## ==> Sticky: User Created 70 Sample Questions with answers

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### ==> Sticky: User Created 70 Sample Questions with answers

Questions 1-70 in this thread are questions that imitate those of the real PGRE test. For those of you who want to practise only on ETS official questions there are directions on how to do this (the 5 practice tests etc.). The questions I post here periodically are for those who want to practise on PGRE questions beyond the official material. The questions in this thread are updated when possible!

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Notice:
ALL ANSWERS TO THE FOLLOWING SAMPLE QUESTIONS ARE GIVEN BELOW IN THIS THREAD (TBA answers will be given soon!)
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Time alloted: Use as much as you need for practice!

SAMPLE QUESTION 1:
Suppose and are the ground state wavefunctions of two single (non-interacting) potential wells #1 and #2 respectively. Consider the following wavefunctions representing the ground state of the system of the two aforementioned wells (now seen as a double well):

I.

II.

III.

Given the above information which of the following statements is FALSE?

(A) Wavefunction (I) can represent the ground state of a system of two identical wells.
(B) Wavefunction (II) can represent the ground state of an asymmetric double well.
(C) Wavefunction (III) cannot represent the ground state of a symmetric double well.
(D) If the double well is described by wavefunction (II), then potential well #2 is deeper than potential well #1.
(E) If the double well is described by wavefunction (I) its fundamental energy level lies higher than the fundamental energy levels of the non-interacting wells.

SAMPLE QUESTION 2:
A beam of radioactive particles is measured as it shoots through a laboratory. It is found that, on average, each particle "lives" for a time of 20 ns. When at rest in the laboratory, the same particles "live" 7 ns on average. How fast do the particles in the beam move?

(A) 0.50c
(B) 0.88c
(C) 0.12c
(D) 0.65c
(E) 0.93c

{c = speed of light}

SAMPLE QUESTION 3:
A diffraction grating with a width of 2.0 cm contains 1000 lines/cm across that width. For an incident wavelength of 500 nm, what is the smallest wavelength difference this grating can resolve in the second order?

(A) 0.125 nm
(B) 0.25 nm
(C) 0.50 nm
(D) 8 nm
(E) 2 nm

SAMPLE QUESTION 4:
If the temperature of an ideal gas is increased at constant pressure, what happens to the mean free path of its molecules/atoms?

(A) It decreases in proportion to .
(B) It decreases in proportion to .
(C) It increases in proportion to .
(D) It increases in proportion to .
(E) It is not affected by the temperature change.
Last edited by physics_auth on Tue Jan 16, 2018 4:03 pm, edited 68 times in total.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### SAMPLE QUESTIONS 5 - 11 AND HOW TO FIND ETS RELEASED SAMPLE

SAMPLE QUESTION 5:
A homogeneous disk of mass M = 2 kg and radius R is rotated about an axis perpendicular to its plane that passes through its center. Initially, the disk rotates at an angular speed of 40 rad/sec. At time t = 0, sand starts dropping uniformly onto the area of the disk at a rate of 0.2 kg/sec. By how much did the angular speed of the system (disk + sand) change in the time interval from 10 to 30 secs?

(A) It decreased by 30 rad/s.
(B) It decreased by 20 rad/s.
(C) It decreased by 10 rad/s.
(D) It increased by 10 rad/s.
(E) It increased by 20 rad/s.

SAMPLE QUESTION 6:
The work function for sodium is 2.28 eV. A portion of sodium is irradiated separately and successively by the following three types of electromagnetic radiation

I. ultraviolet radiation
II. blue optical radiation
III. infrared radiation

For which radiation or radiations does the photoelectric effect take place?

(A) I and II only
(B) I only
(C) II and III only
(D) I, II and III
(E) III only

SAMPLE QUESTION 7:
An atom transits from an excited state to the ground state emitting a photon of energy 4.7 eV. The lifetime of the excited state is 0.1 picosec. What is approximately (i.e. the order of magnitude of) the spectral line width Δν/ν of the photon? v stands for frequency.

(A)
(B) 0.001
(C) 1
(D) 10
(E) 100

SAMPLE QUESTION 8:
A block of mass M is attached to the free end of a horizontal spring of stiffness constant k (the other end of the spring is fixed to a vertical wall). A projectile of mass m (m < M) moves horizontally and directs ahead to the block approaching it at a speed u. The projectile is embedded into the block. Friction from the floor is negligible. What is the amplitude A of the oscillation of the system projectile-block?

(A)

(B)

(C)

(D)

(E)

SAMPLE QUESTION 9:
In some experiment, we have a velocity selector whose disks are separated by 0.5 m and its transmission axes (slits) make a relative angle of π rad. It is found that molecules pass through the selector when it turns at a rate of 600 rev/sec. What is the maximum speed of a molecule that passes the selector?

