KEAM Physics Syllabus

Define stress, strain, and Young's modulus.

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

State Hooke's law and define the elastic limit.

Hooke's law: within the elastic limit, stress is proportional to strain. The elastic limit is the maximum stress up to which a body returns to its original shape on removing the load.

Define Pascal's law and state how pressure varies with depth in a fluid.

Pascal's law: pressure applied to an enclosed fluid is transmitted undiminished to all parts. Pressure at depth h: P = P0 + rho g h.

State Archimedes' principle.

A body fully or partially immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.

State Bernoulli's equation for streamline flow.

P + (1/2)rho v^2 + rho g h = constant along a streamline, expressing conservation of energy for an ideal incompressible fluid.

Give the equation of continuity for fluid flow.

A1 v1 = A2 v2 (Av = constant): for an incompressible fluid the volume flow rate is constant, so velocity increases where cross-section decreases.

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

alpha = (1/L)(dL/dT). For isotropic solids: beta (area) = 2 alpha and gamma (volume) = 3 alpha.

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

Conduction, convection, radiation. Conduction (steady state): rate of heat flow H = kA(T1 - T2)/L, where k is thermal conductivity.

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

Stefan-Boltzmann: power radiated per unit area E = sigma T^4 (sigma = 5.67 x 10^-8 W/m^2K^4). Wien: lambda_max x T = b (b = 2.9 x 10^-3 m K).

State the first law of thermodynamics.

dQ = dU + dW: heat supplied to a system equals the increase in internal energy plus the work done by the system.

Compare isothermal and adiabatic processes.

Isothermal: temperature constant, dU = 0, follows PV = constant. Adiabatic: no heat exchange (dQ = 0), follows PV^gamma = constant; adiabatic curves are steeper than isothermal on a P-V diagram.

State the second law of thermodynamics (Kelvin-Planck statement) and Carnot efficiency.

No process can convert heat completely into work with no other effect. Carnot efficiency eta = 1 - T_cold/T_hot (temperatures in kelvin), the maximum possible for given reservoirs.

State the kinetic theory expression for the pressure of an ideal gas.

P = (1/3)(N/V) m v_rms^2 = (1/3) rho v_rms^2, where v_rms is the root-mean-square molecular speed.

Give the three molecular speeds (rms, average, most probable) for a gas.

v_rms = sqrt(3RT/M); v_avg = sqrt(8RT/(pi M)); v_mp = sqrt(2RT/M). Order: v_mp < v_avg < v_rms.

State the law of equipartition of energy.

Each degree of freedom of a molecule contributes (1/2)k_B T to the average energy per molecule. A monatomic gas has 3 translational degrees of freedom, giving (3/2)k_B T.

Write the displacement equation and time period for simple harmonic motion of a spring-mass system.

x = A sin(omega t + phi); for a spring, omega = sqrt(k/m), so T = 2 pi sqrt(m/k).

Give the time period of a simple pendulum and the KE/PE expressions in SHM.

Simple pendulum: T = 2 pi sqrt(L/g). In SHM: KE = (1/2)m omega^2 (A^2 - x^2), PE = (1/2)m omega^2 x^2; total energy = (1/2)m omega^2 A^2 (constant).

Give the speed of a transverse wave on a string and the relation between v, f, and lambda.

v = sqrt(T/mu), where T is tension and mu is linear mass density. Wave relation: v = f lambda.

Distinguish transverse and longitudinal waves with examples.

Transverse: particle motion perpendicular to wave direction (e.g. waves on a string, light). Longitudinal: particle motion parallel to wave direction (e.g. sound in air).

State the conditions for resonance (fundamental frequency) in (a) a closed pipe and (b) an open pipe of length L.

Closed pipe (one end closed): f1 = v/(4L), only odd harmonics. Open pipe (both ends open): f1 = v/(2L), all harmonics present.

State the beat frequency and the Doppler effect formula for sound.

Beat frequency = |f1 - f2|. Doppler (general): f' = f (v +/- v_observer)/(v -/+ v_source), with signs chosen so approach raises the observed frequency.

