MHT CET Physics Syllabus

Define simple harmonic motion and give its defining equation.

SHM is oscillatory motion in which the restoring force (or acceleration) is directly proportional to displacement from the mean position and always directed towards it. Defining equation: a = −ω²x.

Write the expressions for velocity and acceleration of a particle in SHM as functions of displacement x (amplitude A).

v = ±ω√(A² − x²) (max ωA at mean, zero at extremes). a = −ω²x (zero at mean, max ω²A at extremes).

Give the period of a simple pendulum and of a mass on a spring.

Simple pendulum: T = 2π√(L/g). Mass–spring: T = 2π√(m/k).

Write the expressions for kinetic, potential and total energy of a particle of mass m executing SHM (amplitude A, angular frequency ω).

KE = (1/2)mω²(A² − x²); PE = (1/2)mω²x²; Total E = (1/2)mω²A² = constant.

What is the phase difference between displacement, velocity and acceleration in SHM?

Velocity leads displacement by π/2 (90°); acceleration leads displacement by π (180°), i.e. acceleration is opposite in phase to displacement.

State the principle of superposition of waves.

When two or more waves overlap, the resultant displacement at any point at any instant equals the vector (algebraic) sum of the displacements due to the individual waves.

For a stationary (standing) wave on a string, where do nodes and antinodes occur and what is their spacing?

Nodes are points of zero displacement; antinodes are points of maximum displacement. Adjacent nodes (or adjacent antinodes) are separated by λ/2; a node and the nearest antinode are λ/4 apart.

State the fundamental frequency of a vibrating string of length L, tension T and linear mass density m (μ).

n = (1/2L)√(T/m). Overtones (harmonics) are integral multiples: n, 2n, 3n, …

Compare the harmonics produced in a closed pipe and an open pipe.

Closed pipe (one end closed): fundamental n = v/4L; only odd harmonics (n, 3n, 5n…). Open pipe (both ends open): fundamental n = v/2L; all harmonics present (n, 2n, 3n…).

What are beats, and what is the beat frequency?

Beats are periodic variations in loudness caused by superposition of two waves of slightly different frequencies. Beat frequency = |n₁ − n₂| (the difference of the two frequencies).

State the general Doppler effect formula for the apparent frequency of sound.

n' = n (v ± v_observer)/(v ∓ v_source), where v is the speed of sound. Signs are chosen so that relative approach increases the frequency and relative recession decreases it.

Using the Doppler effect, how does the apparent frequency change when a source moves toward, and away from, a stationary observer?

Source approaching: n' = n·v/(v − v_s) (frequency increases, pitch rises). Source receding: n' = n·v/(v + v_s) (frequency decreases, pitch falls).

Define coefficient of linear, areal and volume (cubical) expansion and state their relationship.

α = (ΔL/L)/ΔT, β = (ΔA/A)/ΔT, γ = (ΔV/V)/ΔT. For an isotropic solid: β = 2α and γ = 3α, so α : β : γ = 1 : 2 : 3.

State the three modes of heat transfer and define them.

Conduction: heat transfer through a medium without bulk motion of particles (solids). Convection: heat transfer by actual movement of heated fluid (liquids/gases). Radiation: heat transfer by electromagnetic waves, requiring no medium.

State Newton's law of cooling.

The rate of loss of heat (or rate of fall of temperature) of a body is directly proportional to the difference between its temperature and that of the surroundings, provided this difference is small. dQ/dt ∝ (θ − θ₀).

State Stefan–Boltzmann law and define a perfectly black body.

The power radiated per unit area by a black body is E = σT⁴ (σ = 5.67 × 10⁻⁸ W/m²K⁴). A perfectly black body absorbs all radiation incident on it (absorptivity = 1) and is the best emitter.

State Wien's displacement law.

The wavelength at which a black body emits maximum energy is inversely proportional to its absolute temperature: λ_max·T = b, where b = 2.898 × 10⁻³ m·K (Wien's constant).

State Kirchhoff's law of radiation.

At a given temperature and wavelength, the ratio of emissive power to absorptive power (emissivity to absorptivity) is the same for all bodies and equals the emissive power of a perfect black body. Good absorbers are good emitters.

State the postulates and the basic pressure relation of the kinetic theory of gases.

Gas consists of a large number of tiny molecules in random motion, colliding elastically with no intermolecular forces and negligible volume. Pressure: P = (1/3)(N/V)m c̄² = (1/3)ρ c̄², where c̄² is mean square speed.

Give expressions for rms speed of gas molecules and average translational KE per molecule.

v_rms = √(3RT/M) = √(3kT/m). Average translational KE per molecule = (3/2)kT (k = Boltzmann constant).

State the law of equipartition of energy and the degrees of freedom of monatomic and diatomic gases.

Each degree of freedom carries average energy (1/2)kT per molecule. Monatomic: 3 (translational); diatomic: 5 (3 translational + 2 rotational) at ordinary temperatures.

State the first law of thermodynamics with sign convention.

