IPU CET Physics Syllabus

State the law of conservation of angular momentum and give an example.

If net external torque is zero, total angular momentum L = Iω remains constant; e.g. a spinning skater speeds up by pulling arms in (reducing I increases ω).

State Newton's law of universal gravitation.

Every two point masses attract with force F = G m₁m₂ / r^2 along the line joining them, where G = 6.67×10^-11 N·m^2/kg^2.

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

At height: g' = g(1 − 2h/R) for h≪R; at depth: g' = g(1 − d/R). So g decreases with both, and is zero at Earth's centre.

Write the formulas for orbital velocity and escape velocity.

Orbital velocity v(o) = sqrt(GM/r) (≈7.9 km/s near Earth); escape velocity v(e) = sqrt(2GM/R) = sqrt(2)·v(o) ≈ 11.2 km/s.

State Kepler's three laws of planetary motion.

1st: Orbits are ellipses with the Sun at one focus. 2nd: The line joining planet and Sun sweeps equal areas in equal times (constant areal velocity). 3rd: T^2 ∝ a^3 (square of period ∝ cube of semi-major axis).

Define stress, strain, and Young's modulus.

Stress = force per unit area (F/A); strain = fractional deformation (ΔL/L); Young's modulus Y = longitudinal stress / longitudinal strain.

State Hooke's law and define the elastic limit.

Within the elastic limit, stress is directly proportional to strain (stress = E × strain). The elastic limit is the maximum stress up to which a body returns to its original shape on removal of the load.

Define bulk modulus and modulus of rigidity (shear modulus).

Bulk modulus K = −V·(dP/dV) = volumetric stress / volumetric strain; modulus of rigidity η = shearing stress / shearing strain.

State Pascal's law and give its application.

Pressure applied to an enclosed fluid is transmitted equally in all directions; applied in hydraulic lifts/brakes where a small force on a small piston produces a large force on a large piston.

State Archimedes' principle and the condition for floating.

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

State Bernoulli's theorem (equation) for ideal fluid flow.

P + (1/2)ρv^2 + ρgh = constant along a streamline; total energy (pressure + kinetic + potential) per unit volume is conserved.

State the equation of continuity for fluid flow.

A₁v₁ = A₂v₂ (Av = constant); the volume flow rate of an incompressible fluid is constant, so speed increases where the cross-section narrows.

Define coefficient of viscosity and state Stokes' law.

Viscosity η relates viscous force to velocity gradient: F = ηA(dv/dx). Stokes' law: viscous force on a sphere = 6πηrv, giving terminal velocity v(t) = 2r^2(ρ−σ)g / 9η.

Distinguish heat capacity, specific heat, and latent heat.

Heat capacity = heat to raise a body's temperature by 1 K (J/K); specific heat = per unit mass (J/kg·K); latent heat = heat per unit mass to change phase at constant temperature (Q = mL).

Compare conduction, convection, and radiation.

Conduction = heat transfer through matter without bulk motion (solids); convection = transfer by actual movement of fluid; radiation = transfer by electromagnetic waves, requiring no medium.

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

Stefan-Boltzmann: E = σT^4 (power radiated per unit area of a black body). Wien's law: λ(max)·T = b (= 2.9×10^-3 m·K), so peak wavelength decreases as temperature rises.

State the first law of thermodynamics.

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

Distinguish isothermal, adiabatic, isobaric, and isochoric processes.

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

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

Heat cannot spontaneously flow from a colder to a hotter body / no engine is 100% efficient (entropy of an isolated system never decreases). Carnot efficiency η = 1 − T₂/T₁.

State the postulates and key result of the kinetic theory of gases (pressure formula).

Gas consists of tiny molecules in random motion with negligible volume and only elastic collisions. Pressure P = (1/3)(m N / V) v(rms)^2 = (1/3)ρ v(rms)^2.

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

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

Write the rms speed of gas molecules and how it depends on temperature.

v(rms) = sqrt(3RT/M) = sqrt(3kT/m); it is directly proportional to the square root of absolute temperature and inversely to the square root of molar mass.

Define simple harmonic motion and write its defining equation.

SHM is motion where acceleration is directly proportional to displacement and directed toward the mean position: a = −ω^2 x. Displacement x = A sin(ωt + φ).

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

Simple pendulum: T = 2π sqrt(L/g); spring-mass: T = 2π sqrt(m/k).

Write the kinetic, potential, and total energy of a particle in SHM.

KE = (1/2)mω^2(A^2 − x^2); PE = (1/2)mω^2 x^2; Total energy = (1/2)mω^2 A^2 (constant).

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

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

Write the speed of a transverse wave on a string and of sound in a gas (Newton-Laplace).

