A point charge Q is placed at the center of a hollow, conducting spherical shell of inner radius a and outer radius b, as shown above. A net charge q is placed on the conducting shell. If the electric potential is assumed to be 0 at infinity, the magnitude of the electric potential at r, where a < r < b, is

The figure above shows three arrangements of one electron (e) and two protons (p). Which of the following is true about the magnitude F of the net electrostatic force acting on the electron due to the protons?

A series AC circuit with impedance Z consists of resistor R, inductor L, and capacitor C, as shown above. The ideal emf source has a sinusoidal output given by E = Eₐₓ sin(ωt), and the current is given by I = Iₐₓ sin(ωt − φ). What is the average power dissipated in the circuit? (I₍ᵣ₎ is the root-mean-square current.)

The quantum efficiency of a photon detector is 0.1. If 100 photons are sent into the detector, one after the other, the detector will detect photons

Two students perform an experiment in which they drop a ball from rest from a known height above the ground and measure the speed of the ball just before it strikes the ground. From repeated measurement, the students estimate the uncertainty in the measured speed of the ball to be 10 percent. Which of the following gives the uncertainty in the kinetic energy of the ball? (Assume the uncertainty in the ball’s mass is negligibly small.)

Which of the following wave functions represents a solution to the Schrödinger equation for an electron in the 2s state of a hydrogen atom? (c is a constant and a₀ is the Bohr radius.)

A particle in an infinite square well has as its initial wave function an equal mixture of the first three orthonormal stationary states: Ψ(x,0) = A [ψ₁(x) + ψ₂(x) + ψ₃(x)] The value of the normalization constant A is equal to which of the following?

A matter wave of energy E > 0 and wave number k is incident from the left on a potential well of width L and depth V₀. The top of the well is at zero energy and the bottom of the well is at −V₀, as shown in the figure above. The spatial part of the wave function in region 3 has which of the following forms? (A is a constant.)

1 has force constant k₁ and spring 2 has force constant k₂, where k₁ > k₂. If the same external force is applied to both springs, which of the following is true about the extensions (Δx₁ and Δx₂) and the stored potential energies (U₁ and U₂) of the two springs?

A stone is glued to the top of a light wooden block that floats in a pool of water, as shown in Figure 1 above. Assume that exactly 50 percent of the block is under water, and that the stone has half the weight of the block. If the block and stone are flipped over, as shown in Figure 2, and replaced in the pool, the amount of the block under water will be

A uniform solid disk starts from rest and rolls down an inclined plane without slipping. After some time, what fraction of the disk’s total kinetic energy is rotational kinetic energy?

Two projectiles are launched from ground level with the same initial speed. The maximum height *h₁* reached by projectile 1 is twice the maximum height *h₂* reached by projectile 2. If θ₁ and θ₂ denote the respective launch angles, these angles satisfy which of the following relationships?

When an object is located 25 cm from lens 1, an inverted image is produced 100 cm from the lens, as shown in Figure 1 above. A second lens with a focal length of +20 cm is placed 110 cm from the first lens, as shown in Figure 2 above. Which of the following is true of the image produced by lens 2?

A grating spectrometer can just barely resolve two wavelengths of 500 nm and 502 nm, respectively. Which of the following gives the resolving power of the spectrometer?

A gas cell with an optical path length of 10 cm is placed in one arm of a Michelson interferometer. If the light source for the interferometer is a laser with wavelength λ = 632.2 nm, then 100 fringes are counted as the gas cell is evacuated. What is the index of refraction of the original gas?

A microwave line has a laboratory wavelength of 1 μm. If the Hubble constant H ≈ 75 (km/s)/Mpc, the observed wavelength for the line from a galaxy 100 Mpc distant is about:

The Fourier series expansion of a function f(x) that is periodic with period 2π is

f(x) = a₀/2 + Σ₌₁^∞ aₙ cos(nx) + Σ₌₁^∞ bₙ sin(nx)

If f(x) is given by the graph above, which of the following statements about the coefficients is true?

A sample of N molecules has the distribution of speeds shown in the figure above. P(v) dv is an estimate of the number of molecules with speeds between v and v + dv, and this number is nonzero only up to 3v₀, where v₀ is constant. Which of the following gives the value of a?

Which of the following statements is (are) true for a Maxwell-Boltzmann description of an ideal gas of atoms in equilibrium at temperature T?

I. The average velocity of the atoms is zero.

II. The distribution of the speeds of the atoms has a maximum at u= 0.

III. The probability of finding an atom with zero kinetic energy is zero.

Low-energy electrons are accelerated between electrodes in a tube filled with a gas in the Franck-Hertz apparatus. A plot of current collected versus accelerating voltage is also shown. The data provide evidence for which of the following?

A photon of wavelength λ is scattered from an electron through an angle θ. Which of the following correctly gives the wavelength λ′ of the scattered photon?

Excited states of the helium atom can be characterized as para- (antiparallel electron spins) and ortho- (parallel electron spins). The observation that an ortho-state has lower energy than the corresponding para-state can be understood in terms of which of the following?

A particle of mass m and spin zero is in a three-dimensional isotropic well described by V(r) = (1/2) mω² r², where r² = x² + y² + z². How many states have energy (7/2) ħω?

The operators for the total angular momentum and its three projections are Ĵ, Ĵₓ, Ĵᵧ, Ĵ_z. The commutator is [Â, B̂] ≡ ÂB̂ – B̂Â. Which of the following is true?

