KCET Physics Syllabus

How does acceleration due to gravity g vary with height h and depth d?

At height: g_h = g(1 − 2h/R) for h ≪ R. At depth: g_d = g(1 − d/R). g is maximum at the surface and zero at the centre of the Earth.

Give the formulas for orbital velocity and escape velocity from a planet of mass M, radius R.

Orbital velocity v_o = √(GM/R) = √(gR). Escape velocity v_e = √(2GM/R) = √(2gR) = √2 · v_o ≈ 11.2 km/s for Earth.

State Kepler's three laws of planetary motion.

1st (Law of Orbits): planets move in ellipses with the Sun at one focus. 2nd (Law of Areas): the line joining a planet to the Sun sweeps equal areas in equal times (constant areal velocity). 3rd (Law of Periods): T² ∝ a³.

Define stress, strain, and Young's modulus.

Stress = force/area (N/m²); strain = change in dimension/original dimension (dimensionless); Young's modulus Y = longitudinal stress/longitudinal strain.

State Hooke's law and the energy stored per unit volume in a stretched wire.

Hooke's law: within the elastic limit, stress ∝ strain. Elastic potential energy per unit volume = ½ × stress × strain.

What are the bulk modulus, shear (rigidity) modulus, and Poisson's ratio?

Bulk modulus K = volumetric stress/volumetric strain (resistance to compression). Shear modulus η = shearing stress/shearing strain. Poisson's ratio σ = lateral strain/longitudinal strain.

State Pascal's law and the principle of a hydraulic lift.

Pascal's law: pressure applied to an enclosed fluid is transmitted undiminished to every part. A hydraulic lift uses F₁/A₁ = F₂/A₂ to amplify force via differing piston areas.

State Bernoulli's equation for streamline flow.

P + ½ρv² + ρgh = constant along a streamline (sum of pressure energy, kinetic energy, and potential energy per unit volume is conserved for an ideal incompressible fluid).

Define surface tension and give the excess pressure inside a soap bubble vs a liquid drop.

Surface tension = force per unit length (N/m) along a liquid surface. Excess pressure inside a drop: 2T/R; inside a soap bubble (two surfaces): 4T/R.

State Stokes' law and the expression for terminal velocity.

Viscous drag on a sphere: F = 6πηrv. Terminal velocity v_t = 2r²(ρ − σ)g/(9η), reached when drag plus buoyancy balance weight.

Give the relation between Celsius, Fahrenheit, and Kelvin temperature scales.

K = °C + 273.15; °F = (9/5)°C + 32. The absolute zero is 0 K = −273.15 °C.

What are the coefficients of linear, areal, and volume thermal expansion, and how are they related?

For isotropic solids, β = 2α and γ = 3α, where α (linear), β (areal), and γ (volume) are the expansion coefficients.

Compare conduction, convection, and radiation as modes of heat transfer.

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

State Newton's law of cooling and the Stefan-Boltzmann law.

Newton's law of cooling: rate of cooling ∝ temperature difference with surroundings (for small differences). Stefan-Boltzmann law: power radiated per unit area = σεT⁴, σ = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴.

State the first law of thermodynamics.

ΔQ = ΔU + ΔW, i.e. heat supplied to a system equals the increase in internal energy plus work done by the system. It is the conservation of energy applied to heat.

Give the work done and conditions for isothermal and adiabatic processes.

Isothermal (T constant): W = nRT ln(V₂/V₁), PV = constant. Adiabatic (Q = 0): PVᵞ = constant, W = (P₁V₁ − P₂V₂)/(γ − 1).

State the second law of thermodynamics and the efficiency of a Carnot engine.

Second law: heat cannot spontaneously flow from cold to hot (Clausius); no engine can convert all heat into work (Kelvin-Planck). Carnot efficiency η = 1 − T_c/T_h (temperatures in kelvin).

What are the molar specific heats Cp and Cv, and Mayer's relation?

Cv = heat to raise 1 mole by 1 K at constant volume; Cp at constant pressure. Mayer's relation: Cp − Cv = R, and γ = Cp/Cv.

State the kinetic theory expression for gas pressure and the RMS speed of molecules.

P = ⅓ρ⟨v²⟩ = (1/3)(N/V)m⟨v²⟩. RMS speed v_rms = √(3RT/M) = √(3kT/m).

State the law of equipartition of energy and the average KE of a gas molecule.

Each degree of freedom carries ½kT of energy. Average translational KE of a molecule = (3/2)kT; k = Boltzmann constant = 1.38 × 10⁻²³ J/K.

Define SHM and give the displacement, velocity, and acceleration relations.