(A) 300/π m/s
(B) 100/π m/s
(C) 600 m/s
(D) 300 m/s
(E) 600/π m/s

SAMPLE QUESTION 10:
If the internal electrons of lithium atom (Z = 3) are considered to screen fully the nucleus from the outer (valence) electron, then the ionization work of this atom will be most nearly equal to:

(A) 13.6 eV
(B) 1.5 eV
(C) 54.4 eV
(D) 3.4 eV
(E) 17 eV

SAMPLE QUESTION 11:
In a series of experiments, three unpolarized beams of neutral atoms in their ground state are sent consecutively through a Stern-Gerlach apparatus. The first beam consists of sodium atoms, and it is known that sodium belongs to the third row and the first column of the periodic table of elements. The second beam consists of magnesium atoms, and it is known that magnesium is next to sodium in the periodic table. Finally, the third beam consists of nitrogen atoms, and it is known that the ground state electron configuration of nitrogen is . What are the results that a detector in the output would record for each one of the three experiments?

______(Na atoms)________(Mg atoms)__________(N atoms)

(A)____ 1 beam __________ 1 beam ___________ 3 beams
(B)____ 2 beams _________ 2 beams __________ 3 beams
(C)____ 2 beams _________ 1 beam ___________ 4 beams
(D)____ 2 beams _________ 3 beams __________ 4 beams
(E)____ 2 beams _________ 1 beam ___________ 1 beam
Last edited by physics_auth on Tue Jan 16, 2018 4:50 am, edited 45 times in total.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### PGRE SAMPLE QUESTIONS 12-15

SAMPLE QUESTION 12:
An object is 20 cm to the left of a lens of focal length +10 cm. A second lens, of focal length +12.5 cm, is 30 cm to the right of the first lens. What is the distance between the original object and the final image?

(A) 28 cm
(B) 50 cm
(C) 100 cm
(D) 0 cm
(E)

SAMPLE QUESTION 13:
In a piece of metal at an equilibrium temperature of 0 Kelvin, what does the Fermi energy represent?

(A) The energy of the top of the valence band.
(B) The energy of the bottom of the conduction band.
(C) The mean thermal energy of the electrons.
(D) The highest energy that an electron of the metal can have.
(E) The energy gap between the top of the valence band and the bottom of the conduction band.

SAMPLE QUESTION 14:
A laboratory source of electromagnetic waves is placed opposite a perfect conducting reflecting surface of large dimensions. Between the source and the reflecting surface is placed a small receiver which can move along a straight line that is perpendicular to the reflecting surface. When the receiver is displaced by 15 cm, exactly ten rises and falls of the intensity are registered. What is the frequency of the electromagnetic waves?

(A) Hz
(B) HZ
(C) Hz
(D) Hz
(E) Hz

SAMPLE QUESTION 15:
The potential energy of quantum harmonic oscillator is given by , where m is the mass and the angular frequency of the oscillator. What is the position uncertainty of a quantum harmonic oscillator in its first excited state?

(A)

(B)

(C)

(D)

(Ε)
Last edited by physics_auth on Wed Jan 17, 2018 2:36 am, edited 15 times in total.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### PGRE SAMPLE QUESTIONS 16 - 19

SAMPLE QUESTION 16:
A particle is in the second excited state of an infinite square well of width . The probability of NOT finding the particle in the region of the well is equal to:

(A) 2/3
(B) 3/4
(C) 1/3
(D) 1/2
(E) 1

SAMPLE QUESTION 17:
The number of particles emitted each minute by a radioactive source is recorded for a period of 10 hours. A total of 60 counts are registered. During how many 1-minute intervals, approximately, should we expect to observe no particles?

(A) 60 1-minute intervals
(B) 540 1-minute intervals
(C) 54 1-minute intervals
(D) 600 1-minute intervals
(E) 90 1-minute intervals

SAMPLE QUESTION 18:
A sodium atom (Na) consists of 11 electrons. What is the ground state electron configuration of doubly ionized sodium, i.e. of ?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 19:
After traveling a distance of 10cm in a material medium, the intensity of a beam of photons has decreased by 75%. The mean free path of the photons in this medium is most nearly equal to which of the following? (ln2 = 0.69)

(A) 0.029 cm
(B) 0.14 cm
(C) 7.2 cm
(D) 13.6 cm
(E) 34.8 cm
Last edited by physics_auth on Mon Jul 11, 2011 7:11 pm, edited 11 times in total.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### PGRE SAMPLE QUESTIONS 20 -23

SAMPLE QUESTION 20:
Operator which operates on a space of two states and is given by the formula: . Assuming that , where i,j = 1, 2, what are the eigenvalues of operator ?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 21:
The one end of a pendulum of length is fixed on the ceiling of an elevator (the elevator moves within the gravitational field of the Earth). The elevator moves upwards with an acceleration (where is the gravitational acceleration on the surface of the Earth). If the pendulum's motion is simple harmonic, what is the frequency of oscillation ?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 22:
A point particle with charge +q is to be brought from far away to a point near an electric dipole. Suppose that the dipole is along the x-axis of an Oxyz coordinate system and that the positions of the charges of the dipole, -Q and +Q, are (-s/2,0,0) and (+s/2,0,0) respectively (i.e. s is the distance between the two charges). Where should the final position of the point particle be so that the net work done for its transference is equal to zero?

