GRE Subject Test: Physics

A particle moves in one dimension with position x(t) = t³ − 6t² + 9t (meters, t in seconds). At what times is the particle momentarily at rest?

• At = 1 s and t = 3 s
• Bt = 2 s only
• Ct = 0 s and t = 2 s
• Dt = 3 s only

A block of mass m slides down a frictionless inclined plane of angle θ. What is the acceleration of the block along the plane?

• Ag sin θ
• Bg cos θ
• Cg tan θ
• Dg

A 2 kg block compresses a spring (k = 800 N/m) by 0.10 m and is then released from rest on a frictionless surface. What is the speed of the block when it leaves the spring?

• A2.0 m/s
• B4.0 m/s
• C√2 m/s
• D1.0 m/s

A uniform rigid rod of mass M and length L is pivoted at one end and held horizontal. When released, what is the angular acceleration immediately after release?

• A3g/(2L)
• Bg/L
• Cg/(2L)
• D2g/L

Two point masses m₁ = 3 kg and m₂ = 1 kg undergo a perfectly inelastic collision. Before the collision, m₁ moves at 4 m/s and m₂ is at rest. What is the kinetic energy lost in the collision?

• A12 J
• B24 J
• C6 J
• D18 J

A satellite orbits Earth in a circular orbit at radius r from Earth's center. If the radius is increased to 4r, by what factor does the orbital period change?

• AIncreases by factor 8
• BIncreases by factor 4
• CIncreases by factor 2
• DDecreases by factor 2

A simple pendulum of length L swings with small amplitude on the surface of a planet where the gravitational acceleration is g/4 (one-quarter of Earth's g). Compared to the same pendulum on Earth, the period on this planet is:

• A2T
• BT/2
• C4T
• DT/4

In the Lagrangian formulation, a generalized coordinate q and its conjugate momentum p = ∂L/∂q̇ satisfy Hamilton's equations. For a free particle of mass m in one dimension with Hamiltonian H = p²/(2m), which of the following correctly gives the equations of motion?

• Aq̇ = p/m and ṗ = 0
• Bq̇ = p/(2m) and ṗ = 0
• Cq̇ = 2p/m and ṗ = −p
• Dq̇ = p/m and ṗ = −kq

A 1 kg ball is attached to a string and swung in a horizontal circle of radius 0.5 m at a speed of 3 m/s. What is the tension in the string (ignoring gravity)?

• A18 N
• B9 N
• C6 N
• D3 N

The Lagrangian for a system is L = ½mẋ² − ½kx². Which of the following is the equation of motion derived from the Euler-Lagrange equation?

• Amẍ + kx = 0
• Bmẍ − kx = 0
• Cẍ + (k/m)x² = 0
• Dẍ = k/m

Two equal point charges +q are fixed at positions (0, +d) and (0, −d) on the y-axis. What is the electric field at the origin?

• AZero
• B2kq/d² in the +y direction
• C2kq/d² in the −y direction
• Dkq/d² in the +x direction

A parallel-plate capacitor has plate area A, separation d, and is filled with a dielectric of constant κ. Which expression gives its capacitance?

• Aκε₀A/d
• Bε₀A/(κd)
• Cκε₀d/A
• Dε₀A/d

A long straight wire carries a steady current I. Using Ampere's law, the magnetic field at distance r from the wire is:

• Aμ₀I/(2πr)
• Bμ₀I/(4πr²)
• Cμ₀I/(πr)
• Dμ₀Ir/(2π)

A conducting loop of resistance R and area A is placed in a uniform magnetic field B(t) = B₀ sin(ωt) perpendicular to the loop. What is the amplitude of the induced current?

• AωB₀A/R
• BB₀A/R
• CωB₀A/(2R)
• DB₀/(ωAR)

In a vacuum, Maxwell's equations predict electromagnetic waves traveling at speed c = 1/√(ε₀μ₀). If a medium has relative permittivity εᵣ = 4 and relative permeability μᵣ = 1, what is the speed of light in this medium?