ΔQ = ΔU + W: heat supplied to a system equals the increase in its internal energy plus the work done by the system. Q is positive when heat is added; W is positive when work is done by the gas.

For an ideal gas, write the work done in isothermal and adiabatic processes.

Isothermal: W = nRT ln(V₂/V₁) = 2.303 nRT log(V₂/V₁). Adiabatic: W = (P₁V₁ − P₂V₂)/(γ − 1) = nR(T₁ − T₂)/(γ − 1), with PV^γ = constant.

State the second law of thermodynamics (Kelvin–Planck and Clausius statements).

Kelvin–Planck: no process is possible whose sole result is the complete conversion of heat into work. Clausius: heat cannot flow spontaneously from a colder to a hotter body without external work.

What is the efficiency of a Carnot engine and the coefficient of performance of a refrigerator?

Carnot efficiency η = 1 − T_C/T_H (temperatures in kelvin). Refrigerator COP = Q_C/W = T_C/(T_H − T_C).

State Coulomb's law and define the SI unit of charge.

Force between two point charges: F = (1/4πε₀)·q₁q₂/r², acting along the line joining them. 1/4πε₀ = 9 × 10⁹ N·m²/C². The coulomb (C) is the SI unit of charge.

Give the electric field and potential due to a point charge q at distance r.

E = (1/4πε₀)·q/r² (vector, directed radially). V = (1/4πε₀)·q/r (scalar). Relation: E = −dV/dr.

State Gauss's law and give the field of a charged conducting sphere outside and inside.

Gauss's law: total electric flux through a closed surface = q_enclosed/ε₀. For a charged conducting sphere: outside E = (1/4πε₀)q/r² (acts as point charge); inside E = 0.

Define capacitance and give the energy stored in a charged capacitor.

Capacitance C = Q/V (SI unit farad). For a parallel-plate capacitor C = ε₀A/d. Energy stored U = (1/2)CV² = (1/2)QV = Q²/2C.

How do you combine capacitors in series and in parallel?

Series: 1/C = 1/C₁ + 1/C₂ + … (charge same on each). Parallel: C = C₁ + C₂ + … (voltage same across each).

State Ohm's law and the relation between resistance, resistivity and dimensions of a conductor.

Ohm's law: V = IR (current ∝ potential difference at constant temperature). Resistance R = ρL/A, where ρ is resistivity, L length, A cross-sectional area.

State Kirchhoff's two circuit laws.

Junction (current) law: the algebraic sum of currents at any junction is zero (ΣI = 0) — conservation of charge. Loop (voltage) law: the algebraic sum of EMFs and potential drops around any closed loop is zero (ΣE = ΣIR) — conservation of energy.

Give the balance condition of a Wheatstone bridge.

The bridge is balanced (no galvanometer current) when P/Q = R/S, i.e. the ratio of resistances in the two arms are equal.

State the Biot–Savart law and the magnetic field at the centre of a circular current loop.

Biot–Savart: dB = (μ₀/4π)·(I dl sinθ)/r². Field at centre of a circular loop of radius R carrying current I: B = μ₀I/2R (for N turns, B = μ₀NI/2R).

Give the magnetic field due to a long straight current-carrying wire and inside a long solenoid.

Straight wire: B = μ₀I/2πr. Inside a long solenoid: B = μ₀nI, where n is turns per unit length.

State the expression for the force on a current-carrying conductor and on a moving charge in a magnetic field.

On a conductor: F = BIL sinθ (F = I L × B). On a moving charge: F = qvB sinθ (F = q v × B); the force is perpendicular to v, so it does no work.

State Faraday's laws of electromagnetic induction and Lenz's law.

Faraday: an induced EMF appears whenever magnetic flux linked with a circuit changes; its magnitude e = −N dΦ/dt. Lenz's law: the induced current opposes the change in flux that causes it (the source of the minus sign; expresses energy conservation).

Define self-inductance and mutual inductance.

Self-inductance L: e = −L dI/dt; flux linkage NΦ = LI (unit henry). Mutual inductance M: EMF in coil 2 due to changing current in coil 1, e₂ = −M dI₁/dt.

For an AC circuit, define rms value and give it in terms of peak value.

The rms (root-mean-square) value is the DC equivalent that produces the same heating. I_rms = I₀/√2 = 0.707 I₀; similarly V_rms = V₀/√2.

Define inductive reactance, capacitive reactance and impedance in a series LCR circuit.

X_L = ωL = 2πfL; X_C = 1/ωC = 1/2πfC. Impedance Z = √(R² + (X_L − X_C)²). Current I = V/Z.

State the condition for resonance in a series LCR circuit and the resonant frequency.

Resonance occurs when X_L = X_C, so impedance is minimum (Z = R) and current is maximum. Resonant frequency f₀ = 1/(2π√(LC)).

State the laws of reflection and the mirror formula with magnification.

Laws of reflection: angle of incidence = angle of reflection; incident ray, reflected ray and normal lie in one plane. Mirror formula: 1/f = 1/v + 1/u. Magnification m = −v/u = h_image/h_object.

