AMUEEE Physics Syllabus

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

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

State Kepler's three laws of planetary motion.

1st (Orbits): planets move in ellipses with the Sun at one focus. 2nd (Areas): the line joining planet and Sun sweeps equal areas in equal times. 3rd (Periods): T^2 ∝ a^3.

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

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

Define stress, strain, and Young's modulus.

Stress = force/area (N/m^2); 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 directly proportional to strain (stress = E x strain). The elastic limit is the maximum stress up to which the body returns to its original shape on removing the load.

Distinguish among Young's modulus, bulk modulus, and shear modulus.

Young's modulus: resistance to length change (tensile). Bulk modulus: resistance to volume change (B = -P/(ΔV/V)). Shear (rigidity) modulus: resistance to shape change under tangential stress.

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

Pascal's law: pressure applied to an enclosed fluid is transmitted undiminished to all parts. A hydraulic lift uses this: a small force on a small piston produces a large force on a large piston (F1/A1 = F2/A2).

State Archimedes' principle and the condition for floating.

Archimedes' principle: a body immersed in fluid experiences an upward buoyant force equal to the weight of displaced fluid. A body floats when its weight equals the buoyant force (average density ≤ fluid density).

State Bernoulli's theorem for streamline flow.

For an ideal, incompressible, non-viscous fluid in steady flow: P + ½ρv^2 + ρgh = constant along a streamline (sum of pressure, kinetic, and potential energy per unit volume).

Define viscosity and state Stokes' law.

Viscosity is the internal friction opposing relative motion between fluid layers (F = ηA dv/dx). Stokes' law: viscous drag on a sphere of radius r moving at speed v is F = 6πηrv.

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

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

Distinguish between heat capacity and specific heat capacity.

Heat capacity = heat required to raise a body's temperature by 1 K (J/K). Specific heat capacity = heat to raise unit mass by 1 K (J/kg·K); it is heat capacity per unit mass.

Give the formulae for linear, areal, and volumetric thermal expansion coefficients and their relation.

ΔL = LαΔT, ΔA = AβΔT, ΔV = VγΔT. They relate as α : β : γ = 1 : 2 : 3 for isotropic solids.

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

Conduction (Fourier: Q/t = kA ΔT/L), Convection (bulk fluid movement), and Radiation (Stefan-Boltzmann: E = σT^4 for a black body).

State Newton's law of cooling and Wien's displacement law.

Newton's law of cooling: rate of cooling ∝ temperature difference with surroundings (dT/dt ∝ (T - T_s)). Wien's law: λ_max T = b (b = 2.9 x 10^-3 m·K).

State the postulates and the fundamental result of the kinetic theory of gases for pressure.

Postulates: gas = many tiny molecules in random motion, negligible volume, elastic collisions, no intermolecular forces. Pressure P = (1/3)(ρ v_rms^2) = (1/3)(Nm/V)v_rms^2.

Give the rms speed of gas molecules and the average kinetic energy per molecule.

v_rms = √(3RT/M) = √(3kT/m). Average translational KE per molecule = (3/2)kT; per mole = (3/2)RT.

State the law of equipartition of energy.

Each degree of freedom of a molecule, in thermal equilibrium, has an average energy of ½kT. A monatomic gas has 3, diatomic 5 (3 trans + 2 rot), at moderate temperatures.

Give the ratio of specific heats (γ = Cp/Cv) for monatomic and diatomic ideal gases.

Monatomic: Cv = (3/2)R, Cp = (5/2)R, γ = 5/3 ≈ 1.67. Diatomic: Cv = (5/2)R, Cp = (7/2)R, γ = 7/5 = 1.4. (Cp - Cv = R: Mayer's relation.)

State the first law of thermodynamics.

ΔQ = ΔU + ΔW: heat supplied to a system equals the increase in its internal energy plus the work done by the system. It expresses conservation of energy.

Define isothermal, adiabatic, isobaric, and isochoric processes.

Isothermal: constant T (PV = const). Adiabatic: no heat exchange (PV^γ = const). Isobaric: constant P. Isochoric: constant V (no work done).

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

Kelvin-Planck: no engine can convert all absorbed heat completely into work. Clausius: heat cannot spontaneously flow from a colder to a hotter body without external work.

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

Carnot efficiency η = 1 - T2/T1 (T in kelvin). Refrigerator COP = Q2/(Q1 - Q2) = T2/(T1 - T2).

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

a = -ω^2 x (restoring acceleration ∝ -displacement). For a spring: ω = √(k/m), period T = 2π√(m/k).