The suspension cable of a 1,000 kg elevator snaps, sending the elevator moving downward through its shaft. The emergency brakes of the elevator stop the elevator shortly before it reaches the bottom of the shaft. If the elevator fell a distance of 100 m from rest, the heat that the brakes must dissipate to bring the elevator safely to rest is:

A uniform rod of length L and mass M is released from rest at θ = 0 and rotates about a horizontal axis through its base. What is the angular acceleration of the rod as a function of θ?

Two identical ideal springs, each with force constant k, are attached in series and hung vertically. A block of mass m is attached to the system. What is the angular frequency of oscillation?

A block attached to a spring is moving along the x-axis on a frictionless horizontal surface. What is the Hamiltonian for the block?

A conducting sphere is solid except for three spherical cavities inside. Cavity A contains a point charge of +2q, cavity B contains a point charge of –4q, and cavity C is empty, as shown above. What charges are induced on the inner surfaces of the spherical cavities?

A magnetic field is directed perpendicular to the plane of a circular coil of area 0.2 m² and 250 turns. If the magnetic field is increased from 0.01 T to 0.06 T during a time interval of 0.25 s, the average induced EMF in the coil is:

A beam of particles with E > 0 is incident from the left on a step potential: U(x) = 0 for x ≤ 0 (Region 1), U(x) = –U₀ for x > 0 (Region 2). The reflection coefficient R at the interface x = 0 is:

Consider the Pauli spin matrices σₓ, σᵧ, and σ_z. The product σₓσᵧ is equal to:

The binding energy per nucleon is greatest for which of the following nuclei?

The negative muon, μ⁻, has properties most similar to which of the following?

Which of the following correctly gives the quark and antiquark content of a lepton and a baryon?

Under certain conditions, a beam of electrons impinging on a crystal surface will diffract. What is the approximate kinetic energy of the electrons needed in order to see the pattern? (Assume the lattice spacing of the crystal is 0.4 nm.)

A beam of positive ions moves in the +x direction with nonrelativistic velocity through a velocity selector. The electric field E is along +y and the magnetic field B is along +z. The critical speed v_c at which the beam is not deflected is:

Under ideal conditions, the electric and magnetic fields inside a superconductor are zero. What must be true just outside the surface?

A positive charge +q oscillates up and down. What is the direction of the Poynting vector S at point P to the right of +q?

A block of mass m₁ slides on a frictionless table and is attached to a string over a pulley connected to a hanging mass m₂. What is the tension in the string?

What is the tension in the string?

What is the value of M′?

Of the following, the most strongly reflected wavelength is:

What is the angle α?

What is the relative speed of the quasar?

Protons used in cancer therapy are accelerated to about 0.6c. How much work must be done on a particle of mass mmm in order for it to reach this speed, assuming it starts at rest?

The sign of charge carriers in a doped semiconductor can be determined by:

In the experimental setup above, two masses, m1m_1m1​ and m2m_2m2​, are connected by a massless string over a massless pulley. Mass m1m_1m1​ slides on a frictionless surface. The values of the two masses can be measured, as well as the distance ddd and the speed of mass m1m_1m1​ as it passes x1x_1x1​ and again at x2x_2x2​. The experiment can be used to do which of the following?

I. Demonstrate momentum conservation
II. Demonstrate energy conservation
III. Measure the value of the acceleration due to gravity

An airplane drops a payload while traveling due north at a constant speed of 100 m/s. If air resistance is neglected, what is the velocity of the payload relative to the plane 4.0 s after it is released?

Two balls, identical in every way except that one has twice the mass of the other, are dropped from rest from the same height so that they both reach terminal speed before hitting the ground. If the drag force varies like the speed squared, what is the ratio of the terminal speeds of the balls?

One end of a horizontal, massless spring is attached to a wall. A mass of 90. One end of a horizontal, massless spring is attached to a wall. A mass of 0.30 kg is attached to the other end of the spring and rests on a table. The mass is displaced 0.030 m from its equilibrium position and released. It has a speed of 0.040 m/s as it passes through its equilibrium position. In the absence of friction, what is the total mechanical energy of the system? is attached to the other end of the spring and rests on a table. The mass is displaced from its equilibrium position and released. It has a speed of as it passes through its equilibrium position. In the absence of friction, what is the total mechanical energy of the system?

Ratio of heat Q_bc to work done?

The first capacitor is charged to a voltage V0V_0V0​ and then disconnected from the battery. The other two capacitors, initially uncharged and connected in series, are then connected across the first capacitor. What is the final voltage on the first capacitor?

A charge of −5.0 μC-5.0 \, \mu C−5.0μC is distributed uniformly around a ring of 1.0 m in radius. A point charge of +3.0 μC+3.0 \, \mu C+3.0μC is at the center of the ring. The work required to move the point charge 1.0 m in a direction normal to the plane of the ring is most nearly:

The magnetic field inside a long coil of wire (solenoid) has a certain magnitude and direction when the coil is air-filled. If a diamagnetic material is inserted in the coil, how do the magnitude and direction of the magnetic field change?

Lagrangian?

Mössbauer absorption spectrum (14.4 keV transition). Lifetime of excited state is approximately:

The spacing between the parallel Bragg planes in a certain crystal is ddd. Electrons of fixed energy, corresponding to a given wavelength λ, are incident on the crystal. Which of the following is the minimal condition for strong reflection for at least two different angles?

onsider an electron in the n=4,ℓ=1 state in hydrogen. Which of the following final states can NOT be reached by an allowed transition?