A transverse wave on a string has displacement described by (y(x,t)=A\sin(kx-\omega t)). Which physical quantity does (k) represent? A. Angular frequency B. Wave number (spatial angular frequency) C. Phase velocity D. Group velocity Answer: B
Two sinusoidal waves of identical amplitude and frequency travel in opposite directions along a string. The resulting standing wave has nodes at positions where A. The time derivative of displacement is maximum B. The amplitude is zero for all times C. The phase advances linearly with time D. Energy is locally maximal Answer: B
In a medium where wave speed depends on frequency, a short pulse will spread because different frequency components travel with different A. Phase velocities only B. Group velocities C. Amplitudes always equal D. Polarization states only Answer: B
For sound waves in air, intensity level in decibels is defined using (20\log_{10}) of pressure ratio or (10\log_{10}) of power ratio. The reason for the factor of 20 (not 10) when using pressure is that acoustic power is proportional to A. Pressure (directly) B. Pressure squared C. Pressure cubed D. Inverse of pressure Answer: B
A piano string and a flute pipe both produce the same fundamental frequency. Which statement is correct about their harmonic series? A. Both must have only odd harmonics B. A string fixed at both ends produces harmonics at integer multiples; an open pipe produces integer harmonics too, but closed pipes can produce only odd harmonics C. Both always produce only even harmonics D. Flute pipes never support harmonics Answer: B
Doppler shift for sound is influenced by both source and observer motion. If the source approaches a stationary observer, the observed frequency A. Decreases B. Increases C. Stays same D. Becomes undefined Answer: B
In an organ pipe open at both ends, the fundamental frequency is (f=\frac{v}{2L}). If one end is closed, the fundamental becomes approximately A. (v/L) B. (v/2L) (unchanged) C. (v/4L) D. (2v/L) Answer: C
The intensity of a spherical sound wave decreases as (1/r^2) because acoustic energy spreads over an area proportional to A. r B. (r^2) (surface area of sphere) C. (r^3) D. log r Answer: B
In optics, a real image formed by a converging lens can be captured on a screen when the object is placed A. Inside the focal length B. At infinity only C. Beyond the focal length (outside focal point) D. Exactly at the focal point Answer: C
The thin-lens equation (\frac{1}{f}=\frac{1}{u}+\frac{1}{v}) assumes which approximation? A. Large-angle rays (no paraxial approximation) B. Paraxial approximation (small angles relative to axis) C. No refraction at surfaces D. Lenses are infinitely thick Answer: B
A telescope that forms an image using only lenses (objective + eyepiece) is called a A. Newtonian reflector B. Refracting telescope (Keplerian or Galilean designs) C. Cassegrain only D. Radio interferometer Answer: B
When monochromatic light passes through two narrow slits separated by distance (d), the condition for constructive interference on a screen at angle (\theta) is A. (d\sin\theta = m\lambda) B. (d\cos\theta = m\lambda) C. (d\tan\theta = m\lambda) D. (d = m\lambda) only Answer: A
Diffraction from a single slit of width (a) produces minima at angles satisfying A. (a\sin\theta = m\lambda) where (m) is nonzero integer B. (a\sin\theta = \lambda/2) only C. (a\cos\theta = m\lambda) D. No minima occur for single slit Answer: A
Resolving power of an optical instrument is fundamentally limited by A. Chromatic aberration only B. Diffraction (finite aperture) — Rayleigh criterion C. The shape of the object only D. Number of lenses used only Answer: B
Brewster’s angle corresponds to incidence where reflected light is perfectly polarized because the reflected and refracted rays are A. Parallel B. Perpendicular (90°) to each other C. Coincident D. Both at 45° exclusively Answer: B
In a double-slit experiment, increasing the slit separation (d) while keeping wavelength constant will A. Increase fringe spacing on the screen B. Decrease fringe spacing (more closely spaced fringes) C. Not affect fringe spacing D. Remove interference entirely Answer: B
Constructive interference of two light waves of equal amplitude but phase difference (\pi) results in A. Maximum intensity (constructive) B. Destructive interference (zero intensity) C. Half the maximum intensity only D. Intensity dependent on polarization only Answer: B
The principle of superposition of waves fails when waves A. Have different frequencies only B. Interact nonlinearly at large amplitudes or in nonlinear media C. Are of different polarizations only D. Always holds — never fails in physics Answer: B
Coulomb’s law in vacuum states that force between two point charges is proportional to (1/r^2). The constant of proportionality involves (\varepsilon_0), which physically represents A. Magnetic permeability of free space B. Electric permittivity of free space (ability of vacuum to permit electric field) C. Thermal conductivity of vacuum D. Refractive index of vacuum Answer: B
Gauss’s law states that net electric flux through a closed surface equals charge enclosed over (\varepsilon_0). For a point charge at the center of a spherical Gaussian surface, the field magnitude falls as A. (1/r) B. (1/r^2) C. Constant with r D. (r^2) Answer: B
Electric potential is defined as the negative line integral of electric field. If the field is conservative, potential difference between two points is path A. Dependent B. Independent (only endpoints matter) C. Complex and undefined D. Dependent on time only Answer: B
A parallel-plate capacitor with area (A) and separation (d) is filled with dielectric of permittivity (\varepsilon). Its capacitance is A. (C=\frac{\varepsilon_0 A}{d}) regardless of dielectric B. (C=\frac{\varepsilon A}{d}) (dielectric increases capacitance) C. (C=\varepsilon A d) D. Independent of dielectric constant Answer: B
In steady current, the current density (\mathbf{J}) and charge density (\rho) satisfy continuity equation (\nabla\cdot\mathbf{J} + \partial\rho/\partial t =0). For steady current (\partial\rho/\partial t =0), so (\nabla\cdot\mathbf{J}=) A. Nonzero constant B. Zero (current is divergence-free) C. Infinity D. Undefined Answer: B
The drift velocity of electrons in a conductor is usually small because A. Electrons are massless B. The net motion is average of many random collisions and electric field produces tiny net drift superposed on thermal speeds C. Electrons are stationary permanently D. There are no collisions in metals Answer: B
In Ohm’s law (V=IR), resistance (R) for a uniform conductor depends on resistivity (\rho) as (R=\rho L/A). Increasing temperature of a metallic conductor typically A. Decreases resistivity (more free electrons) B. Increases resistivity (more phonon scattering) C. Leaves resistivity unchanged always D. Makes conductor superconducting at room temperature Answer: B
Kirchhoff’s loop rule is a consequence of which fundamental principle? A. Conservation of mass B. Conservation of energy (sum of EMFs and potential drops in closed loop is zero) C. Speed of light invariance D. Conservation of charge only Answer: B
