation

hν = φ + K_max K_max = eV₀ hν₀ = φ E(eV) = 1240/λ(nm)

φ = work function

V₀ = stopping potential

Note:Intensity changes the current, not V₀.

de Broglie wavelength

λ = h/p = h/√(2mK) = h/√(2mqV) electron: λ = 1.227/√V nm

K = kinetic energy

V = accelerating voltage

Ammeter and voltmeter

shunt: S = I_g G / (I − I_g) series resistance: R = V/I_g − G

G = galvanometer resistance

I_g = full-scale current

Wheatstone and meter bridge

balanced: P/Q = R/S meter bridge: R/S = l/(100 − l)

l = balancing length in cm

Potentiometer

E₁/E₂ = l₁/l₂ r = R(l₁ − l₂)/l₂

r = internal resistance of the cell

Bohr model

r ∝ n²/Z v ∝ Z/n E = −13.6 Z²/n² eV KE = −E, PE = 2E

n = orbit number

Z = atomic number

Hydrogen spectrum

1/λ = RZ²(1/n₁² − 1/n₂²) Lyman n₁=1, Balmer 2, Paschen 3

R = 1.097 × 10⁷ m⁻¹

Radioactive decay

N = N₀e^(−λt) T½ = 0.693/λ τ = 1/λ = 1.44 T½ after n half-lives N = N₀/2ⁿ

λ = decay constant

First law

ΔQ = ΔU + ΔW ΔU = nC_vΔT

ΔW = work done BY the gas

Processes

isothermal: W = nRT ln(V₂/V₁) adiabatic: PV^γ = constant, W = (P₁V₁ − P₂V₂)/(γ − 1)

γ = C_p/C_v

Carnot engine and refrigerator

η = 1 − T₂/T₁ COP = T₂/(T₁ − T₂)

Temperatures in kelvin

Variation of g

height: g R²/(R + h)² ≈ g(1 − 2h/R) depth: g(1 − d/R)

R = Earth's radius

Note:The small-height form fails at h ≈ R: there g is exactly g/4.

Orbits

v_o = √(GM/r) T² ∝ r³ E = −GMm/2r

r = orbit radius

Escape velocity

v_e = √(2GM/R) = √(2gR) = √2 × v_o (at the surface)

Independent of the body's mass and launch direction

Lens and mirror formulas

lens: 1/v − 1/u = 1/f mirror: 1/v + 1/u = 1/f P = 1/f (m)

Cartesian sign convention

Lensmaker and lenses in contact

1/f = (μ − 1)(1/R₁ − 1/R₂) P = P₁ + P₂

In a liquid: (μ_lens/μ_liquid − 1)

Apparent depth and TIR

apparent depth = real depth / μ sin C = 1/μ

C = critical angle

Prism

μ = sin((A + δ_m)/2) / sin(A/2) thin prism: δ = (μ − 1)A

A = prism angle

δ_m = minimum deviation

Doppler effect

f' = f (v + v_o)/(v − v_s) (approach) f' = f (v − v_o)/(v + v_s) (recession)

v = speed of sound

v_o = observer

v_s = source

Speed of sound in a gas

v = √(γRT/M) v ∝ √T

Independent of pressure at fixed temperature