VITEEE Physics Syllabus

Define surface tension and explain capillary rise direction.

Surface tension is the force per unit length acting along the surface of a liquid (energy per unit area), T = F/L. Liquids that wet the tube (e.g. water in glass) rise; those that don't wet (e.g. mercury) are depressed. Rise h = 2T cosθ/(rρg).

State Stokes' law and define terminal velocity.

Stokes' law: viscous drag on a small sphere moving in a fluid is F = 6πηrv. Terminal velocity is the constant velocity attained when drag plus buoyancy balance gravity: v_t = 2r²(ρ−σ)g/(9η).

What is simple harmonic motion (SHM) and its defining equation?

SHM is oscillatory motion in which the restoring force (or acceleration) is directly proportional to displacement and directed toward the mean position: a = −ω²x. Displacement: x = A sin(ωt + φ).

Give the time period of (a) a simple pendulum and (b) a mass-spring system.

(a) Simple pendulum: T = 2π√(L/g). (b) Mass-spring: T = 2π√(m/k), where k is the spring constant.

In SHM, where are kinetic and potential energy maximum, and what is the total energy?

KE is maximum at the mean position (x = 0); PE is maximum at the extreme positions (x = ±A). Total energy is constant: E = ½kA² = ½mω²A².

Distinguish transverse and longitudinal waves and give the wave speed relation.

In transverse waves particles oscillate perpendicular to wave propagation (e.g. light, string waves); in longitudinal waves they oscillate parallel (e.g. sound). Wave speed v = fλ = ω/k.

State the conditions and result for beats, and give the speed of sound in a gas (Newton-Laplace).

Beats arise when two waves of slightly different frequencies superpose; beat frequency = |f₁ − f₂|. Speed of sound in a gas: v = √(γP/ρ) (Laplace's adiabatic correction), where γ = Cp/Cv.

What is the Doppler effect, and how does observed frequency change as a source approaches?

The Doppler effect is the apparent change in observed frequency due to relative motion between source and observer. General formula: f' = f(v ± v_o)/(v ∓ v_s). When the source approaches, the observed frequency increases (apparent pitch rises).

Define coefficient of linear expansion and relate the three thermal expansion coefficients.

Linear expansion coefficient α = ΔL/(L·ΔT). For isotropic solids, area coefficient β = 2α and volume coefficient γ = 3α (so α : β : γ = 1 : 2 : 3).

Define specific heat capacity and latent heat.

Specific heat capacity c is the heat needed to raise the temperature of unit mass by one degree: Q = mcΔT. Latent heat L is the heat per unit mass absorbed/released during a phase change at constant temperature: Q = mL.

State the three modes of heat transfer and the law governing conduction.

Conduction, convection, and radiation. Conduction (Fourier's law): rate of heat flow H = kA(ΔT)/L, where k is thermal conductivity, A the area, and L the thickness.

State Stefan-Boltzmann law and Wien's displacement law.

Stefan-Boltzmann law: power radiated per unit area by a black body E = σT⁴ (σ = 5.67×10⁻⁸ W·m⁻²·K⁻⁴). Wien's law: λ_max·T = b (b = 2.9×10⁻³ m·K), so peak wavelength is inversely proportional to temperature.

State the postulates of the kinetic theory of gases.

Gas molecules are tiny point masses in constant random motion; collisions between molecules and with walls are perfectly elastic; intermolecular forces are negligible except during collisions; time of collision is negligible; molecular motion obeys Newton's laws and average KE is proportional to absolute temperature.

Give the kinetic-theory expressions for gas pressure and average translational kinetic energy.

Pressure P = (1/3)(mN/V)·v̄² = (1/3)ρ·v_rms². Average translational KE per molecule = (3/2)k_BT, where k_B is Boltzmann's constant.

Define rms speed and state the law of equipartition of energy.

rms speed v_rms = √(3k_BT/m) = √(3RT/M). Equipartition: each degree of freedom contributes ½k_BT of energy per molecule (½RT per mole) on average.