In an RC circuit charged through a resistor, the voltage across the capacitor reaches (63.2%) of the final value after one time constant (\tau), where (\tau) equals A. (R/C) B. (RC) C. (1/RC) D. (R+C) Answer: B
In a series RLC circuit driven at angular frequency (\omega), resonance occurs when the inductive reactance equals the capacitive reactance, i.e., (\omega L = 1/\omega C). At resonance, the circuit’s impedance is A. Maximum (purely inductive) B. Minimum and purely resistive (equal to R) C. Infinite always D. Purely capacitive only Answer: B
The root-mean-square (rms) value of a sinusoidal current (I(t)=I_0\sin\omega t) is A. (I_0) B. (I_0/\sqrt{2}) C. (I_0/2) D. 0 Answer: B
Reactance of an inductor increases with frequency as (X_L=\omega L). Therefore, at very high frequency an inductor behaves approximately as A. Short circuit (zero impedance) B. Open circuit (large impedance) C. Pure resistor only D. Negative impedance device Answer: B
For an AC circuit, power factor defined as (\cos\phi) equals real power divided by apparent power. A lagging power factor indicates the load is predominantly A. Capacitive B. Inductive (current lags voltage) C. Resistive only D. Superconductive Answer: B
A transformer operating under ideal conditions conserves which quantity between primary and secondary? A. Voltage only B. Power (neglecting losses) — (V_p I_p = V_s I_s) C. Current only D. Resistance only Answer: B
Maxwell’s correction to Ampère’s law introduced the displacement current term (\varepsilon_0\partial\mathbf{E}/\partial t) to make the law consistent with A. Conservation of energy only B. Conservation of charge and Gauss’s law (continuity equation) — making (\nabla\cdot \mathbf{J}+\partial\rho/\partial t=0) compatible C. Quantum mechanics only D. Thermodynamics exclusively Answer: B
Faraday’s law of induction relates induced emf in a loop to time rate of change of magnetic flux. Lenz’s law adds that the induced emf opposes the change, which enforces A. Conservation of momentum B. Conservation of energy (direction of induced current opposes flux change) C. Conservation of charge only D. Newton’s third law exclusively Answer: B
Electromagnetic waves in vacuum propagate at speed (c) where (c=1/\sqrt{\mu_0\varepsilon_0}). If (\varepsilon_0) were hypothetically doubled while (\mu_0) unchanged, the speed would A. Increase by (\sqrt{2}) B. Decrease by (1/\sqrt{2}) C. Remain unchanged D. Become imaginary Answer: B
The Poynting vector (\mathbf{S}=\mathbf{E}\times\mathbf{H}) represents electromagnetic energy A. Density only B. Flux (power per unit area) and direction of energy flow C. Charge distribution only D. Magnetic field strength only Answer: B
Rutherford’s gold foil experiment revealed the atomic nucleus because most alpha particles passed through foil while some were deflected at large angles, implying the atom is mostly A. Solid uniformly dense matter B. Empty space with concentrated positive charge at small nucleus C. A diffuse continuous positive medium D. A lattice of protons immobile in space Answer: B
The Bohr model successfully explains hydrogen spectral lines by quantizing angular momentum. The quantized angular momentum condition is (mvr=n\hbar). The energy levels scale with (n) as A. (E_n \propto n) B. (E_n \propto 1/n^2) (energy becomes less negative as n increases) C. (E_n \propto n^2) D. Independent of n Answer: B
De Broglie wavelength for a particle of momentum (p) is given by (\lambda = h/p). Electrons accelerated through higher potentials therefore have A. Longer wavelengths (since p decreases) B. Shorter wavelengths (momentum increases) C. Wavelength independent of acceleration D. Negative wavelength Answer: B
X-rays are produced in an X-ray tube by two main processes: bremsstrahlung and characteristic X-rays. Characteristic X-rays result from A. Nuclear transitions only B. Electronic transitions when an inner-shell electron is ejected and an outer electron fills the vacancy, emitting photon with element-specific energy C. Thermal radiation of filament only D. Neutron capture exclusively Answer: B
Radioactive decay law describes number of nuclei (N(t)=N_0 e^{-\lambda t}). The mean lifetime (\tau) relates to (\lambda) as A. (\tau = \lambda) B. (\tau = 1/\lambda) C. (\tau = \ln 2/\lambda) D. (\tau = \lambda^2) Answer: B
In beta minus ((\beta^-)) decay a neutron transforms into a proton while emitting A. A positron and neutrino B. An electron and an antineutrino C. Only a gamma photon D. An alpha particle Answer: B
The binding energy per nucleon is a measure of nuclear stability. The peak of binding energy per nucleon occurs near which region of atomic mass? A. Very light nuclei (A ≈ 4) only B. Medium nuclei around iron (A ≈ 56) — most stable C. Very heavy nuclei only (A > 200) D. Binding energy per nucleon is constant for all A Answer: B
For a particle in an infinite potential well of width (L), the energy levels scale with quantum number (n) as A. (E_n \propto n) B. (E_n \propto n^2) C. (E_n \propto 1/n) D. Independent of n Answer: B
The Rayleigh criterion for resolving two point light sources with a circular aperture uses angular separation (\theta \approx 1.22 \lambda/D). The factor 1.22 is associated with the first zero of the A. Sinc function (one-dimensional slit) B. Bessel function (Airy disk from circular aperture) C. Cosine function only D. Gaussian beam width only Answer: B
For small oscillations of a stretched string of linear density (\mu) under tension (T), wave speed is (v=\sqrt{T/\mu}). Doubling tension will change speed by factor A. 4 B. 2 C. (\sqrt{2}) D. 1/2 Answer: C
A standing wave on a string has a node at (x=0) and an antinode at (x=\lambda/4). The string length corresponds to which fraction of wavelength if it supports the fundamental? A. (L=\lambda/2) B. (L=\lambda) C. (L=\lambda/4) D. (L=3\lambda/4) Answer: A
The phenomenon of beats arises when two waves of slightly different frequencies superpose. The beat frequency equals A. Sum of the two frequencies B. Difference between the two frequencies (|f1−f2|) C. Product of the frequencies D. Twice the average frequency always Answer: B
The Mach number (M) is ratio of object speed to local speed of sound. Supersonic flows have (M>1). Shock waves in supersonic regime are associated with A. Smooth, reversible compression only B. Sudden irreversible changes in pressure, temperature, and density across shock front C. Decrease in entropy always D. Purely isentropic flow everywhere Answer: B
For plane-polarized light passing through a quarter-wave plate oriented at 45° to its polarization, the emerging light becomes A. Unpolarized B. Circularly polarized (if retardation exactly (\lambda/4)) C. Linearly polarized at 90° only D. Absorbed completely Answer: B
In Young’s double-slit with slits separated by 0.5 mm and screen distance large, using light of (\lambda=500) nm, the fringe spacing ( \Delta y = \frac{\lambda D}{d}). Increasing (\lambda) will A. Decrease fringe spacing B. Increase fringe spacing proportionally C. Not affect fringe spacing D. Make fringes disappear altogether Answer: B