Give the time period of a simple pendulum and the expressions for KE, PE, and total energy in SHM.

Simple pendulum: T = 2π√(L/g). In SHM: KE = ½mω^2(A^2 - x^2), PE = ½mω^2 x^2, Total E = ½mω^2 A^2 (constant).

Give the speed of a transverse wave on a string and a longitudinal wave (sound) in a medium.

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

State the relation between wave speed, frequency, and wavelength, and the principle of superposition.

v = fλ. Superposition: when two waves overlap, the resultant displacement is the vector sum of the individual displacements at each point.

Distinguish between progressive and stationary waves.

A progressive wave transfers energy and moves through the medium with all particles having equal amplitude. A stationary wave (interference of two opposite waves) transfers no net energy and has fixed nodes (zero amplitude) and antinodes (max amplitude).

State the conditions for resonance in a closed and an open organ pipe.

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

Define beats and give the beat frequency.

Beats are the periodic variation in sound intensity from superposition of two waves of slightly different frequencies. Beat frequency = |f1 - f2|.

State the Doppler effect formula for sound (observer and source moving).

f' = f (v ± v_o)/(v ∓ v_s), where upper signs apply when motion is toward the other; v = speed of sound, v_o = observer speed, v_s = source speed.

State Coulomb's law and give the value of 1/4πε₀.

F = (1/4πε₀) q1 q2 / r^2, directed along the line joining the charges. 1/4πε₀ ≈ 9 x 10^9 N·m^2/C^2.

Define electric field and electric potential, and give the field/potential of a point charge.

E = F/q (force per unit charge, N/C); V = work per unit charge to bring a charge from infinity (J/C). For a point charge: E = kq/r^2, V = kq/r.

State Gauss's law and the field of an infinite charged plane and a charged sphere.

Gauss's law: Φ_E = ∮E·dA = q_enclosed/ε₀. Infinite plane sheet: E = σ/2ε₀. Outside a charged sphere: E = kQ/r^2 (acts as point charge).

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

C = ε₀A/d (vacuum), or Kε₀A/d with dielectric. Energy U = ½CV^2 = ½QV = Q^2/2C.

How do capacitors combine in series and parallel?

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

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

Ohm's law: V = IR. Resistivity ρ = RA/L (material property). For metals, ρ increases with temperature: ρ = ρ₀(1 + αΔT).

State Kirchhoff's two circuit laws.

Junction rule (KCL): the sum of currents entering a junction equals the sum leaving (charge conservation). Loop rule (KVL): the sum of EMFs and potential drops around any closed loop is zero (energy conservation).

How do resistors combine in series and parallel, and what is the formula for a Wheatstone bridge balance?

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

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

Biot-Savart: dB = (μ₀/4π)(I dl x r̂)/r^2. Field at centre of a loop of radius R: B = μ₀I/2R.

Give the magnetic field of a long straight wire and inside a long solenoid.

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

Give the Lorentz force on a charge and the force per unit length between two parallel currents.

Lorentz force: F = q(E + v x B), magnetic part F = qvB sinθ. Two parallel wires: F/L = μ₀I1I2/2πd (attract if currents are parallel, repel if antiparallel).

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

Faraday's law: induced EMF = -dΦ/dt (rate of change of magnetic flux). Lenz's law: the induced current opposes the change producing it (the minus sign; conserves energy).

Define self-inductance and mutual inductance, and give the EMF for self-induction.

Self-inductance L: EMF = -L dI/dt; energy stored = ½LI^2. Mutual inductance M relates EMF in one coil to dI/dt in another: EMF2 = -M dI1/dt.

In an AC series circuit, give the inductive reactance, capacitive reactance, and impedance.

X_L = ωL = 2πfL; X_C = 1/ωC = 1/2πfC; Impedance Z = √(R^2 + (X_L - X_C)^2).

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

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

Relate rms and peak values of AC, and define the power factor.

I_rms = I₀/√2, V_rms = V₀/√2. Average power P = V_rms I_rms cosφ; power factor = cosφ = R/Z.

What is the source of electromagnetic waves and their speed in vacuum?

EM waves are produced by accelerating (oscillating) charges. They are transverse, with mutually perpendicular E and B fields, travelling at c = 1/√(μ₀ε₀) = 3 x 10^8 m/s in vacuum.

List the electromagnetic spectrum in order of increasing frequency.

Radio waves < microwaves < infrared < visible light < ultraviolet < X-rays < gamma rays (frequency increases, wavelength decreases in this order).