(A) On the axis of the dipole, on the segment from -s/2 to +s/2 (i.e. between the two charges).
(B) On the axis of the dipole, on the segment from -s/2 to -infinity.
(C) On the axis of the dipole, on the segment from +s/2 to +infinity.
(D) On a line that is perpendicular to the dipole moment and passes through the midpoint.
(E) On a line that makes an angle of 45 degrees with the dipole moment.

SAMPLE QUESTION 23:
When we keep a circular copper (ohmic) conductor at a constant temperature , thermal energy is produced along it at a rate and the magnetic field at its center has magnitude . Then, we heat the conductor to a higher constant temperature (i.e.). At temperature , let and be the rate of dissipation of energy and the magnitude of the magnetic field at its center respectively. Which of the following is TRUE, if ALL other factors remain the same?

(A) It holds that and .
(B) It holds that and .
(C) It holds that and .
(D) It holds that and .
(E) It holds that and .
Last edited by physics_auth on Mon Jul 11, 2011 7:08 pm, edited 13 times in total.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### 8 NEW SAMPLE PHYSICS GRE QUES. WITH THEIR ANSWERS (24-42)

SAMPLE QUESTION 24:
A neutral particle is at rest in a uniform magnetic field of magnitude B. At time t = 0 it decays into two charged particles each of mass m. The two particles move off in separate orbits, both of which lie in a plane perpendicular to the magnetic field. The charge of one of the particles is +q. What is going to happen at a future time t > 0?

(A) The particles will collide after a time interval equal to 2πm/qB.
(B) The particles will collide after a time interval equal to πm/qB.
(C) The particles will collide after a time interval equal to πm/2qB.
(D) The particles will recede from each other until they are infinitely apart.
(E) The particles will recede from each other, moving along a straight line and subsequently approach each other (moving along the same line) under the action of the mutual Coulomb attraction.

SAMPLE QUESTION 25:
A point charge +Q is placed at the vertex of a cube. What is the electric flux through the cube?

(A) 0
(B) +
(C) +
(D) +
(E) +

SAMPLE QUESTION 26:
The mass density of a certain planet has spherical symmetry but varies in such a way that the mass inside every spherical surface with center at the center of the planet is proportional to the radius of the surface. If r is the distance from the center of the planet to a point mass inside the planet, the gravitational force on this mass is:

(A) not dependent on r

(B) proportional to

(C) proportional to r

(D) proportional to

(E) proportional to

SAMPLE QUESTION 27: (This is a tough question - a more analytical answer is provided in the thread below)
A soap film immersed in air is illuminated by white light almost normal to its surface. The index of refraction of the film is 1.50. Wavelengths of 480 nm and 800 nm are ONLY intensified in the reflected beam. (No other wavelengths between them are intensified.) The thickness of the film is:

(A) 150 nm
(B) 240 nm
(C) 360 nm
(D) 400 nm
(E) 600 nm

SAMPLE QUESTION 28:
A certain nucleus, after absorbing a neutron, undergoes beta minus decay and then splits into two alpha particles. Which of the following can be the A and Z of the original nucleus?

(A) A = 6 _____ Z = 2
(B) A = 6 _____ Z = 3
(C) A = 7 _____ Z = 3
(D) A = 7 _____ Z = 2
(E) A = 8 _____ Z = 4

SAMPLE QUESTION 29:
The energy supplied by a thermal neutron in an induced fission event is essentially equal to:

(A) its rest energy
(B) its kinetic energy
(C) its binding energy to the nucleus which undergoes fission
(D) the total energy of the initial fission fragments
(E) the energy released during the fission process

SAMPLE QUESTION 30:
A baryon with strangeness 0 decays into two particles, one of which is a baryon with strangeness +1. Which of the following could be the other particle?

(A) a baryon with strangeness 0
(B) a baryon with strangeness -1
(C) a lepton
(D) a meson with strangeness +1
(E) a meson with strangeness -1

SAMPLE QUESTION 31:
Two bodies move with speeds 0.8c and 0.6c respectively. If the two bodies have the same rest mass, what is the ratio of their relativistic kinetic energies?

(A) 16/9
(B) 4/3
(C) 3/2
(D) 8/3
(E) 32/27

SAMPLE QUESTION 32:
A large transparent slab of uniform thickness and index of refraction is initially immersed in the air. A monochromatic beam of light is incident on the slab at an angle such that the reflected and the refracted beam emerge on mutually orthogonal directions. The previous experiment is then repeated (i.e. same angle of incidence for the aforementioned monochromatic beam), this time with the slab immersed in a liquid with index of refraction . In terms of the angle of incidence and the refraction indices and , what is the angle between the emergent reflected and refracted beams in the latter case?

(A) They are still orthogonal to each other.

(B) It is equal to .

(C) It is equal to .

(D) It is equal to .

(E) It is equal to .