A Fabry–Pérot interferometer produces sharp transmission peaks when the cavity length is such that multiple reflections produce constructive interference. Increasing mirror reflectivity does what to the finesse? A. Decreases finesse B. Increases finesse (sharper, narrower peaks) C. Eliminates interference D. Changes central wavelength only Answer: B
The concept of group velocity (v_g) and phase velocity (v_p) is important in dispersive media. Which statement is true? A. Group velocity equals phase velocity always B. Group velocity describes propagation of energy/information and can differ from phase velocity in dispersive media C. Phase velocity carries energy always faster than group velocity D. Neither velocity has physical meaning Answer: B
In electrostatics, the potential inside a uniformly charged spherical shell is A. Varies linearly with r B. Constant (same as potential at surface) — field inside is zero C. Inversely proportional to r D. Oscillatory with r Answer: B
Electric field lines begin and end on charges. The divergence of (\mathbf{E}) equals charge density divided by (\varepsilon_0). Therefore (\nabla\cdot\mathbf{E}=0) in regions where A. Free charge density (\rho) is zero (charge-free regions) B. There are point charges only C. Electric field is maximal only D. Magnetic field is zero only Answer: A
A point charge +Q is at the center of a hollow conducting spherical shell carrying net charge −Q. The field outside the conductor is equivalent to that of A. Zero net charge (fields cancel completely) B. A dipole only C. A point charge at center with net charge 0 (net enclosed charge zero), so field outside is zero D. The total net charge on conductor plus point charge; here zero so no field outside Answer: D
In a dielectric material placed in an external electric field, polarization reduces the effective field inside. The dielectric constant (\kappa) relates permitivity by (\varepsilon=\kappa\varepsilon_0). Increasing (\kappa) typically A. Reduces capacitance of capacitor with dielectric B. Increases capacitance (by factor (\kappa)) C. Has no effect on capacitance D. Reverses sign of stored charge Answer: B
The Hall effect in a conductor yields a transverse voltage when current flows in magnetic field. The sign of Hall voltage can indicate whether dominant charge carriers are A. Photons or electrons B. Electrons (negative) or holes (positive) depending on sign of voltage C. Always positive only D. Only neutrons moving inside conductor Answer: B
For current density (\mathbf{J}=\sigma\mathbf{E}), (\sigma) is conductivity. In highly doped semiconductors, conductivity increases mainly because carrier concentration A. Decreases B. Increases (more carriers available) C. Remains zero always D. Converts to photons only Answer: B
The superposition of two harmonic oscillations of equal amplitude but slightly different frequencies leads to amplitude modulation with envelope frequency equal to half the difference of frequencies. True or false? A. True (envelope frequency equals (f1−f2)/2) B. False — envelope (beat) frequency equals |f1−f2| (not half) C. True only for light waves D. False — no envelope forms in superposition Answer: B
In electromagnetic waves, polarization refers to orientation of which vector? A. Magnetic field only B. Electric field vector direction in transverse plane (for plane waves) C. Poynting vector only D. Wave number vector only Answer: B
A plane electromagnetic wave in vacuum has (\mathbf{E}), (\mathbf{B}), and (\mathbf{k}) mutually perpendicular. If (\mathbf{E}) oscillates in x-direction and (\mathbf{k}) along +z, (\mathbf{B}) will oscillate in A. y-direction (perpendicular to both) B. x-direction too C. z-direction only D. Random directions always Answer: A
The skin depth (\delta) of electromagnetic waves in a good conductor decreases with frequency as (\delta\propto 1/\sqrt{\omega}). Thus higher frequency waves penetrate A. Deeper into conductor B. Less deeply (smaller skin depth) C. Equally as low frequency waves D. Indefinitely — no attenuation Answer: B
Gauss’s law for magnetism (\nabla\cdot\mathbf{B}=0) implies there are no magnetic monopoles; field lines of (\mathbf{B}) are A. Divergent from monopoles B. Closed loops (no beginning or end) C. Ending at electric charges only D. Nonexistent in vacuum Answer: B
The magnetic moment of a current loop is given by (\mu=IA) (area vector). For a loop in uniform magnetic field, torque (\tau=\mu B\sin\theta). This torque tends to A. Increase potential energy always B. Align the magnetic moment with the field (minimize potential energy) C. Destroy the current in loop D. Produce linear acceleration only Answer: B
Ampère’s law in integral form (\oint \mathbf{B}\cdot d\mathbf{l}=\mu_0 I_{enc}) must be modified by Maxwell for time-varying electric fields to include displacement current, otherwise it contradicts A. Newton’s laws only B. Charge conservation (continuity equation) for capacitors in circuits C. Hooke’s law only D. Thermodynamic cycles Answer: B
The Biot–Savart law gives magnetic field due to steady current elements. For a long straight wire carrying current I, magnetic field at distance r is (B=\frac{\mu_0 I}{2\pi r}). Doubling I doubles B; doubling r A. Doubles B B. Halves B C. Reduces B by factor of 4 (since 1/r^2) D. Has no effect Answer: B
A uniform magnetic field does no work on a charged particle because the magnetic force is perpendicular to velocity. Therefore magnetic field can change direction of velocity but not its kinetic energy. True or false? A. True B. False — magnetic field always changes speed too C. True only for stationary charges D. False — magnetic force is parallel to velocity Answer: A
In Lenz’s law, the induced current produces magnetic flux opposing the change in original flux. This is analogous to which mechanical principle? A. Newton’s first law (inertia) — system resists change B. Hooke’s law only C. Energy creation principle D. Huygens’ principle Answer: A
In a cyclotron, particles are accelerated across a gap by an alternating potential and bend in a magnetic field. The cyclotron frequency ( \omega = qB/m) is independent of particle speed for nonrelativistic particles, so as speed increases their radius A. Decreases B. Increases (r = mv/qB) C. Remains constant always D. Oscillates randomly Answer: B
Photoelectric effect demonstrates that light can eject electrons when above threshold frequency. The kinetic energy of emitted electrons depends on incident photon energy minus work function: (K_{max}=h\nu – \phi). Increasing intensity at fixed (\nu) below threshold will A. Eject electrons with higher kinetic energy B. Not eject electrons at all (no photoemission below threshold regardless of intensity) C. Change threshold frequency only D. Create photons of higher energy spontaneously Answer: B
Compton scattering of X-rays by electrons results in shift in wavelength depending on scattering angle (\theta): (\Delta\lambda = \frac{h}{m_e c}(1-\cos\theta)). The shift is maximum for (\theta=) A. 0° B. 90° C. 180° (backscatter) D. 45° only Answer: C
For a standing sound wave in a tube closed at one end and open at the other, nodes occur at closed end for displacement and antinodes at open end. The harmonic series includes only A. All integer harmonics B. Odd harmonics (1st, 3rd, 5th…) C. Even harmonics only D. No harmonics at all Answer: B