SHM: acceleration ∝ negative displacement (a = −ω²x). x = A sin(ωt + φ); v = ω√(A² − x²); a = −ω²x. Restoring force F = −kx.

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

Simple pendulum: T = 2π√(L/g). Spring-mass: T = 2π√(m/k). Energy in SHM: E = ½kA² = ½mω²A² (constant).

Give the speed of a transverse wave on a string and of sound in a gas.

On a string: v = √(T/μ), T = tension, μ = mass per unit length. Sound in a gas (Laplace): v = √(γP/ρ).

What is the relation between wave speed, frequency, and wavelength, and the equation of a progressive wave?

v = fλ. A progressive wave: y = A sin(ωt − kx), where ω = 2πf and k = 2π/λ (wave number).

Compare standing waves in a closed pipe vs an open pipe (harmonics produced).

Closed pipe (one end closed): only odd harmonics, fundamental f = v/4L. Open pipe (both ends open): all harmonics, fundamental f = v/2L.

What are beats and how is beat frequency calculated?

Beats are periodic variations in loudness from superposition of two waves of slightly different frequencies. Beat frequency = |f₁ − f₂|.

State the Doppler effect formula for sound when source and observer move along the line joining them.

f' = f(v ± v_o)/(v ∓ v_s), where upper signs (toward each other) increase frequency; v = speed of sound, v_o = observer speed, v_s = source speed.

State Coulomb's law and the electric field due to a point charge.

F = (1/4πε₀)·q₁q₂/r², with 1/4πε₀ = 9 × 10⁹ N·m²/C². Field of a point charge E = (1/4πε₀)·q/r², directed radially.

State Gauss's law and give the field due to an infinite line and infinite sheet of charge.

Gauss's law: Φ = ∮E·dA = q_enclosed/ε₀. Infinite line charge: E = λ/(2πε₀r). Infinite charged sheet: E = σ/(2ε₀), independent of distance.

What is electric dipole moment and the torque on a dipole in a uniform field?

Dipole moment p = q·2a (from −q to +q). Torque τ = p × E = pE sinθ; potential energy U = −p·E = −pE cosθ.

Define electric potential and give the energy stored in a capacitor.

Electric potential V = work per unit charge to bring a charge from infinity (V = q/4πε₀r for a point charge). Capacitor energy U = ½CV² = ½QV = Q²/2C.

Give the capacitance of a parallel-plate capacitor and the effect of a dielectric.

C = ε₀A/d (vacuum). Inserting a dielectric of constant K gives C = Kε₀A/d, increasing capacitance K-fold.

How do capacitors combine in series and parallel?

Series: 1/C = 1/C₁ + 1/C₂ + … (smaller than smallest). Parallel: C = C₁ + C₂ + … (sum). Resistors follow the opposite rules.

State Ohm's law and the relation between resistivity, drift velocity, and current.

V = IR. Resistance R = ρL/A. Current I = neAv_d, where n = charge density, v_d = drift velocity; conductivity σ = 1/ρ = ne²τ/m.

State Kirchhoff's two circuit laws.

Junction (current) rule: ΣI = 0 at a node (charge conservation). Loop (voltage) rule: ΣV = 0 around a closed loop (energy conservation).

State the conditions for a balanced Wheatstone bridge and the meter bridge use.

Wheatstone bridge balanced when P/Q = R/S (no current through galvanometer). The meter bridge applies this to find an unknown resistance via a sliding contact length ratio.

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

Biot-Savart: dB = (μ₀/4π)·I dl × r̂/r². Field at centre of a loop: B = μ₀I/2R. μ₀ = 4π × 10⁻⁷ T·m/A.

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

Ampere's law: ∮B·dl = μ₀I_enclosed. Inside a long solenoid: B = μ₀nI, where n = turns per unit length (field is uniform).

What is the force on a charge and on a current-carrying wire in a magnetic field?

On a charge: F = qv × B (magnitude qvB sinθ). On a wire: F = IL × B (magnitude BIL sinθ). The Lorentz force is F = q(E + v × B).

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

Faraday's law: induced EMF ε = −dΦ/dt (Φ = magnetic flux). Lenz's law: the induced current opposes the change in flux producing it (the negative sign), conserving energy.

Define self-inductance and mutual inductance, and the energy stored in an inductor.

Self: ε = −L dI/dt. Mutual: ε₂ = −M dI₁/dt. Energy stored in an inductor U = ½LI².

For an AC circuit, give the reactances of an inductor and capacitor and the resonance frequency of an LCR circuit.

Inductive reactance X_L = ωL; capacitive reactance X_C = 1/ωC. Resonance when X_L = X_C, at f = 1/(2π√(LC)), where impedance is minimum.

Define RMS value of AC and power factor.