On a string: v = sqrt(T/μ) (T = tension, μ = mass per length). In a gas: v = sqrt(γP/ρ) (Laplace's correction).

Describe beats and standing waves.

Beats: periodic loudness variation when two waves of slightly different frequencies superpose; beat frequency = |f₁ − f₂|. Standing waves: formed by two identical opposite-moving waves, having fixed nodes and antinodes.

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

f' = f(v ± v₀)/(v ∓ v(s)), where upper signs apply when source and observer approach each other; v is the speed of sound. Frequency rises on approach and falls on recession.

State Coulomb's law and the principle of superposition for charges.

F = (1/4πε₀)·q₁q₂/r^2 along the line joining the charges. Superposition: net force on a charge is the vector sum of forces due to all other charges.

Define electric field and electric potential due to a point charge.

E = (1/4πε₀)·q/r^2 (force per unit positive test charge); potential V = (1/4πε₀)·q/r (work per unit charge to bring it from infinity).

State Gauss's law and its result for a uniformly charged sphere/plane.

Total electric flux through a closed surface = q(enclosed)/ε₀. Field of an infinite sheet = σ/2ε₀; field outside a charged sphere = kQ/r^2 (as if charge were at the centre).

Define capacitance and give the energy stored and parallel-plate capacitance.

C = Q/V. Parallel-plate: C = ε₀A/d (× dielectric constant K with a dielectric). Energy stored U = (1/2)CV^2 = (1/2)QV = Q^2/2C.

Give the formula for combining capacitors in series and in parallel.

Series: 1/C = 1/C₁ + 1/C₂ + ...; Parallel: C = C₁ + C₂ + ... .

State Ohm's law and define resistivity.

V = IR (current ∝ potential difference at constant temperature). Resistivity ρ relates to resistance by R = ρL/A; it is a material property independent of dimensions.

State Kirchhoff's two laws for circuits.

Junction (current) law: sum of currents entering a node = sum leaving (charge conservation). Loop (voltage) law: algebraic sum of EMFs and IR drops around a closed loop = 0 (energy conservation).

Give the formula for resistors in series and in parallel.

Series: R = R₁ + R₂ + ...; Parallel: 1/R = 1/R₁ + 1/R₂ + ... .

State Joule's law of heating and Faraday's laws of electrolysis (chemical effect of current).

Joule heating: H = I^2 R t. Faraday's 1st law: mass deposited m ∝ charge (m = Zq). 2nd law: masses of different substances by the same charge are proportional to their chemical equivalents.

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

dB = (μ₀/4π)·(I dl × r̂)/r^2. Field at centre of a circular loop of radius R: B = μ₀NI/2R.

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

Long straight wire: B = μ₀I/2πr. Inside a long solenoid: B = μ₀nI (n = turns per unit length).

Write the force on a moving charge (Lorentz) and on a current-carrying wire in a magnetic field.

On a charge: F = q(v × B), magnitude qvB sinθ. On a wire: F = I(L × B), magnitude BIL sinθ.

Define magnetic dipole moment of a current loop and torque on it in a field.

m = NIA (direction by right-hand rule). Torque τ = m × B = NIAB sinθ, tending to align the loop with the field.

Compare diamagnetic, paramagnetic, and ferromagnetic materials.

Diamagnetic: weakly repelled, relative permeability μ(r) slightly <1 (e.g. bismuth). Paramagnetic: weakly attracted, μ(r) slightly >1 (e.g. aluminium). Ferromagnetic: strongly attracted, μ(r) ≫1 (e.g. iron).

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

Induced EMF ε = −dΦ/dt; its magnitude equals the rate of change of magnetic flux. Lenz's law (the minus sign): the induced current opposes the change in flux that produced it (energy conservation).

Define self-inductance and mutual inductance.

Self-inductance L: ε = −L(dI/dt); energy stored = (1/2)LI^2. Mutual inductance M relates EMF in one coil to current change in another: ε₂ = −M(dI₁/dt).

Define RMS value of AC and relate it to peak value.

RMS (root-mean-square) value is the DC equivalent producing the same heating. For sinusoidal AC: I(rms) = I₀/√2 and V(rms) = V₀/√2.

Define reactance, impedance, and resonance in a series LCR circuit.

Inductive reactance X(L) = ωL; capacitive X(C) = 1/ωC; impedance Z = sqrt(R^2 + (X(L) − X(C))^2). Resonance occurs at ω = 1/sqrt(LC), where Z is minimum (= R) and current is maximum.

Define power factor and average power in an AC circuit.

Power factor = cosφ = R/Z. Average power P = V(rms) I(rms) cosφ. For a pure inductor or capacitor cosφ = 0, so average power is zero (wattless current).