The resolving power of a diffraction grating with N slits and spacing d for wavelength λ is proportional to A. N (number of slits) times order m: (R=mN) — more slits increases resolving power B. d only C. λ only D. Independent of N and m Answer: A
Snell’s law (n_1\sin\theta_1 = n_2\sin\theta_2) follows from Fermat’s principle of least time. Total internal reflection occurs when light travels from medium with higher n to lower n and angle of incidence exceeds A. Zero degrees B. Critical angle (\theta_c = \sin^{-1}(n_2/n_1)) C. 90° always D. Brewster’s angle only Answer: B
In interference experiments using polychromatic light, fringe visibility typically decreases because different wavelengths have different fringe spacing, causing A. Enhanced fringe contrast always B. Washout of fringes except near central orders where overlap occurs C. No effect on interference pattern D. Only affects diffraction, not interference Answer: B
The electric potential due to an infinite line of charge (linear charge density (\lambda)) diverges at infinity; potentials are defined up to additive constant. Electric field around line charge behaves as A. (1/r^2) in 3D B. (1/r) (field magnitude ∝ 1/r for infinite line) C. Constant independent of r D. Zero outside the line Answer: B
A Wheatstone bridge balanced condition allows measurement of unknown resistance when ratio of two arms equals ratio of other two arms. The bridge is most sensitive when the resistances are A. Extremely different by orders of magnitude B. Nearly equal (close to balance) to detect small changes accurately C. All zero always D. Infinite only Answer: B
In the AC analysis of circuits, complex impedance of capacitor is (Z_C=1/(j\omega C)) and of inductor is (Z_L=j\omega L). At very low frequency (ω→0), capacitor behaves approximately as A. Short circuit (zero impedance) B. Open circuit (infinite impedance) C. Pure resistor equal to 1/C D. Negative impedance element Answer: B
The resonance curve of an RLC circuit shows quality factor (Q=\omega_0 L/R) (series). A high Q means A. Broad resonance (large bandwidth) B. Sharp, narrow resonance (small damping) and higher energy storage relative to losses C. No resonance possible D. Circuit burns out always Answer: B
Maxwell’s equations predict transverse electromagnetic waves in vacuum where E and B fields satisfy wave equation with speed c. Which equation specifically describes how a time-varying magnetic field produces an electric field? A. Gauss’s law for electricity B. Faraday’s law of induction ((\nabla\times\mathbf{E} = -\partial\mathbf{B}/\partial t)) C. Ampère–Maxwell law only D. Gauss’s law for magnetism Answer: B
In a photoelectric experiment, stopping potential (V_s) measures maximum kinetic energy of emitted electrons via (eV_s = K_{max}). If incident frequency is increased, the stopping potential A. Decreases linearly with frequency B. Increases linearly with frequency (slope = h/e) C. Remains independent of frequency D. Becomes negative always Answer: B
Beta-plus ((\beta^+)) decay (positron emission) requires nucleus to have excess A. Neutrons relative to protons B. Protons relative to neutrons (proton converted to neutron + positron + neutrino) C. Equal numbers only D. No relation to proton/neutron excess Answer: B
The Rutherford scattering formula predicts differential cross-section for alpha scattering off nucleus. Large-angle scattering is sensitive to which property of nucleus? A. Overall atomic mass only B. Nuclear charge (Z) and its concentrated positive charge (Coulomb scattering) C. Electron cloud only D. Magnetic dipole moment only Answer: B
In the quantum mechanical hydrogen atom, the radial probability density for n=2, l=0 (2s) shows a node. Nodes in wavefunctions correspond to radii where probability density is A. Maximum B. Zero (zero probability of finding electron at node) C. Infinite always D. Undefined only for l>0 Answer: B
The photoelectric effect cannot be explained by classical wave theory because classical theory would predict that increasing intensity at a frequency below threshold would eventually eject electrons. Experimentally this does not occur because photons have discrete energy (h\nu). Which observation supports photon model? A. Kinetic energy of emitted electrons depends on intensity only B. Kinetic energy of photoelectrons depends on frequency, not intensity C. Emission occurs only after long time delay predicted classically D. Photoelectric effect shows continuous energy distribution contradictory to photons Answer: B
In a diffraction grating, angular separation of close spectral lines increases with increasing grating order (m). However higher orders may overlap; to avoid overlap for wavelength range you must satisfy A. mλmax < d (grating spacing condition for given order) for orders not to exceed sinθ=1 B. m always greater than N only C. Overlap never occurs for any m D. Orders are independent of d and λ Answer: A
Ray optics (geometrical) fails when aperture or obstacle sizes are comparable to wavelength; in such cases wave optics (diffraction) must be used. An example is the formation of A. Perfect images with infinite resolution B. Diffraction-limited spot sizes and Airy disk patterns C. Sound waves in vacuum only D. Classical Newton rings nonexistent Answer: B
The electric field inside a conductor in electrostatic equilibrium is zero. As a corollary, any excess charge resides A. Uniformly distributed throughout the volume of conductor B. On the surface of the conductor only C. Concentrated at center of conductor always D. In the interior pockets only Answer: B
A semicircular loop of wire in a uniform magnetic field experiences a net torque but no net force if field is uniform and loop is symmetric. The net torque tends to align magnetic moment with field; this is used in devices like A. Galvanometer or galvanometer-based instruments (moving-coil meter) B. Thermocouples only C. Capacitors only D. Piezoelectric sensors always Answer: A
Inverse-square laws apply to point sources in three dimensions. For waves confined to two dimensions (e.g., surface waves on pond), amplitude falls off approximately as A. (1/r^2) B. (1/\sqrt{r}) or (1/r) depending on energy distribution (intensity ∝ 1/r for 2D) C. Constant with r D. Exponential growth with r Answer: B
For a series RLC circuit, the phase angle between supply voltage and current at frequency below resonance is A. Positive (current leads voltage) for capacitive dominance B. Negative (current lags voltage) for inductive dominance C. Zero always below resonance D. Undefined for sinusoidal steady state Answer: A
The amplitude of oscillation in a driven damped harmonic oscillator at resonance is inversely proportional to damping. Reducing damping increases amplitude but also narrows bandwidth; this is analogous to which electrical parameter? A. Increasing resistance in RLC (reduces Q) B. Decreasing resistance (increases Q and amplitude at resonance) C. Changing inductance alone does not affect Q D. Increasing capacitance always reduces Q only Answer: B