SAMPLE QUESTION 33:
The largest number of beats per second will be heard from which of the following pairs of tuning forks?

(A) 200 and 201 Hz
(B) 256 and 260 Hz
(C) 534 and 540 Hz
(D) 763 and 774 Hz
(E) 8420 and 8422 Hz

SAMPLE QUESTION 34:
A beam of particles of energy E = 9 eV strikes on a step potential and 25% of the beam's particles is reflected back. What is the height of the step potential?

(A) 4 eV
(B) 8 eV
(C) 3 eV
(D) 1 eV
(E) 5 eV

SAMPLE QUESTION 35:
The magnetic dipole moment of a current-carrying loop of wire is in the positive z direction. The magnetic dipole is placed in space where there is a magnetic field , where is some positive constant and , the unit vectors along directions x and y respectively. What is the direction of the magnetic torque on the loop?

(A) It is along the negative z direction.
(B) It is along the line y = -x in the forth quadrant.
(C) It is along the line y = x, in the third quadrant.
(D) It is along the line y = -x, in the second quadrant.
(E) It is along the line x = y = z towards positive x,y and z.

SAMPLE QUESTION 36:
A system is composed of 4000 non-interacting particles distributed among three possible energy states , and . A particular partition corresponds to the occupation numbers and for the first two energy states. The total number of particles of the system remains constant. What is approximately the average energy of this configuration?

(A)
(Β)
(C)
(D)
(E)

SAMPLE QUESTION 37:
The positive terminals of two batteries with emf's of and , respectively, are connected together. It is . The circuit is completed by connecting the negative terminals. If each battery has an internal resistance r, what is the rate with which electrical energy is converted to chemical energy in the smaller battery?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 38:
The Lagrangian for a mechanical system is , where is a generalized coordinate and . What is the Hamiltonian of this system?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 39:
Massless and inextensible string is wrapped around the periphery of a homogeneous cylinder of radius R = 0.5 m and mass m = 2 kg. The string is pulled straight away from the upper part of the periphery of the cylinder, without relative slipping. The cylinder moves on a horizontal floor, for which the friction coefficient (μ) is 0.4. What is most nearly the maximum force that can be exerted on the free end of the string so that the cylinder rolls without sliding?

(A) = 24 N
(B) = 12 N
(C) = 8 N
(D) = 6 N
(E) = 8/3 N

SAMPLE QUESTION 40:
Which of the following facts could be a remnant of the Big Bang theory for the evolution of the universe from a space-time singularity?

I. Uniform distribution of microwave background radiation.
II. Uniform distribution of background electrons.
III. Uniform distribution of background neutrinos.
IV. Uniform distribution of gluons and quarks.

(A) I and II only
(B) I, II and III only
(C) I and III only
(D) I, III and IV only
(E) II and III only

SAMPLE QUESTION 41:
Six identical point charges +q are placed on the vertices of a regular hexagon of side of length l. There is one charge on each vertex. The hexagon is rotated about an axis that passes through its center of symmetry and is perpendicular to its plane. If the frequency of revolution is f, what is the magnitude of the induced magnetic field B at the center of the hexagon?

(A)
(B)
(C)
(D)
(E)

= magnetic susceptibility of free space

SAMPLE QUESTION 42:
A Carnot engine operates using a monoatomic gas as its working substance. Which of the following procedures could lead to the greatest possible increase of the efficiency of the Carnot thermal engine?

(A) The increase of the temperature of the hot reservoir by 40 K.
(B) The lowering of the temperature of the cold reservoir down to 0 K.
(C) The substitution of the monoatomic gas by a diatomic gas.
(D) The increase of the temperature of the hot reservoir by 20 K and the simultaneous decrease of the temperature of the cold reservoir by 20 K.
(E) The substitution of the reversible mode of operation of the engine by an irreversible one.
Last edited by physics_auth on Tue Jan 30, 2018 5:41 am, edited 79 times in total.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Questions 43-70

SAMPLE QUESTION 43:
A particle is initially in the second excited level of an infinite square well and makes a transition to the first excited level. The transition is accompanied by the emission of a photon of wavelength 1200 A (). What is the minimum possible energy that the particle can have in the well?

(A) 1 eV
(B) 2 eV
(C) 4 eV
(D) 8 eV
(E) 10 eV

SAMPLE QUESTION 44:
Consider a system of four non-identical spin 1/2 particles. What are the possible values of the total spin of the four-particle system and their corresponding degeneracy?

(A) which is two-fold degenerate, and which is two-fold degenerate
(B) which is two-fold degenerate, which is three-fold degenerate, and which
is non-degenerate
(C) which is two-fold degenerate, and which is non-degenerate
(D) which is two-fold degenerate, which is nine-fold degenerate, and which
is five-fold degenerate
(E) which is non-degenerate, which is three-fold degenerate, and which
is five-fold degenerate

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SAMPLE QUESTIONS 45 & 46:
In a region of space where there are no charges (), the electric field is given by , where are unit vectors along x-, y- and z-directions respectively. The y-component of the electric field was found to vary only along y-direction (i.e. it doesn't change along x- or z-direction).