• Ac/2
• Bc/4
• C2c
• Dc/√2

A resistor R and inductor L are connected in series with an AC voltage source V₀ cos(ωt). At resonance frequency of an RLC series circuit (with capacitor C also present), the impedance of the circuit is:

• AR
• B√(R² + (ωL − 1/(ωC))²)
• CωL
• D√(R² + ω²L²)

An electric dipole with dipole moment p is placed in a uniform electric field E. The torque on the dipole is maximum when the angle between p and E is:

• A90°
• B0°
• C180°
• D45°

Young's double-slit experiment uses light of wavelength λ = 500 nm. The slit separation is d = 0.1 mm and the screen is at distance L = 1.0 m. What is the fringe spacing (distance between adjacent bright fringes)?

• A5.0 mm
• B0.5 mm
• C50 mm
• D0.05 mm

A converging lens of focal length f = 20 cm has an object placed 30 cm in front of it. Where is the image formed?

• A60 cm on the far side
• B60 cm on the same side
• C12 cm on the far side
• D20 cm on the far side

Light of wavelength λ strikes a diffraction grating with N slits per unit length. The condition for the m-th order principal maximum is:

• Ad sin θ = mλ, where d = 1/N
• Bd sin θ = (m + ½)λ, where d = 1/N
• Cd cos θ = mλ, where d = 1/N
• DNd sin θ = mλ

A sound source emits at frequency f₀ and moves toward a stationary observer at speed v_s. If the speed of sound is v, what frequency does the observer hear (Doppler effect)?

• Af₀v/(v − v_s)
• Bf₀v/(v + v_s)
• Cf₀(v + v_s)/v
• Df₀(v − v_s)/v

The first law of thermodynamics for a closed system states ΔU = Q − W. For a reversible adiabatic expansion of an ideal gas, which of the following is true?

• AQ = 0 and the gas cools
• BW = 0 and temperature is unchanged
• CQ = W and ΔU = 0
• DΔU = 0 and T increases

An ideal gas undergoes a Carnot cycle between a hot reservoir at T_H = 600 K and a cold reservoir at T_C = 300 K. What is the efficiency of the engine?

• A50%
• B25%
• C75%
• D100%

For a monatomic ideal gas, the internal energy is U = (3/2)nRT. When the gas undergoes a reversible isothermal expansion at temperature T, the work done by the gas is:

• AnRT ln(V_f/V_i)
• BnRT(V_f/V_i − 1)
• C(3/2)nR ΔT
• DP_i(V_f − V_i)

In special relativity, a rod of proper length L₀ moves parallel to its length at speed v = 0.6c relative to an observer. What length does the observer measure?

• A0.8L₀
• B0.6L₀
• CL₀/√(1 − 0.36)
• D1.25L₀

A Carnot refrigerator operates between T_C = 250 K and T_H = 500 K. What is its coefficient of performance (COP)?

• A1
• B2
• C0.5
• D3

The Maxwell-Boltzmann speed distribution for a gas of N molecules at temperature T peaks at the most probable speed. For a gas of molecular mass m, the most probable speed v_p is:

• A√(2k_BT/m)
• B√(3k_BT/m)
• C√(8k_BT/πm)
• D√(k_BT/m)

A system has three accessible microstates with equal probability. The entropy of the system is:

• Ak_B ln 3
• B3k_B
• Ck_B ln 2
• Dk_B/3

For a particle in an infinite square well of width L, the energy eigenvalues are E_n = n²π²ℏ²/(2mL²). What is the ratio E_3/E_1?

• A9
• B3
• C6
• D√3

The time-independent Schrödinger equation for a free particle (V = 0) in one dimension has solutions of the form:

• Aψ(x) = Ae^(ikx) + Be^(−ikx), where k = √(2mE)/ℏ
• Bψ(x) = A sin(x) only
• Cψ(x) = Ae^(−αx²) only
• Dψ(x) = A/x

An electron is described by quantum numbers n = 3, ℓ = 2, m_ℓ = −1, m_s = +1/2. Which spectroscopic notation correctly identifies this state?

• A3d
• B3p
• C3f
• D3s

The energy levels of hydrogen are E_n = −13.6 eV/n². The photon emitted in the transition from n = 3 to n = 2 has energy:

• A1.89 eV
• B3.4 eV
• C0.66 eV
• D1.51 eV

The quantum harmonic oscillator has equally spaced energy levels E_n = (n + ½)ℏω. The zero-point energy (ground state energy) is:

• Aℏω/2
• B0
• Cℏω
• D3ℏω/2

An electron has spin quantum number m_s = +1/2. The magnitude of its spin angular momentum is:

• A(√3/2)ℏ
• Bℏ/2
• Cℏ
• D(√2/2)ℏ

A particle is in a superposition state |ψ⟩ = (1/√3)|0⟩ + (√2/√3)|1⟩, where |0⟩ and |1⟩ are energy eigenstates with eigenvalues E_0 and E_1. What is the probability of measuring E_1?