Kirchhoff’s current law (KCL) at a network node is a manifestation of which conservation law? A. Conservation of energy only B. Conservation of electric charge (sum of currents into node = 0) C. Conservation of momentum D. Conservation of entropy only Answer: B
The Hall coefficient (R_H) for a simple metal with single carrier type is (R_H = -1/(nq)). A measured positive Hall coefficient indicates dominant carriers are A. Electrons (negative) B. Holes (positive charge carriers) C. Neutrons only D. Photons always Answer: B
In alternating current circuits, complex power (S=VI^*) has real part (P) (average power) and imaginary part (Q) (reactive power). Reactive power represents energy that A. Is dissipated as heat only B. Oscillates between source and reactive elements (stored and returned each cycle) C. Is converted to mass per E=mc^2 D. Is always zero for ideal inductors and capacitors Answer: B
When a charged particle moves in combined electric and magnetic fields, the Lorentz force is (\mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B})). For a particle with velocity parallel to B and no E, motion will be A. Helical always B. Straight line (no magnetic force if v parallel to B) C. Circular in plane perpendicular to B D. Random walk always Answer: B
The skin effect causes alternating current to crowd near the surface of a conductor at high frequencies, increasing effective resistance. This occurs because induced eddy currents in conductor oppose penetration of changing fields per A. Lenz’s law and Maxwell–Faraday induction effects B. Newton’s law only C. Fermat’s principle always D. Unrelated quantum tunneling Answer: A
In the context of wave optics, Huygens’ principle states that every point on a wavefront acts as a source of secondary wavelets. This principle helps explain A. Conservation of charge only B. Reflection and refraction as emergent from secondary wavelet interference C. Chemical bonding patterns D. Nuclear stability schemes only Answer: B
In Rutherford scattering, the scattering angle distribution is more forward-peaked as incident kinetic energy increases because higher-energy projectiles are less strongly deflected by Coulomb repulsion; this qualitatively means scattering becomes A. More isotropic at high energy B. Strongly forward-peaked (small-angle scattering dominant) C. Independent of incident energy D. Always 180° for all energies Answer: B
Standing longitudinal waves in air columns produce pressure nodes at displacement antinodes. For a tube open at both ends, the pressure nodes occur at ends and the lowest mode has wavelength (\lambda = 2L). If L is halved, fundamental frequency A. Halves B. Doubles (frequency ∝ 1/L) C. Quadruples D. Is unchanged Answer: B
The acoustic impedance (Z=\rho c) of a medium determines reflection at an interface between two media. Maximum reflection occurs when impedance mismatch is A. Zero (identical impedances) B. Large (big difference in (\rho c)) C. Negative always D. Complex only for solids Answer: B
The phenomenon of acoustic resonance in wind instruments is strongly affected by end corrections because the effective length differs from physical length due to antinodes lying slightly outside open ends. End correction is roughly proportional to A. Pipe diameter (scale with radius) B. Square of length only C. Inverse of frequency always D. Negligible for all practical instruments Answer: A
In the context of geometrical optics, spherical aberration arises because rays far from the axis are focused differently than paraxial rays. A common way to reduce spherical aberration is to use A. Single thin lenses only always B. Aspheric lenses or stop down aperture (use smaller aperture) C. Increase lens thickness indefinitely D. Use ultraviolet light only Answer: B
In interference, optical path difference ( \Delta = n_1 d_1 – n_2 d_2) matters. A thin-film of refractive index n on substrate shows constructive or destructive interference depending on film thickness and phase changes on reflection; a π phase shift occurs when light reflects from medium with A. Lower refractive index to higher refractive index (phase change of π on reflection) B. Higher to lower n (π shift) C. No reflection ever produces phase shift D. Gas to vacuum always Answer: A
Diffraction-limited resolution of microscopes can be improved by using immersion oil (n increases). According to Abbe’s diffraction limit, resolution (d=\frac{\lambda}{2n\sin\alpha}). Increasing n or numerical aperture NA improves resolution because denominator A. Decreases B. Increases (improves resolving power) C. Stays same always D. Flips sign making resolution negative Answer: B
In electrostatics, image charge method is useful for solving potential near conducting planes by replacing induced surface charges with fictitious image charges placed in mirror positions. For a point charge q at distance d above infinite grounded conducting plane, the image charge is A. +q at +d B. −q at mirror position (−d) producing zero potential at plane C. Zero charge required always D. +2q at +d only Answer: B
In dielectrics, hysteresis is observed in ferroelectric materials (not in linear dielectrics). Hysteresis loops show remanent polarization. This property is analogous to magnetic hysteresis and is exploited in A. Capacitors with stable linear behavior only B. Nonvolatile memory devices (ferroelectric RAM) and sensors C. Optical lenses only D. Pure resistors only Answer: B
The mobility (\mu) of charge carriers relates drift velocity (v_d) to electric field: (v_d=\mu E). For a semiconductor, increasing temperature typically A. Decreases carrier mobility due to increased phonon scattering, but may increase carrier concentration via intrinsic excitation — net conductivity behavior depends on doping and T B. Always increases mobility and conductivity monotonically C. Makes mobility infinite at room temperature D. Has no effect on mobility or conductivity Answer: A
In circuits, an ideal inductor resists change in current; the energy stored is (U=\frac{1}{2}LI^2). Rapid change in current can produce large induced emf according to (V=L\frac{dI}{dt}). To limit spikes when switching inductive loads, a common practice is to place A. A capacitor in series only B. A flyback diode (for DC circuits) or snubber RC network (for AC) to clamp voltage spikes C. A short to ground across supply always D. Remove the inductor permanently Answer: B
The dispersion relation for electromagnetic waves in plasma yields cutoff below plasma frequency (\omega_p). Radio waves below (\omega_p) are reflected by ionospheric plasma while above (\omega_p) they propagate. Plasma frequency depends on electron density (n_e) as (\omega_p \propto \sqrt{n_e}). Increasing (n_e) thus A. Lowers plasma frequency B. Raises plasma frequency, reflecting higher-frequency waves C. Has no effect on propagation D. Converts plasma into solid metal instantly Answer: B
The Lorentz force law plus Maxwell’s equations lead to concept of electromagnetic momentum density. The momentum carried by EM fields can be transferred to matter, e.g., in radiation pressure. Radiation pressure on an absorbing surface with intensity I is approximately A. I/c (pressure = intensity/c for perfect absorber) B. I^2 always C. Zero regardless of intensity D. Infinite for visible light only Answer: A