How many degrees of freedom and what is γ (= Cp/Cv) for monatomic and diatomic ideal gases?

Monatomic: 3 degrees of freedom, γ = 5/3 ≈ 1.67. Diatomic (at moderate temperature): 5 degrees of freedom, γ = 7/5 = 1.4.

State the first law of thermodynamics and the sign conventions.

ΔU = Q − W, where Q is heat added to the system, W is work done by the system, and ΔU is the change in internal energy. Q is positive when heat is added; W is positive when work is done by the system.

Compare isothermal and adiabatic processes for an ideal gas.

Isothermal: T constant, PV = constant, ΔU = 0, so Q = W. Adiabatic: no heat exchange (Q = 0), PVᵍ = constant, and ΔU = −W. Adiabatic curves are steeper than isothermal curves on a P-V diagram.

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

Kelvin-Planck: no process can convert heat completely into work with no other effect. Clausius: heat cannot spontaneously flow from a colder to a hotter body without external work. Both forbid 100% efficient heat engines/ideal refrigerators.

Give the efficiency of a Carnot engine and coefficient of performance of a refrigerator.

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

State Coulomb's law and define the permittivity of free space.

Coulomb's law: force between two point charges F = (1/4πε₀)·q₁q₂/r², acting along the line joining them. ε₀ = 8.85×10⁻¹² C²·N⁻¹·m⁻² is the permittivity of free space; 1/4πε₀ ≈ 9×10⁹ N·m²/C².

Define electric field and electric flux, and state Gauss's law.

Electric field E = F/q₀ (force per unit positive test charge, N/C). Flux Φ = ∮E·dA. Gauss's law: the net flux through a closed surface equals the enclosed charge divided by ε₀: Φ = q_enc/ε₀.

Give the electric field due to (a) an infinite line charge and (b) an infinite charged sheet.

(a) Line charge: E = λ/(2πε₀r). (b) Infinite charged sheet: E = σ/(2ε₀), independent of distance. (For a conductor's surface, E = σ/ε₀.)

Define electric potential and relate it to the electric field.

Electric potential V at a point is the work done per unit positive charge to bring it from infinity to that point: V = W/q. The field is the negative gradient of potential: E = −dV/dr. Point charge: V = (1/4πε₀)·q/r.

Define capacitance and give the capacitance of a parallel-plate capacitor with a dielectric.

Capacitance C = Q/V (farads). For a parallel-plate capacitor: C = Kε₀A/d, where K is the dielectric constant, A the plate area, and d the separation. Vacuum: C = ε₀A/d.

Give energy stored in a capacitor and the rules for series and parallel combinations.

Energy U = ½CV² = ½QV = Q²/2C. Series: 1/C_eq = 1/C₁ + 1/C₂ + … Parallel: C_eq = C₁ + C₂ + … (opposite of resistor combination rules).

State Ohm's law and define resistivity and its temperature dependence.

Ohm's law: V = IR (current proportional to voltage at constant temperature). Resistance R = ρL/A; resistivity ρ is material-dependent. For metals ρ increases with temperature: ρ_T = ρ₀[1 + α(T − T₀)].

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 potential differences around any closed loop is zero (ΣV = 0) — conservation of energy.

Give the rules for resistors in series and parallel, and the condition for a balanced Wheatstone bridge.

Series: R_eq = R₁ + R₂ + … Parallel: 1/R_eq = 1/R₁ + 1/R₂ + … Wheatstone bridge is balanced (no galvanometer current) when P/Q = R/S.

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

Biot-Savart law: dB = (μ₀/4π)·(I dl × r̂)/r². Field at the centre of a circular loop of radius R: B = μ₀I/(2R) (for N turns, B = μ₀NI/2R).

State Ampère's circuital law and give the field inside a long solenoid.

Ampère's law: ∮B·dl = μ₀I_enc (line integral of B around a closed loop equals μ₀ times enclosed current). Inside a long solenoid: B = μ₀nI, where n is the number of turns per unit length.