SAMPLE QUESTION 45:
What is the value of the component?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 46:
Which of the following statements is TRUE?

(A) The aforementioned electric field is electrostatic.
(B) The displacement current is nonzero.
(C) If we place a small circular loop with its surface perpendicular to the z-direction, induced current will appear.
(D) The aforementioned electric field is due to the presence of a time-varying magnetic field.
(E) There is a net conductivity current along z-direction.
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SAMPLE QUESTION 47:
Suppose that the temperature of an initially very hot gas of hydrogen atoms is continually lowered until room temperature is reached, and that the intensity of the a-Lyman spectral line is observed with the help of a high resolution spectroscope. Which of the following statements is/are true for the process described above?

I. The width of the a-Lyman line continually decreases until it becomes vanishing.
II. The number of atoms that the ground level accomodates increases during the process.
III. The image of the a-Lyman line becomes more and more pronounced.
IV. Resonant fluoresence stops taking place by the time the temperature of the gas reaches room temperature.

(A) I and II only
(B) II and IV only
(C) II only
(D) I, II and III only
(E) II, III and IV only

SAMPLE QUESTION 48:
A cube has proper volume . What volume is calculated by an observer O' who moves at a velocity of 0.8c relative to the cube, in a direction parallel to one edge (of the cube)?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 49:
Two metalic spheres of radii and respectively, with are placed at a distance from each other, so that . There is a very thin conducting wire connecting the two far-apart spheres. A total charge is distributed between them. How much charge does the larger sphere carry (i.e. the sphere of radius ) ?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 50:
Solid A, with mass M is at its melting point . It is placed in thermal contact with solid B, with heat capacity and initially at temperature , where . The combination is thermally isolated. A has latent heat of fusion L and when it has melted has heat capacity . Supposing that A completely melts, what is the final common temperature of both A and B?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 51:
Two idential disks with mass M and radius R roll without sliding across a horizontal floor with the same speed and then up inclines. The two inclines are identical. Disk A rolls up its incline without sliding whereas disk B rolls up a frictionless incline. Disk A reaches a height of 12 cm above the horizontal floor before rolling down again. At what height does disk B reach above the horizontal floor before rolling down again?

(A) 24 cm
(B) 18 cm
(C) 12 cm
(D) 8 cm
(E) 6 cm

SAMPLE QUESTION 52:
Pi mesons at rest have a half-life of . If a beam of pi mesons is travelling at a speed of over what distance is the intensity of the beam halved? {}

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 53:
What is the ratio of the wavelength of the x-ray line for Nb (Z=41) to that of Ga (Z=31)?

(A) 9/16
(B) 16/9
(C) 3/4
(D) 4/3
(E) 41/31

SAMPLE QUESTION 54:
Which of the following is most essential for laser action to occur between two energy levels of an atom?

(A) The upper level should be a rapidly decaying state.
(B) The lasing material should be a gas.
(C) The lower level should be the ground state.
(D) There should be more atoms in the lower level than in the upper level.
(E) The upper level should be metastable.

SAMPLE QUESTION 55:
A light emitting diode (LED) emits light when:

(A) electrons are excited from the valence band to the conduction band.
(B) electrons collide with atoms.
(C) electrons are accelerated by the electric field in the depletion region.
(D) electrons from the conduction band recombine with holes from the valence band.
(E) the temperature of the junction has significantly increased.

SAMPLE QUESTION 56:
Suppose the operator where could in general be complex numbers. Under what conditions is a hermitian operator?

(A) Both and should be real numbers.
(B) Both and should be imaginary.
(C) should be imaginary and should be real number.
(D) should be real and should be imaginary.
(E) and should be complex conjugates of each other.

SAMPLE QUESTION 57:
Two ideal monatomic gases are in thermal equilibrium with each other. Gas A is composed of molecules with mass , while gas B is composed of molecules with mass . What is the ratio of the average molecular speeds ?

(A) 1/4
(B) 1/2
(C) 1
(D) 2
(E) 4

SAMPLE QUESTION 58:
In a certain mass spectrometer, an ion beam passes firstly through a velocity filter consisting of mutually perpendicular fields and . Afterwards, the beam enters a region of another magnetic field perpendicular to the beam. The radius of curvature of the resulting ion beam is proportional to which of the following?

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 59:
A vibrating tuning fork is held over a water column with one end closed and the other open. As the water level is allowed to fall, a loud sound is heard for water levels separated by 17 cm. If the speed of sound in air is 340 m/s, what is the frequency of the tuning fork?

(A) 250 Hz
(B) 500 Hz
(C) 1000 Hz
(D) 2000 Hz
(E) 5780 Hz

SAMPLE QUESTION 60:
A long straight cylindrical shell has inner radius and outer radius . It carries a current , uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow region (). The magnetic field is zero everywhere in the hollow region. Which of the following statements is TRUE?