Rutherford’s atomic model failed to explain atomic stability because accelerating electrons orbiting nucleus should radiate energy and spiral inward. The quantum solution required quantization of allowed states; Bohr’s postulate that electron angular momentum is quantized prevents classical radiation in stationary states. Which experimental fact supported Bohr besides spectral lines? A. Existence of blackbody radiation peak only B. Quantized energy differences matched observed hydrogen emission wavelengths (Rydberg formula) C. Photoelectric threshold independence of frequency only D. Compton shift behavior only Answer: B
The fine structure of hydrogen spectral lines arises from relativistic corrections and spin–orbit coupling. Spin–orbit coupling depends on coupling between electron’s spin magnetic moment and A. External gravitational field only B. Effective magnetic field due to electron’s motion in central Coulomb field (orbital motion) C. Nuclear weak interactions only D. Thermal fluctuations exclusively Answer: B
Pair production of electron-positron requires photon energy exceeding (2m_e c^2) and occurs near nucleus to conserve momentum. Minimum photon energy required is approximately A. (m_e c^2) B. (2 m_e c^2 ) (~1.022 MeV) C. 10 eV only D. Always infinite Answer: B
In Compton scattering, scattered photon loses energy to recoil electron; conservation of energy and momentum yields wavelength shift formula. This effect demonstrates particle-like properties of photons because photons impart momentum (p=h/\lambda). Which observation supports particle nature? A. Continuous diffraction patterns only B. Discrete wavelength shift dependent on scattering angle (Compton shift) C. Interference fringes only D. No interaction with electrons observed Answer: B
The intensity of radiation falling on a surface from a point isotropic source varies as (1/r^2). Therefore luminous flux through spherical surface of radius r is constant and equals source power. If two identical incoherent sources are placed close together, intensity at far point adds as A. Square root of individual intensities only B. Sum of intensities (incoherent addition) — no phase coherence C. Complex vector sum always D. Cancel each other always Answer: B
A Michelson interferometer can be used to measure small length changes by monitoring fringe shifts. One fringe shift corresponds to mirror displacement of A. (\lambda) only B. (\lambda/2) (because change in path difference is twice mirror movement) C. (\lambda/4) only D. No displacement detectable Answer: B
The quality factor Q for mechanical or electrical resonators is defined as (Q=\omega_0/\Delta\omega) where (\Delta\omega) is bandwidth. High Q resonators have long energy storage times and low damping; energy decay time (\tau) relates to Q approximately as A. (\tau = Q/\omega_0) B. (\tau = \omega_0/Q) C. (\tau=Q^2/\omega_0) D. No relation exists Answer: A
In a DC circuit with capacitor initially uncharged, switching to connect a DC battery through resistor leads to exponential charge curve. The initial current immediately after closing switch is (I_0 = V/R). Over time current decays to A. V/R always nonzero B. Zero as capacitor becomes fully charged (steady state no DC current through ideal capacitor) C. Infinity eventually D. Random oscillations only Answer: B
The polarization of light transmitted through an ideal linear polarizer oriented at angle θ relative to incident polarization is reduced in intensity by Malus’s law: (I = I_0\cos^2\theta). Passing unpolarized light through polarizer yields transmitted intensity of A. (I_0) (unchanged) B. (I_0/2) (half the incident intensity) C. (I_0/4) only D. Zero always Answer: B
A plano-convex lens has one flat surface and one convex surface. For imaging, placing plane side toward image or object can reduce certain aberrations depending on symmetry; lensmaker equation relates focal length f to radii and refractive index (n). For thin lens approximation, focal length is determined primarily by A. Radii of curvature and refractive index differences (1/f=(n-1)(1/R_1 – 1/R_2)) for thin lens in air B. Mass of lens only C. Color of light only D. Temperature only Answer: A
In a conducting loop moving into a region of uniform magnetic field, the induced emf equals rate of change of magnetic flux. If loop area inside field changes linearly with time, induced emf is A. Constant (proportional to dϕ/dt) B. Zero because field uniform C. Oscillatory only D. Nonphysical negative always Answer: A
In superconductors, below critical temperature (T_c), resistance drops to zero and magnetic flux can be expelled (Meissner effect). Type II superconductors allow partial flux penetration in vortices between lower and upper critical fields, enabling practical high-field applications. Which of following increases critical current density? A. Removing all impurities always B. Introducing pinning centers (defects) that anchor flux vortices and prevent motion C. Heating above (T_c) D. Reducing carrier density to zero Answer: B
The de Broglie hypothesis implies wave–particle duality. Electrons in electron diffraction experiments produce patterns with angular spacing dependent on wavelength. Using higher accelerating voltage reduces electron wavelength and therefore diffraction angles become A. Larger (wider) B. Smaller (narrower) — inversely related to momentum C. Unchanged D. Infinite Answer: B
The minimum resolvable distance in electron microscopy is much smaller than optical microscopy because electrons have much shorter de Broglie wavelengths at typical accelerating energies. However practical resolution is limited by lens aberrations and A. Vacuum level only B. Chromatic and spherical aberrations of electromagnetic lenses and sample damage limitations C. Number of detectors only D. Ambient sound levels exclusively Answer: B
In the photoelectric effect, the stopping potential is independent of intensity but depends linearly on frequency. The slope of stopping potential vs frequency gives Planck’s constant (h) divided by elementary charge e. Experimentally this was key in determining A. Speed of light only B. Numerical value of (h) (Planck’s constant) via photoelectric experiments C. Boltzmann constant only D. Avogadro’s number only Answer: B
Radioactive half-life is the time for half the nuclei to decay. For two isotopes with same initial number of nuclei, the one with shorter half-life will have higher initial activity (decays per second) given same starting quantity because activity (A=\lambda N). If isotope A has half-life 1 day and isotope B 2 days, then (\lambda_A/\lambda_B) equals A. 1/2 B. 2 (since λ∝1/T_{1/2}) C. 4 D. 0.5 Answer: B
In alpha decay, alpha particles are emitted with discrete energies characteristic of parent-daughter nuclear levels. Alpha particles, being helium nuclei, have relatively short ranges in matter due to high charge and mass and lose energy mainly by A. Nuclear reactions only B. Coulomb interactions with electrons (ionization and excitation), resulting in short penetration depth C. Gamma emission only D. Magnetic interactions exclusively Answer: B