Give the force on a moving charge (Lorentz force) and the force per unit length between two parallel current-carrying wires.

Lorentz force: F = q(E + v × B); magnetic part F = qvB sinθ. Force per unit length between parallel wires: f = μ₀I₁I₂/(2πd) — attractive for like-directed currents, repulsive for opposite.

Classify diamagnetic, paramagnetic, and ferromagnetic materials by their relative permeability and susceptibility.

Diamagnetic: μ_r slightly < 1, susceptibility χ small and negative (weakly repelled). Paramagnetic: μ_r slightly > 1, χ small positive (weakly attracted). Ferromagnetic: μ_r ≫ 1, χ large positive (strongly attracted, e.g. iron).

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

Faraday: an induced EMF is produced when magnetic flux through a circuit changes, with EMF = −dΦ/dt (N turns: ε = −N dΦ/dt). Lenz's law: the induced current opposes the change in flux that produced it (the minus sign), conserving energy.

Define self-inductance and mutual inductance.

Self-inductance L relates EMF to changing current in the same coil: ε = −L dI/dt; Φ = LI. Mutual inductance M relates EMF in one coil to changing current in a neighbouring coil: ε₂ = −M dI₁/dt.

For an AC circuit, give the rms value of current and the inductive and capacitive reactances.

I_rms = I₀/√2 (and V_rms = V₀/√2). Inductive reactance X_L = ωL = 2πfL. Capacitive reactance X_C = 1/(ωC) = 1/(2πfC).

Give the impedance and resonance condition of a series LCR circuit.

Impedance Z = √(R² + (X_L − X_C)²). At resonance X_L = X_C, so Z = R (minimum), current is maximum, and the resonant frequency is f₀ = 1/(2π√(LC)).

State the displacement current concept and the speed of electromagnetic waves.

Maxwell introduced displacement current I_d = ε₀(dΦ_E/dt) to account for changing electric fields producing magnetic fields. EM waves travel at c = 1/√(μ₀ε₀) ≈ 3×10⁸ m/s in vacuum, with E and B perpendicular to each other and to propagation.

List the electromagnetic spectrum in order of increasing frequency (decreasing wavelength).

Radio waves → microwaves → infrared → visible light → ultraviolet → X-rays → gamma rays (increasing frequency and energy, decreasing wavelength).

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

Mirror formula: 1/v + 1/u = 1/f. Lens-maker's formula: 1/f = (n − 1)(1/R₁ − 1/R₂), where n is the refractive index relative to the surroundings. (Lens equation: 1/v − 1/u = 1/f.)

State Snell's law and define total internal reflection with its conditions.

Snell's law: n₁ sinθ₁ = n₂ sinθ₂. Total internal reflection occurs when light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle θ_c, where sinθ_c = n₂/n₁ (n₂ < n₁).

Define magnifying power of a compound microscope and an astronomical telescope (normal adjustment).

Compound microscope: M = (L/f_o)(D/f_e), where D = 25 cm (least distance of distinct vision). Telescope (normal adjustment): M = f_o/f_e, with tube length = f_o + f_e.

State Huygens' principle.

Every point on a wavefront acts as a source of secondary spherical wavelets that spread out in the forward direction at the wave's speed; the new wavefront is the forward envelope (tangent surface) of these secondary wavelets.

Give the conditions for constructive and destructive interference and the fringe width in Young's double-slit experiment.

Constructive: path difference = nλ (bright fringes). Destructive: path difference = (n + ½)λ (dark fringes). Fringe width β = λD/d, where D is slit-to-screen distance and d is slit separation.

For single-slit diffraction, give the condition for minima; and state what polarization demonstrates.

Single-slit minima occur at a sinθ = nλ (n = 1, 2, 3…), where a is slit width. Polarization (restriction of vibrations to one plane) demonstrates that light is a transverse wave; Brewster's law: tanθ_p = n.

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

Einstein's equation: hf = φ + KE_max, i.e. KE_max = hf − φ. Work function φ is the minimum energy to eject an electron. Threshold frequency f₀ = φ/h is the minimum frequency below which no emission occurs regardless of intensity.