I_rms = I₀/√2, V_rms = V₀/√2. Average power P = V_rms·I_rms·cosφ, where cosφ = R/Z is the power factor (φ = phase difference).

List the electromagnetic spectrum in order of increasing frequency.

Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays (increasing frequency, decreasing wavelength). All travel at c = 3 × 10⁸ m/s in vacuum.

What did Maxwell add to Ampere's law, and what is the speed of EM waves?

Maxwell added displacement current (I_d = ε₀ dΦ_E/dt) to account for changing electric fields. EM wave speed c = 1/√(μ₀ε₀); E and B are perpendicular to each other and to propagation.

State the laws of reflection and the mirror formula with sign convention.

Angle of incidence = angle of reflection. Mirror formula: 1/v + 1/u = 1/f, with f = R/2; distances measured from the pole, with the Cartesian sign convention.

State Snell's law, the lens maker's formula, and the lens formula.

Snell's law: n₁ sinθ₁ = n₂ sinθ₂. Lens maker's: 1/f = (n − 1)(1/R₁ − 1/R₂). Lens formula: 1/v − 1/u = 1/f; power P = 1/f (in dioptres).

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

Critical angle θ_c = sin⁻¹(1/n) for light going from denser to rarer medium. TIR occurs when the angle of incidence exceeds θ_c (used in optical fibres).

Give the magnifying power of a simple microscope, compound microscope, and telescope.

Simple microscope: M = 1 + D/f. Compound microscope: M = (L/f_o)(D/f_e). Astronomical telescope (normal adjustment): M = f_o/f_e, length = f_o + f_e.

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

Constructive (bright): path difference = nλ. Destructive (dark): path difference = (n + ½)λ. Fringe width β = λD/d.

State Huygens' principle and the condition for the first minimum in single-slit diffraction.

Huygens' principle: every point on a wavefront acts as a source of secondary wavelets; their envelope forms the new wavefront. First diffraction minimum: a sinθ = λ (a = slit width).

What is polarisation and Brewster's law?

Polarisation restricts light vibrations to one plane (transverse-wave evidence). Brewster's law: at the polarising angle θ_p, tanθ_p = n, and the reflected ray is fully polarised, perpendicular to the refracted ray.

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

K_max = hν − φ₀, where φ₀ = work function = hν₀ (minimum energy to eject an electron), ν₀ = threshold frequency. Photon energy E = hν; h = 6.63 × 10⁻³⁴ J·s.

State the de Broglie wavelength formula for a particle.

λ = h/p = h/mv = h/√(2mKE). For an electron accelerated through V volts: λ ≈ 1.227/√V nm.

State Bohr's postulates for the hydrogen atom and the energy of the nth orbit.

Electrons occupy stationary orbits where L = nℏ (angular momentum quantised); radiation occurs only on transitions (hν = E₂ − E₁). Energy E_n = −13.6/n² eV; radius r_n ∝ n².

Give the Rydberg formula for hydrogen spectral lines and name the series.

1/λ = R(1/n₁² − 1/n₂²), R = 1.097 × 10⁷ m⁻¹. Series: Lyman (n₁=1, UV), Balmer (n₁=2, visible), Paschen/Brackett/Pfund (n₁=3,4,5, IR).

Define mass defect, binding energy, and the relation E = mc².

Mass defect Δm = (sum of nucleon masses) − (nuclear mass). Binding energy = Δm·c²; 1 u ≈ 931.5 MeV. Higher binding energy per nucleon means a more stable nucleus (peak near iron).

State the radioactive decay law and define half-life.

N = N₀e^(−λt), λ = decay constant. Half-life T₁/₂ = ln2/λ = 0.693/λ; mean life τ = 1/λ. Activity A = λN.

Compare alpha, beta, and gamma radiation.

Alpha (He nucleus): +2 charge, least penetrating, most ionising. Beta (electron/positron): ±1 charge, moderate penetration. Gamma (photon): no charge, most penetrating, least ionising.

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

Intrinsic: pure, n_e = n_h. n-type: doped with pentavalent (donor) impurity, majority carriers are electrons. p-type: doped with trivalent (acceptor) impurity, majority carriers are holes.

How does a p-n junction diode behave under forward and reverse bias?

Forward bias (p to +): depletion region narrows, low resistance, current flows easily after the barrier voltage (~0.7 V for Si). Reverse bias: depletion widens, high resistance, only tiny leakage current until breakdown.

Distinguish half-wave from full-wave rectification, and name the diode used as a voltage regulator.

Half-wave rectifier conducts during one half-cycle (uses 1 diode); full-wave conducts during both half-cycles (uses 2 diodes or a bridge of 4). A Zener diode (operated in reverse breakdown) acts as a voltage regulator.