In a Michelson interferometer used with white light, the central white fringe occurs when path difference is near zero; moving one mirror by λ/2 shifts fringes by one fringe. For broadband source, interference fringes are visible only when path difference is within coherence length determined by spectral bandwidth. Narrower bandwidth gives A. Shorter coherence length and less visible fringes B. Longer coherence length and more extended observable fringes C. No change in coherence length D. Interference for all path differences always Answer: B
The ponderomotive force acts on charged particles in oscillating electromagnetic fields and tends to push particles toward regions of lower intensity for high-frequency fields. It is proportional to gradient of intensity and inversely to square of oscillation frequency, so increasing frequency generally A. Increases ponderomotive force B. Decreases ponderomotive force (since ∝ 1/ω^2) C. Has no effect on ponderomotive force D. Reverses its direction always Answer: B
In conductors at microwave frequencies, transmission lines are often used to guide waves; characteristic impedance depends on geometry and medium. To avoid reflections, load impedance must A. Be ill-matched deliberately for better power transfer B. Match characteristic impedance (Z_L = Z_0) for maximum power transfer and no standing waves C. Be zero always D. Be infinite always Answer: B
In relativistic kinematics relevant to high-energy electron beams, as particle speed approaches c, further increases in kinetic energy produce diminishing increases in speed but large increases in relativistic momentum and energy (γ factor). Thus de Broglie wavelength for relativistic electrons must be computed using A. Classical momentum p=mv always B. Relativistic momentum p=γmv (leading to smaller wavelength at same accelerating potential than nonrelativistic approximation) C. p independent of v always D. Planck’s constant variable with speed Answer: B
Brewster’s angle (\theta_B) satisfies (\tan\theta_B = n_2/n_1). At this angle reflected light from an uncoated glass surface is perfectly polarized perpendicular to plane of incidence. For glass n≈1.5 in air, (\theta_B) is approximately A. 0° B. ~56° (tan^-1 1.5 ≈ 56°) C. 90° D. 30° exactly Answer: B
In standing wave ratios (SWR) on transmission lines, a mismatch between load and characteristic impedance produces standing waves; the voltage standing wave ratio (VSWR=\frac{1+|\Gamma|}{1-|\Gamma|}) where (\Gamma) is reflection coefficient. Perfect match yields VSWR of A. Infinity B. 1 (no standing waves) C. 0 only D. 2 always Answer: B
The classical Rayleigh–Jeans law predicted ultraviolet catastrophe for blackbody radiation at short wavelengths; Planck resolved this by quantizing energy of oscillators (E=nh\nu). At high frequencies, quantum theory predicts spectral radiance falls off exponentially rather than diverge. Planck’s resolution introduced constant h with units A. Energy × time (J·s), fundamental quantum of action B. Force × distance only C. Pure number without units D. Frequency only Answer: A
In a diffraction experiment using electrons (matter waves), observed pattern spacing depends on de Broglie wavelength λ=h/p. Doubling accelerating potential roughly increases kinetic energy and reduces λ; as λ decreases diffraction angles scale roughly as A. Increase proportionally to λ B. Decrease proportionally to λ (smaller angles for smaller λ) C. Independent of λ always D. Become infinite Answer: B
The intrinsic carrier concentration (n_i) in a semiconductor increases with temperature approximately as (n_i \propto T^{3/2} e^{-E_g/2kT}). Thus for a given band gap (E_g), as T increases, intrinsic carriers increase rapidly due to A. Decrease in Boltzmann constant only B. Thermal generation across band gap (exponential dependence) dominating behavior C. Freezing out of carriers always D. Independence from temperature Answer: B
In amorphous materials, lack of long-range order broadens spectral lines and reduces sharp diffraction peaks compared to crystalline materials; their electronic density of states near band edges may show localized states causing A. Metallic conduction always B. Tail states and variable-range hopping conduction at low temperatures C. Perfect semiconductor band behavior always D. Infinite mobility of carriers Answer: B
The gyromagnetic ratio relates magnetic moment to angular momentum for charged particles. For electrons, electron spin gives rise to magnetic moment dominant in many magnetic resonance techniques; electron spin resonance detects transitions in magnetic field and is analogous to nuclear magnetic resonance but with much higher resonance frequencies because electron gyromagnetic ratio is A. Much smaller than nuclear gyromagnetic ratios B. Much larger than nuclear gyromagnetic ratios (so electron transitions at higher frequencies for same B-field) C. Equal to zero always D. Negative only making resonance impossible Answer: B
The formation of beats in sound is useful in tuning musical instruments: when two tones are slightly detuned, beats occur at difference frequency. If two strings vibrate at 440 Hz and 442 Hz, beat frequency is A. 442 Hz B. 2 Hz (|440−442|) C. 882 Hz (sum) D. 440 Hz only Answer: B
The optical aberration known as coma causes off-axis point sources to appear comet-shaped and grows with increasing aperture and off-axis angle. Coma can be minimized using symmetrical optical elements or by using A. Larger apertures only B. Apochromatic lens groups and stop down aperture to limit extreme rays C. Defocusing intentionally always D. Only by changing wavelength of light Answer: B
In electrostatics, a dipole in uniform electric field experiences torque (\tau = pE\sin\theta) but no net force. A nonuniform field can exert net force on dipole tending to pull it toward region of higher field if aligned properly. This principle is used in A. Mass spectrometers only B. Dielectrophoresis (manipulation of neutral but polarizable particles in nonuniform fields) C. Ohmmeters exclusively D. Thermal conduction devices only Answer: B
For a given RMS voltage, a purely inductive circuit stores energy alternately in magnetic field and returns it to circuit; average power over cycle is zero (no dissipation). Adding a small resistance causes real power dissipation proportional to (I_{rms}^2 R). Thus dissipation occurs because resistive element converts alternating stored energy into A. Potential energy only B. Heat via Joule heating (ohmic losses) C. Magnetic flux permanently D. Chemical energy exclusively Answer: B
The Wien displacement law states that blackbody spectral radiance maximum wavelength (\lambda_{max}) scales inversely with temperature (T): (\lambda_{max}T=b). This implies hotter objects emit peak radiation at A. Longer wavelengths B. Shorter wavelengths (shift toward blue/UV) C. Same wavelength regardless of T D. Random wavelengths only Answer: B
The quantum mechanical uncertainty principle (\Delta x \Delta p \ge \hbar/2) implies confinement of a particle in smaller region increases uncertainty in momentum and thus minimum kinetic energy (zero-point energy). For a particle in box of width L, ground-state energy scales roughly as A. (1/L) B. (1/L^2) (inversely with square of width) C. L^2 only D. Independent of L Answer: B