(A) The wire is on the cylinder axis and carries current in the same direction as the current in the shell.
(B) The wire may be anywhere in the hollow region but must be carrying current in the direction opposite to that of the current in the shell.
(C) The wire may be anywhere in the hollow region but must be carrying current in the same direction as the current in the shell.
(D) The wire is on the cylinder axis and carries current in the direction opposite to that of the current in the shell.
(E) The wire doesn't carry any current.

SAMPLE QUESTION 61:
Suppose that the Hamiltonian of the (valence) electron of a triply ionized Ti atom (Z = 22) is given by , where and are real numbers (parameters of the problem), and denotes the unit operator. In terms of the given parameters, what are the possible energy eigenstates and their corresponding denegeracy?

(A) which is ten-fold degenerate
(B) which is six-fold degenerate and which is four-fold degenerate
(C) which is five-fold degenerate and which is five-fold degenerate
(D) which is four-fold degenerate and which is six-fold degenerate
(E) which is four-fold degenerate and which is six-fold degenerate

SAMPLE QUESTION 62:
Consider a system with two energy levels and with and total number of particles where and is the number of particles accomodated by the first and second energy level respectively. The system is in contact with a heat reservoir at temperature T. At some moment one particle decays from the upper energy level to the lower one (i.e. we have the transition ). What is the change in the entropy of the system of the two energy levels? ( denotes the Boltzmann constant)

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 63:
Two thermal engines are connected so that the heat rejected by the first thermal engine withefficiency be absorbed by a second thermal engine with efficiency . The efficiency of the combined system of the two thermal engines is

(A)
(B)
(C)
(D)
(E)

SAMPLE QUESTION 64:
Suppose that is a Hermitian operator, and let us further define the operator . Which of the following statements is/are FALSE?

I. The operator is unitary.
II. The determinant of the operator is invariant under a similarity transformation.
III. The determinant of the operator is given by .
IV. The eigenvalues of the operator are real.

(A) Statements I and III only
(B) Statements II and III only
(C) Statement IV only
(D) Statement III only
(E) Statements III and IV only

SAMPLE QUESTION 65:
In a neutron-induced fission process, what is the origin of the delayed neutrons?

(A) They are produced by the moderator material.
(B) They are produced by the original nucleus after it absorbs a neutron.
(C) They are components of the cosmic background radiation.
(D) They are produced by the fission fragments.
(E) They are produced by the control rods of the fission reactor.

SAMPLE QUESTION 66:
In an RLC series circuit the capacity C is variable. The RLC series circuit is driven by an external source of time-varying voltage. By changing the capacity C of the circuit in a continuous manner over a sufficiently wide range two well defined discrete resonances are observed with the help of an oscilloscope, for and . Which of the following statements is/are always TRUE?

I. The external time-varying voltage consists of at least two sinusoidal components of different frequencies.
II. The bandwidth of each resonance is small compared to the difference between the two observed resonant frequencies.
III. If and are the two observed resonant frequencies, then it is .

(A) III only
(B) All of the above statements
(C) II and III only
(D) II only
(E) I and II only

SAMPLE QUESTION 67:
Which of the following statements is NOT true?

(A) A continuous spectrum is one that contains all the wavelengths of visible light, such as that emitted by an incandescent material.
(B) Band spectra are characteristic emissions produced by excited molecules. The bands are actually groups of lines very close together.
(C) Fluorescence is the process by which bodies absorb shorter wavelengths of light and subsequently emit light of longer wavelengths.
(D) Fraunhofer lines are dark lines in the atomic spectrum of helium.
(E) A bright line spectrum consists of bright lines at wavelengths characteristic of the elements emitting them when excited in the gaseous state.

SAMPLE QUESTION 68:
Two point sources, oscillating in phase, produce an interference pattern over the surface of the water of a tank. If the frequency of oscillation of the two point sources is increased by 20%, then the number of the dark fringes (fringes due to destructive interference)

(A) is roughly increased by 40%.
(B) is roughly increased by 20%.
(C) is roughly decreased by 20%
(D) is roughly decreased by 40%.
(E) remains invariant.

SAMPLE QUESTION 69:
A homogeneous uniform rod is initially at rest on a frictionless surface. At some moment, forces of equal magnitude and opposite direction are applied at the two edges of the rod. Each force is applied in a direction normal to the length of the rod, and parallel to the surface on which the latter lies. Which of the following quantities does NOT change after the application of the aforementioned forces?

(A) The angular momentum of the rod with respect to an axis normal to the frictionless surface.
(B) The net torque with respect to the center of mass of the rod.
(C) The total kinetic energy of the rod.
(D) The momentum of the center of mass of the rod.
(E) The total energy of the rod.

SAMPLE QUESTION 70:
A thin uniform and homogeneous rod is suspended on a ceiling and is initially at rest (in a vertical position). When the previous rod is partially immersed into a liquid of density , it comes into equilibrium when half of it is immersed into the liquid, at an angle with the vertical orientation (i.e. within the liquid the new equilibrium position of the rod is not the vertical one any more). What is the density of the rod in terms of the density of the liquid?