State the de Broglie hypothesis and give the wavelength formula.

De Broglie proposed that matter has wave nature: every moving particle has an associated wavelength λ = h/p = h/(mv). For an electron accelerated through potential V: λ = 12.27/√V Å (≈ h/√(2mqV)).

State the postulates of Bohr's model of the hydrogen atom.

1) Electrons revolve in certain stable orbits without radiating. 2) Angular momentum is quantized: mvr = nh/2π. 3) Energy is emitted/absorbed only when an electron jumps between orbits, with hf = E₂ − E₁.

Give the energy of the nth level of hydrogen and the Rydberg formula for spectral lines.

Energy: E_n = −13.6/n² eV (ground state −13.6 eV). Rydberg formula: 1/λ = R(1/n₁² − 1/n₂²), where R = 1.097×10⁷ m⁻¹ (Lyman, Balmer, Paschen series for n₁ = 1, 2, 3).

Define mass defect, binding energy, and explain nuclear stability via binding energy per nucleon.

Mass defect Δm = (sum of nucleon masses) − (actual nuclear mass). Binding energy = Δm·c² (E = mc²). Binding energy per nucleon peaks (~8.8 MeV) near iron (A ≈ 56); higher BE/nucleon means greater stability.

Distinguish nuclear fission and fusion and define the law of radioactive decay.

Fission: a heavy nucleus splits into lighter nuclei, releasing energy (e.g. U-235). Fusion: light nuclei combine into a heavier nucleus, releasing energy (e.g. in stars). Radioactive decay law: N = N₀e^(−λt); half-life T½ = 0.693/λ.

Distinguish conductors, insulators, and semiconductors by their energy band gaps.

Conductors: conduction and valence bands overlap (no gap). Insulators: large band gap (E_g > 3 eV). Semiconductors: small band gap (~1 eV, e.g. Si 1.1 eV, Ge 0.7 eV) so conductivity increases with temperature.

Differentiate intrinsic, n-type, and p-type semiconductors.

Intrinsic: pure semiconductor, electrons = holes. n-type: doped with pentavalent (donor) impurity, majority carriers are electrons. p-type: doped with trivalent (acceptor) impurity, majority carriers are holes. The crystal remains electrically neutral.

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

Forward bias: p-side connected to positive terminal; depletion layer narrows, barrier lowers, large current flows. Reverse bias: p-side to negative; depletion layer widens, only tiny saturation current flows. The diode thus conducts mainly in one direction.

Compare half-wave and full-wave rectification.

A rectifier converts AC to DC. Half-wave (one diode) conducts during one half-cycle only — output efficiency ~40.6%. Full-wave (two diodes/centre tap or bridge of four diodes) uses both half-cycles — efficiency ~81.2% with smoother, higher-frequency ripple.

State the truth tables (outputs) of basic logic gates AND, OR, and NOT.

AND: output 1 only when all inputs are 1 (Y = A·B). OR: output 1 when any input is 1 (Y = A+B). NOT: output is the inverse of input (Y = Ā). NAND and NOR are universal gates.

List the basic elements of a communication system.

Transmitter (encodes/modulates the signal), communication channel/medium (carries the signal, may add noise), and receiver (detects/demodulates and recovers the message). Key sub-blocks include transducer, modulator, repeater, amplifier, and demodulator.

Define modulation and name its three main types for analog signals.

Modulation is superimposing a low-frequency message signal onto a high-frequency carrier wave for transmission. The three types are amplitude modulation (AM), frequency modulation (FM), and phase modulation (PM) — varying the carrier's amplitude, frequency, or phase respectively.

Distinguish ground wave, sky wave, and space wave propagation.

Ground wave: travels along Earth's surface, used for low/medium frequencies (up to ~2 MHz). Sky wave: reflected by the ionosphere, used for short-wave (HF, 3–30 MHz) long-distance. Space wave: line-of-sight propagation for VHF/UHF and microwaves (TV, satellite).