State Snell's law and define refractive index.

Snell's law: n₁ sinθ₁ = n₂ sinθ₂ (sinθ₁/sinθ₂ = constant for a given pair of media). Refractive index n = speed of light in vacuum / speed in medium = c/v = real depth/apparent depth.

What is the critical angle and the condition for total internal reflection?

Critical angle θ_C is the angle of incidence (in the denser medium) for which the refracted ray grazes the boundary at 90°; sinθ_C = 1/n. Total internal reflection occurs when light travels from denser to rarer medium and the angle of incidence exceeds θ_C.

State the lens maker's formula and the thin-lens formula.

Lens maker's: 1/f = (n − 1)(1/R₁ − 1/R₂). Thin-lens: 1/f = 1/v − 1/u. Power P = 1/f (in metres), in dioptres.

State Huygens' principle.

Every point on a wavefront acts as a source of secondary wavelets spreading out in all directions with the speed of the wave; the new wavefront is the forward envelope (tangential surface) of these secondary wavelets.

Give the conditions and the fringe-width formula for Young's double-slit interference.

Constructive (bright): path difference = nλ; destructive (dark): path difference = (2n−1)λ/2. Fringe width X = λD/d, where D = slit-to-screen distance, d = slit separation.

What is the condition for the first minimum in single-slit Fraunhofer diffraction, and how does the central maximum compare with secondary maxima?

First minimum: a sinθ = λ (a = slit width). The central maximum is twice as wide and much brighter than the secondary maxima, whose intensity falls off rapidly.

What is polarisation, and which type of waves can be polarised?

Polarisation is the restriction of the vibrations of a wave to a single plane perpendicular to the direction of propagation. Only transverse waves (e.g. light) can be polarised; longitudinal waves (e.g. sound) cannot.

State the basic properties of electromagnetic waves.

They are transverse waves with mutually perpendicular E and B fields, both perpendicular to the direction of propagation; they require no medium and travel in vacuum at c = 3 × 10⁸ m/s, where c = 1/√(μ₀ε₀) = E₀/B₀.

Arrange the electromagnetic spectrum in order of increasing frequency.

Radio waves < microwaves < infrared < visible light < ultraviolet < X-rays < gamma rays (increasing frequency / decreasing wavelength).

State Einstein's photoelectric equation and define work function and threshold frequency.

Photoelectric equation: KE_max = hν − φ₀ = hν − hν₀. Work function φ₀ is the minimum energy to eject an electron from the metal surface; threshold frequency ν₀ is the minimum frequency below which no photoelectrons are emitted.

What is the de Broglie wavelength of a particle, and how does it depend on momentum?

λ = h/p = h/(mv). The wavelength is inversely proportional to the particle's momentum. For an electron accelerated through potential V: λ = 12.27/√V Å.

State Bohr's postulates for the hydrogen atom.

1) Electrons revolve in certain stable (stationary) orbits without radiating energy. 2) Angular momentum is quantised: mvr = nh/2π. 3) Energy is emitted/absorbed only when an electron jumps between orbits: hν = E₂ − E₁.

Give the radius and energy of the nth Bohr orbit of hydrogen.

Radius r_n = 0.529 n² Å (r ∝ n²). Energy E_n = −13.6/n² eV (ground state −13.6 eV). E ∝ 1/n²; energy is negative because the electron is bound.

What is mass defect and binding energy of a nucleus?

Mass defect Δm = (sum of masses of constituent nucleons) − (actual mass of nucleus). Binding energy = Δm·c² (energy needed to split the nucleus into free nucleons); 1 u corresponds to 931.5 MeV.

Compare nuclear fission and nuclear fusion.

Fission: a heavy nucleus splits into lighter nuclei releasing energy (e.g. U-235), used in reactors and atom bombs. Fusion: light nuclei combine to form a heavier nucleus releasing energy (e.g. H→He in the Sun), requiring very high temperature/pressure.

State the law of radioactive decay and define half-life.

Radioactive decay: N = N₀e^(−λt), dN/dt = −λN, where λ is the decay constant. Half-life T₁/₂ = 0.693/λ is the time for half the nuclei to decay. Mean life τ = 1/λ.

Distinguish between intrinsic and extrinsic (n-type and p-type) semiconductors.

Intrinsic: pure semiconductor; equal numbers of electrons and holes. Extrinsic: doped. n-type (doped with pentavalent donor, e.g. P) has electrons as majority carriers; p-type (doped with trivalent acceptor, e.g. B) has holes as majority carriers.

Explain forward and reverse biasing of a p-n junction diode.

Forward bias: p-side to +, n-side to −; depletion layer narrows, barrier lowered, large current flows. Reverse bias: p-side to −, n-side to +; depletion layer widens, only a tiny leakage current flows until breakdown.

State the function of a Zener diode and of a rectifier.

A Zener diode operates in reverse breakdown at a constant voltage and is used as a voltage regulator. A rectifier (half-wave or full-wave, using diodes) converts alternating current (AC) into direct current (DC).