(A) It is .
(B) It is .
(C) It is .
(D) It is .
(E) It is .
Last edited by physics_auth on Wed Jan 17, 2018 3:26 pm, edited 106 times in total.

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: All 31 posted sample PGRE quest. & ETS-released sample quest

Really nice pool of questions.. i really appreciate it.. can you please post the answers too.. i am planning to take them as a short test..
by the way.. i might be a bit nosy but you don't seem to be a student.. who are you exactly? .

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: Answers to all posted sample questions

ANSWERS TO ALL POSTED SAMPLE QUESTIONS:

SAMPLE QUESTION 1: (E)
SAMPLE QUESTION 2: (E)
SAMPLE QUESTION 3: (A)
SAMPLE QUESTION 4: (C)
SAMPLE QUESTION 5: (C)
SAMPLE QUESTION 6: (A)
SAMPLE QUESTION 7: (B)
SAMPLE QUESTION 8: (E)
SAMPLE QUESTION 9: (C)
SAMPLE QUESTION 10: (D)
SAMPLE QUESTION 11: (C)
SAMPLE QUESTION 12: (D)
SAMPLE QUESTION 13: (D)
SAMPLE QUESTION 14: (C)
SAMPLE QUESTION 15: (A)
SAMPLE QUESTION 16: (A)
SAMPLE QUESTION 17: (B)
SAMPLE QUESTION 18: (A)
SAMPLE QUESTION 19: (C)
SAMPLE QUESTION 20: (B)
SAMPLE QUESTION 21: (Α)
SAMPLE QUESTION 22: (D)
SAMPLE QUESTION 23: (B)
SAMPLE QUESTION 24: TBA
SAMPLE QUESTION 25: (E)
SAMPLE QUESTION 26: (D)
SAMPLE QUESTION 27: (D)
SAMPLE QUESTION 28: (C)
SAMPLE QUESTION 29: (C)
SAMPLE QUESTION 30: (E)
SAMPLE QUESTION 31: (D)
SAMPLE QUESTION 32: TBA
SAMPLE QUESTION 33: (D)
SAMPLE QUESTION 34: (B)
SAMPLE QUESTION 35: (D)
SAMPLE QUESTION 36: TBA
SAMPLE QUESTION 37: (C)
SAMPLE QUESTION 38: (C)
SAMPLE QUESTION 39: (A)
SAMPLE QUESTION 40: (C)
SAMPLE QUESTION 41: (D)
SAMPLE QUESTION 42: TBA
SAMPLE QUESTION 43: (B)
SAMPLE QUESTION 44: TBA
SAMPLE QUESTION 45: (C)
SAMPLE QUESTION 46: (D)
SAMPLE QUESTION 47: (C)
SAMPLE QUESTION 48: (C)
SAMPLE QUESTION 49: (D)
SAMPLE QUESTION 50: (A)
SAMPLE QUESTION 51: (D)
SAMPLE QUESTION 52: (A)
SAMPLE QUESTION 53: (A)
SAMPLE QUESTION 54: (E)
SAMPLE QUESTION 55: (D)
SAMPLE QUESTION 56: (C)
SAMPLE QUESTION 57: (D)
SAMPLE QUESTION 58: (B)
SAMPLE QUESTION 59: (B)
SAMPLE QUESTION 60: (E)
SAMPLE QUESTION 61: (E)
SAMPLE QUESTION 62: TBA
SAMPLE QUESTION 63: TBA
SAMPLE QUESTION 64: E
SAMPLE QUESTION 65: TBA
SAMPLE QUESTION 66: TBA
SAMPLE QUESTION 67: TBA
SAMPLE QUESTION 68: TBA
SAMPLE QUESTION 69: TBA
SAMPLE QUESTION 70: TBA
Last edited by physics_auth on Tue Jan 16, 2018 5:58 am, edited 54 times in total.

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: All 31 posted sample PGRE quest. & ETS-released sample quest

physics_auth wrote:
blackcat007 wrote:Really nice pool of questions.. i really appreciate it.. can you please post the answers too.. i am planning to take them as a short test..
by the way.. i might be a bit nosy but you don't seem to be a student.. who are you exactly? .

No, I am a graduate student who has finished with all tests (not from US), but due to the fact that I missed the November deadlines for PGRE (I sat it in spring and) I have to wait some more time in order to be able to apply for the fall 2010 or the spring 2009, though I have limited opportunities in the latter case. Anyway, I plan to ask advise when is better to do so... .