• A2/3
• B1/3
• C√2/√3
• D1/2

The selection rules for electric dipole transitions in hydrogen forbid certain transitions. Which of the following transitions is FORBIDDEN?

• A2s → 1s (Δℓ = 0)
• B2p → 1s (Δℓ = −1)
• C3d → 2p (Δℓ = −1)
• D4f → 3d (Δℓ = −1)

According to the Bohr model, the radius of the n-th orbit in hydrogen is r_n = n²a_0, where a_0 = 0.053 nm is the Bohr radius. The radius of the n = 4 orbit is:

• A0.848 nm
• B0.212 nm
• C3.39 nm
• D0.053 nm

In the photoelectric effect, electrons are emitted only when the incident light frequency exceeds the threshold frequency ν₀. If the work function of the metal is φ = 2.0 eV and light of frequency ν = 8 × 10¹⁴ Hz is used (h = 6.63 × 10⁻³⁴ J·s), what is the maximum kinetic energy of the emitted electrons?

• A1.31 eV
• B3.31 eV
• C2.0 eV
• D0.69 eV

A beam of electrons (mass m, charge −e) is accelerated through a potential difference V. Using de Broglie's relation, the de Broglie wavelength of these electrons is:

• Ah/√(2meV)
• Bh/(meV)
• C√(h²/(2meV))
• Dh/(2meV)

In special relativity, the relativistic energy of a particle with rest mass m and momentum p is:

• AE = √((pc)² + (mc²)²)
• BE = pc + mc²
• CE = mc²/(1 − v²/c²)
• DE = ½mv² + mc²

A particle moves at speed v = 0.8c relative to the lab. According to special relativity, its Lorentz factor γ is:

• A5/3
• B5/4
• C3/5
• D4/5

Two events are simultaneous in frame S but separated by distance Δx = 3 light-seconds. In frame S′ moving at v = 0.6c relative to S in the +x direction, the magnitude of the time interval |Δt′| between the events is (use γ = 1.25):

• A2.25 s
• B0 s
• C1.80 s
• D3.75 s

The half-life of a muon at rest is 2.2 μs. A muon traveling at v = 0.99c is created 15 km above a detector (γ ≈ 7.09). How many muon-rest-frame half-lives elapse during the trip to the detector?

• AAbout 3.2 half-lives
• BAbout 23 half-lives
• CAbout 0.32 half-lives
• DAbout 7.1 half-lives

A Michelson interferometer has equal arm lengths. When one mirror moves a distance Δd, the number of fringe shifts observed is:

• A2Δd/λ
• BΔd/λ
• C4Δd/λ
• DΔd/(2λ)

In a lab experiment, a student measures a quantity five times and obtains: 9.8, 10.1, 9.9, 10.2, 10.0 (all in cm). What is the mean and the standard error of the mean (SEM)?

• AMean = 10.0 cm, SEM ≈ 0.07 cm
• BMean = 10.0 cm, SEM ≈ 0.16 cm
• CMean = 10.0 cm, SEM ≈ 0.35 cm
• DMean = 9.9 cm, SEM ≈ 0.07 cm

A lock-in amplifier is used in a physics experiment primarily to:

• ADetect small signals buried in noise by phase-sensitive detection at a reference frequency
• BMeasure DC current with high precision
• CAmplify optical signals using laser gain
• DDigitize analog signals at high sampling rates

A voltage divider consists of two resistors R₁ = 1 kΩ and R₂ = 3 kΩ in series, connected to V_in = 12 V. The output voltage across R₂ is:

• A9 V
• B3 V
• C6 V
• D4 V

In nuclear physics, the binding energy per nucleon of ⁵⁶Fe is approximately 8.8 MeV/nucleon. What is the total binding energy of an iron-56 nucleus?

• A492.8 MeV
• B8.8 MeV
• C448 MeV
• D88 MeV