What are electromagnetic waves and their key properties?

EM waves are mutually perpendicular oscillating electric and magnetic fields propagating perpendicular to both; they are transverse, need no medium, travel at c = 1/sqrt(μ₀ε₀) = 3×10^8 m/s in vacuum, and carry energy/momentum.

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 the mirror formula.

Angle of incidence = angle of reflection, and incident ray, reflected ray, and normal lie in one plane. Mirror formula: 1/v + 1/u = 1/f, with magnification m = −v/u.

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

Snell's law: n₁ sinθ₁ = n₂ sinθ₂ (refractive index n = c/v). Lens maker's: 1/f = (n−1)(1/R₁ − 1/R₂), with lens formula 1/v − 1/u = 1/f.

Define critical angle and total internal reflection.

Critical angle C is the angle of incidence in the denser medium for which the refraction angle is 90° (sinC = 1/n). Beyond C, light is totally internally reflected; used in optical fibres and prisms.

Define power of a lens and combination of thin lenses in contact.

Power P = 1/f (in dioptres, f in metres); converging lens has positive P. For lenses in contact: P = P₁ + P₂ + ... .

State Huygens' principle and the condition for constructive/destructive interference.

Every point on a wavefront acts as a source of secondary wavelets; their envelope gives the new wavefront. Constructive: path difference = nλ; destructive: (n + 1/2)λ.

Give the fringe width in Young's double-slit experiment.

β = λD/d, where D is slit-to-screen distance and d is slit separation; fringe width is the same for bright and dark fringes.

Distinguish interference and diffraction, and state Brewster's law for polarization.

Interference is superposition from two coherent sources (uniform fringes); diffraction is bending around obstacles (central maximum brightest, decreasing intensity). Brewster's law: at polarizing angle i(p), tan i(p) = n, and reflected light is fully polarized.

State the photoelectric equation and define work function.

Einstein's equation: hν = φ₀ + (1/2)mv(max)^2, i.e. KE(max) = hν − φ₀. Work function φ₀ is the minimum energy needed to eject an electron; the threshold frequency is ν₀ = φ₀/h.

State the de Broglie hypothesis and the wavelength formula.

Matter has wave nature; the wavelength of a particle is λ = h/p = h/mv. For an electron accelerated through V volts, λ ≈ 12.27/√V Å.

State the Bohr postulates for the hydrogen atom.

Electrons orbit in stationary states without radiating; angular momentum is quantized (mvr = nh/2π); energy is emitted/absorbed only on transitions, with hν = E₂ − E₁.

Give the radius and energy of the nth Bohr orbit and the energy of the ground state.

r(n) ∝ n^2 (= 0.53 n^2 Å); E(n) = −13.6/n^2 eV; ground state (n=1) energy = −13.6 eV. Energy increases (becomes less negative) with n.

Define mass defect, binding energy, and nuclear density.

Mass defect Δm = (sum of nucleon masses) − (nuclear mass); binding energy = Δm·c^2. Nuclear density is nearly constant (~2.3×10^17 kg/m^3) since R = R₀A^(1/3).

Distinguish alpha, beta, and gamma decay.

Alpha: emission of a helium nucleus (A−4, Z−2). Beta-minus: a neutron becomes a proton emitting an electron (Z+1, A same). Gamma: emission of high-energy photons with no change in A or Z.

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

N = N₀ e^(−λt); activity decreases exponentially. Half-life T(1/2) = 0.693/λ is the time for half the nuclei to decay; mean life τ = 1/λ.

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

Intrinsic: pure, equal electrons and holes. n-type: doped with pentavalent atoms, electrons majority. p-type: doped with trivalent atoms, holes majority. Doping greatly increases conductivity.

Describe a p-n junction diode in forward and reverse bias.

Forward bias (p to +): depletion layer narrows, current flows easily. Reverse bias: depletion layer widens, only tiny leakage current flows. The diode thus acts as a one-way valve (rectifier).

Compare half-wave and full-wave rectifiers.

A half-wave rectifier uses one diode and conducts during one half-cycle (low efficiency, ripple frequency = supply f). A full-wave rectifier (two diodes/bridge) conducts both half-cycles (ripple frequency = 2× supply f, higher efficiency).

What is the use of a Zener diode and a light-emitting diode (LED)?

A Zener diode operates in reverse breakdown at a fixed voltage and is used as a voltage regulator. An LED is a forward-biased diode that emits light when electrons and holes recombine.

What is the principle of dimensions used to convert units between systems?

Using n₁u₁ = n₂u₂ with u expressed in [M^a L^b T^c]; the numerical value changes inversely with the size of the chosen units, keeping the physical quantity unchanged.