State Coulomb's law and give the field of a point charge.

F = (1/(4 pi epsilon_0)) q1 q2 / r^2. Electric field of a point charge: E = (1/(4 pi epsilon_0)) q / r^2, directed radially.

State Gauss's law.

The net electric flux through a closed surface equals the enclosed charge divided by epsilon_0: flux = q_enclosed / epsilon_0.

Give the capacitance of a parallel-plate capacitor and the energy stored in a capacitor.

C = epsilon_0 A / d (x dielectric constant K with a dielectric). Energy U = (1/2) C V^2 = Q^2/(2C) = (1/2) Q V.

State Ohm's law and the formula for resistance in terms of resistivity.

V = IR (current proportional to voltage at constant temperature). Resistance R = rho L / A, where rho is resistivity.

State Kirchhoff's two circuit laws.

Junction (current) law: the sum of currents into a node equals the sum out (charge conservation). Loop (voltage) law: the sum of EMFs and potential drops around any closed loop is zero (energy conservation).

Give the formulas for resistors in series and in parallel.

Series: R = R1 + R2 + ... (same current). Parallel: 1/R = 1/R1 + 1/R2 + ... (same voltage).

State the Biot-Savart law and the force on a moving charge in a magnetic field.

Biot-Savart: dB = (mu_0/(4 pi)) I dl x r_hat / r^2. Force on a moving charge (Lorentz magnetic force): F = q v x B, magnitude qvB sin(theta).

Give the magnetic field at the centre of a circular loop and inside a long solenoid.

Centre of a circular loop: B = mu_0 I / (2R). Inside a long solenoid: B = mu_0 n I, where n is turns per unit length.

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

Faraday: induced EMF = -d(flux)/dt; for N turns, EMF = -N d(flux)/dt. Lenz's law: the induced current opposes the change in flux that produces it (the minus sign), conserving energy.

Give the speed of light in terms of epsilon_0 and mu_0, and the order of the EM spectrum by increasing frequency.

c = 1/sqrt(mu_0 epsilon_0) = 3 x 10^8 m/s. Increasing frequency: radio < microwave < infrared < visible < ultraviolet < X-rays < gamma rays.

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

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

State Snell's law and the condition for total internal reflection.

Snell's law: n1 sin(theta1) = n2 sin(theta2). Total internal reflection occurs when light goes from a denser to a rarer medium at an angle exceeding the critical angle theta_c, where sin(theta_c) = n_rarer/n_denser.

State the condition for fringe width in Young's double-slit experiment.

Fringe width beta = lambda D / d, where D is slit-to-screen distance and d is slit separation. Bright fringes: path difference = m lambda; dark fringes: (m + 1/2) lambda.

State the Einstein photoelectric equation and define work function.

K_max = h f - phi, where phi (work function) is the minimum energy to eject an electron. Below the threshold frequency f0 = phi/h, no emission occurs regardless of intensity.

Give the de Broglie wavelength of a particle.

lambda = h/p = h/(mv); for an electron accelerated through potential V, lambda ≈ 1.227/sqrt(V) nm.

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

Energy E_n = -13.6/n^2 eV; radius r_n = 0.529 x n^2 angstrom (Bohr radius). Energy is negative, indicating a bound state.

Define mass defect and binding energy of a nucleus.

Mass defect = (sum of nucleon masses) - (actual nuclear mass). Binding energy = (mass defect) x c^2; higher binding energy per nucleon means a more stable nucleus (peak near iron-56).

State the law of radioactive decay and the relation between half-life and decay constant.

N = N0 e^(-lambda t); activity decreases exponentially. Half-life t_1/2 = ln(2)/lambda = 0.693/lambda; mean life tau = 1/lambda.

Compare intrinsic and extrinsic semiconductors (n-type and p-type).

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

Explain the action of a p-n junction diode in forward and reverse bias, and the truth values of a NAND gate.

Forward bias (p to +): depletion region narrows, diode conducts. Reverse bias: depletion region widens, negligible current (until breakdown). NAND output is 0 only when both inputs are 1; otherwise output is 1.