In an RC differentiator circuit (R>>1/ωC), output approximates derivative of input for high-frequency components; conversely, integrator circuits use R<<1/ωC conditions. These circuits are useful in signal processing for shaping pulses and extracting edges. Which is true about practical differentiators? A. They amplify high-frequency noise unless stabilized by additional filtering B. They always suppress high-frequency components only C. Differentiators are ideal and noiseless in practice D. They convert DC to AC always Answer: A
The classical electron radius (r_e = \frac{e^2}{4\pi\varepsilon_0 m_e c^2}) (~2.8 fm) is a length scale combining classical electrostatics and electron mass. It is not a true radius of electron but emerges in scattering cross-section estimates such as Thomson scattering for low-energy photons; Thomson cross-section (\sigma_T) scales as A. (r_e^2) (classical cross-section proportional to square of classical electron radius) B. r_e only linearly C. Independent of r_e D. Infinity always Answer: A
In X-ray crystallography, constructive interference from lattice planes occurs when Bragg’s law (2d\sin\theta = n\lambda) is satisfied. Changing incident wavelength λ will change Bragg angle θ for given plane spacing d; shorter λ yields A. Larger θ for given n and d B. Smaller θ (because (\sin\theta = n\lambda/2d)) C. No change in θ D. Impossible to satisfy Bragg’s condition Answer: B
Thermal noise (Johnson–Nyquist noise) in resistors has mean-square voltage (\langle V^2\rangle = 4k_BTR\Delta f). Thus thermal noise power increases with bandwidth; doubling bandwidth (\Delta f) at same temperature and resistance will A. Halve the noise power B. Double the noise power (linearly proportional) C. Leave noise power unchanged D. Reduce noise to zero Answer: B
The Fresnel equations give reflection and transmission coefficients for light at an interface for s- and p-polarizations. At Brewster’s angle the reflection coefficient for p-polarized light goes to zero because reflected and refracted rays are at 90°, so reflected p-component A. Is maximized always B. Vanishes (no p-polarized reflection) C. Equals transmitted amplitude exactly D. Becomes purely imaginary only Answer: B
In the context of alternating current, complex representation allows phasor addition. If two sinusoidal voltages of same frequency are (V_1=V_0\angle 0^\circ) and (V_2=V_0\angle 120^\circ), the phasor sum magnitude is less than sum of magnitudes due to phase difference; vector addition yields resultant magnitude equal to A. 2V_0 always B. (V_0\sqrt{3}) (for 120° separation of equal vectors) C. Zero always D. Infinite Answer: B
The process of stimulated emission, essential to laser action, requires a population inversion where more atoms are in excited state than ground state. Achieving population inversion typically requires pumping mechanism and metastable excited states; in three-level lasers population inversion is harder than in four-level systems because A. Lower lasing threshold always B. Ground state involvement makes it difficult to obtain inversion without extremely strong pumping C. No metastable states required D. Stimulated emission does not occur in three-level lasers Answer: B
In classical scattering of charged particles by Coulomb potential, impact parameter b relates to scattering angle θ; small impact parameters produce large-angle scattering. For Rutherford scattering, differential cross-section falls off rapidly with increasing θ for high-energy projectiles making small-angle scattering more probable. Observed deviation from Rutherford at very small angles often arises from A. Detector inefficiency only B. Screening by atomic electrons and multiple scattering effects in target thickness C. Nuclear fission only D. Quantum entanglement only Answer: B
The resonance fluorescence spectrum of atoms under strong driving can show Mollow triplet structure due to quantum interference between scattered fields. Observing such quantum optical signatures requires highly coherent driving fields and isolated atomic systems; such phenomena demonstrate light–matter interactions beyond semiclassical approximations and highlight role of A. Classical wave interference only B. Quantum nature of both light and atomic transitions (quantized field effects) C. Thermal averaging only D. No physical significance in experiments Answer: B
The Debye length in plasmas and electrolytes characterizes screening of electric fields; it scales inversely with square root of charge carrier density. Shorter Debye length means stronger screening and thus potentials from point charges are screened over shorter distances. Increasing temperature generally A. Decreases Debye length always B. Increases Debye length slightly (since thermal motion increases) depending on density and temperature balance C. Eliminates screening entirely D. Makes Debye length infinite always Answer: B
In Rutherford’s scattering, if the target nucleus has finite size (not pointlike), high-energy α particles with impact parameters comparable to nuclear radius can probe nuclear structure. Elastic scattering at large angles that deviates from pure Coulomb expectations gives information on nuclear A. Chemical binding only B. Charge distribution and nuclear radius (form factors) C. Electron shell only D. Ambient temperature only Answer: B
Cyclotron radiation refers to electromagnetic radiation emitted by charged particles spiraling in magnetic fields. For relativistic particles, emitted radiation is beamed forward and spectrum shifts; this is important in astrophysical jets and synchrotron sources. The critical frequency of synchrotron emission scales with particle energy and magnetic field strength as roughly A. Independent of energy and field B. Increases with higher particle energy and stronger magnetic field C. Decreases with energy always D. Depends only on gravitational field Answer: B
In single-photon interference experiments, interference fringes can be produced even when photons are sent one at a time provided path information remains indistinguishable. Which principle is demonstrated by such experiments? A. Classical superposition of waves only B. Quantum superposition and wavefunction interference (single-particle interference) C. Particles cannot interfere individually D. Deterministic hidden variables always determine outcomes Answer: B
The nuclear shell model predicts magic numbers of protons or neutrons for extra stability (e.g., 2, 8, 20, 28, 50, 82, 126). Nuclei with magic numbers exhibit higher binding energy per nucleon and lower reactivity. Observed anomalies from simple shell model led to inclusion of spin–orbit coupling which explains magic numbers by A. Reducing overall level splitting only B. Producing large energy gaps between certain shell levels through spin–orbit interactions, stabilizing particular nucleon counts C. Eliminating concept of nuclear energy levels entirely D. Making nucleons classical particles with no quantum states Answer: B