State the laws of reflection and refraction (Snell's law).

Reflection: angle of incidence = angle of reflection; incident ray, reflected ray, and normal are coplanar. Snell's law: n1 sinθ1 = n2 sinθ2 (refractive index x sine of angle is constant).

Give the mirror formula, lens formula, and definition of power of a lens.

Mirror: 1/v + 1/u = 1/f. Lens: 1/v - 1/u = 1/f. Power P = 1/f (in metres), measured in dioptres (D).

State the condition for total internal reflection and the critical angle relation.

TIR occurs when light travels from a denser to a rarer medium at an angle greater than the critical angle θ_c, where sinθ_c = 1/n (n = refractive index of denser medium relative to rarer).

Give the lensmaker's formula and the relation between focal length and refractive index.

Lensmaker's formula: 1/f = (n - 1)(1/R1 - 1/R2), where n is the lens material's refractive index relative to the surrounding medium and R1, R2 are the radii of curvature.

State the condition 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 (D = slit-to-screen distance, d = slit separation).

What is diffraction, and where does the first minimum occur in single-slit diffraction?

Diffraction is the bending of waves around obstacles/edges and spreading after a slit. First minimum (single slit of width a): a sinθ = λ. Central maximum is the brightest and twice as wide.

State Huygens' principle and the result of polarisation (Malus's law).

Huygens' principle: every point on a wavefront acts as a source of secondary wavelets; their envelope gives the new wavefront. Malus's law: I = I₀ cos^2θ (intensity through a polariser at angle θ to incident polarisation).

State the photoelectric effect equation and define work function and threshold frequency.

Einstein's equation: hf = φ + KE_max, where φ = work function (minimum energy to eject an electron) = hf₀, and f₀ = threshold frequency below which no emission occurs.

Give the de Broglie wavelength of a particle.

λ = h/p = h/(mv), where h = Planck's constant. For an electron accelerated through potential V: λ = 12.27/√V Å.

State the key observations of the photoelectric effect that classical physics could not explain.

Emission is instantaneous; KE_max depends on frequency (not intensity); current depends on intensity; below threshold frequency no emission occurs regardless of intensity. These confirm the photon (quantum) nature of light.

State Bohr's postulates for the hydrogen atom.

1) Electrons orbit in stationary states without radiating. 2) Angular momentum is quantised: L = nh/2π. 3) Radiation is emitted/absorbed when an electron jumps between orbits: hf = E2 - E1.

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

E_n = -13.6/n^2 eV. Rydberg formula: 1/λ = R(1/n1^2 - 1/n2^2), with R = 1.097 x 10^7 m^-1.

Define mass defect, binding energy, and the law of radioactive decay.

Mass defect Δm = (mass of nucleons) - (mass of nucleus). Binding energy = Δm·c^2. Radioactive decay: N = N₀ e^(-λt), with half-life T½ = 0.693/λ.

Distinguish among alpha, beta, and gamma radiation.

Alpha: helium nucleus (He-4), low penetration, high ionisation. Beta: electron/positron, moderate penetration. Gamma: high-energy EM photon, highest penetration, no charge or mass.

Distinguish nuclear fission from nuclear fusion.

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). Both release energy because products have higher binding energy per nucleon.

Distinguish among conductors, insulators, and semiconductors by energy band gap.

Conductors: overlapping/no gap (E_g ≈ 0). Insulators: large gap (E_g > 3 eV). Semiconductors: small gap (E_g ≈ 1 eV), e.g. Si (1.1 eV), Ge (0.7 eV).

Distinguish n-type and p-type semiconductors.

n-type: doped with pentavalent impurity (e.g. P, As), majority carriers are electrons. p-type: doped with trivalent impurity (e.g. B, Al), majority carriers are holes.

Describe the behaviour of a p-n junction diode under forward and reverse bias.

Forward bias (p to +, n to -): depletion layer narrows, low resistance, current flows easily. Reverse bias: depletion layer widens, high resistance, only tiny leakage current flows (until breakdown).

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

AND: output 1 only when both inputs are 1. OR: output 1 if any input is 1. NOT: output is the inverse of the input (1→0, 0→1).

What is a half-wave and a full-wave rectifier, and what is a Zener diode used for?

Half-wave rectifier converts only one half of the AC cycle to DC; full-wave (bridge) rectifier uses both halves. A Zener diode operates in reverse breakdown at a constant voltage and is used as a voltage regulator.