P.S.: If I knew how to post images taken from pdfs i would have posted even more questions. Some questions require a figure or else they will tend to be very lengthy and probably appalling for many of you. The good thing about all this is that when I constructed some questions, I "bumped into" them in the real test, but the irony is that I didn't pay much attention to them before! One such question was about Coriolis effect. Physics_auth

AFAIK spring sems are poorly funded, and since you are an intl student, may be it will be exorbitant for you. i think fall 2010 will be better
well if you have your homepage you can load them there and give the link here. or you may even mail them to the interested members.
hmm coriolis effect?? i thought they never ask such questions.. what else did you encounter new?

oh and yes.. please post the answers for these questions

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Analytic solution of question 27 (soap films)

physics_auth wrote:Question 27:
This is a hard PGRE question. At first, I would like to say that I omitted to say that the soap film is surrounded by air. Anyway. I corrected it. The reflected beam includes the ray that is reflected by the upper surface of the film and that that is reflected by the lower surface of it. The phase difference is in general:
Δφ = phase difference due to different optical path + phase shift due to reflection

In our case it is:
phase difference due to different optical path = (2π/λ) *(2nd) = 4πnd/λ
phase shift due to the reflection off the upper surface of the film = π
thus Δφ = 4πnd/λ + π and for constructive interference it should be Δφ = 2mπ, where m = integer. For constructive interference it is therefore
4πnd/λ + π = 2mπ => {constant quantity} = 4nd = (2m - 1)λ (1)
From (1) it is that as λ increases, the order of interference should decrease so that their product is constant (since d and n are given, constant quantities).
Let's assume that the order of interference that corresponds to λ1 = 480 nm is m1, then since no other wavelength between 480 nm and 800 nm is intensified in the reflected beam, it should be that
m2 = m1 - 1 (2),
where m2 the order of interference of wv λ2 = 800 nm, since according to (1) for λ2 > λ1 it should be m2 < m1 (since the left hand product of (1) is constant quantity). This explains why in (2) we got minus 1 instead of plus 1.
Applying (1) for m1 and m2 and equating the righ-hand members of the equations (i.e eliminating the constant product) we find a relationship between m1 and m2. If in this last equation we substitute m2 from (2), then we have an equation of only one variable -> m1. After some algebra it is found that m1 = 3. By substituting m1 = 3 into (1) and solving for d we end up to answer (D).
Last edited by physics_auth on Mon Aug 17, 2009 6:09 pm, edited 5 times in total.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: All 31 posted sample PGRE quest. & ETS-released sample quest

blackcat007 wrote:
physics_auth wrote:
blackcat007 wrote:Really nice pool of questions.. i really appreciate it.. can you please post the answers too.. i am planning to take them as a short test..
by the way.. i might be a bit nosy but you don't seem to be a student.. who are you exactly? .

No, I am a graduate student who has finished with all tests (not from US), but due to the fact that I missed the November deadlines for PGRE (I sat it in spring and) I have to wait some more time in order to be able to apply for the fall 2010 or the spring 2009, though I have limited opportunities in the latter case. Anyway, I plan to ask for advice when is better to do so... .

P.S.: If I knew how to post images taken from pdfs i would have posted even more questions. Some questions require a figure or else they will tend to be very lengthy and probably appalling for many of you. The good thing about all this is that when I constructed some questions, I "bumped into" them in the real test, but the irony is that I didn't pay much attention to them before! One such question was about Coriolis effect. Physics_auth

AFAIK spring sems are poorly funded, and since you are an intl student, may be it will be exorbitant for you. i think fall 2010 will be better
well if you have your homepage you can load them there and give the link here. or you may even mail them to the interested members.
hmm coriolis effect?? i thought they never ask such questions.. what else did you encounter new?

oh and yes.. please post the answers for these questions

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: Analytic solution of question 27 (soap films)

physics_auth wrote:
physics_auth wrote:Question 27:
This is a hard PGRE question. At first, I would like to say that I omitted to say that the soap film is surrounded by air. Anyway. I corrected it. The reflected beam includes the ray that is reflected by the upper surface of the film and that that is reflected by the lower surface of it. The phase difference is in general:
Δφ = phase difference due to different optical path + phase shift due to reflection

In our case it is:
phase difference due to different optical path = (2π/λ) *(2nd) = 4πnd/λ
phase shift due to the reflection off the upper surface of the film = π
thus Δφ = 4πnd/λ + π and for constructive interference it should be Δφ = 2mπ, where m = integer. For constructive interference it is therefore
4πnd/λ + π = 2mπ => {constant quantity} = 4nd = (2m - 1)λ (1)
From (1) it is that as λ increases, the order of interference should decrease so that their product is constant (since d and n are given, constant quantities).
Let's assume that the order of interference that corresponds to λ1 = 480 nm is m1, then since no other wavelength between 480 nm and 800 nm is intensified in the reflected beam, it should be that
m2 = m1 - 1 (2),
where m2 the order of interference of wv λ2 = 800 nm, since according to (1) for λ2 > λ1 it should be m2 < m1 (since the left hand product of (1) is constant quantity). This explains why in (2) we got minus 1 instead of plus 1.
Applying (1) for m1 and m2 and equating the righ-hand members of the equations (i.e eliminating the constant product) we find a relationship between m1 and m2. If in this last equation we substitute m2 from (2), then we have an equation of only one variable -> m1. After some algebra it is found that m1 = 3. By substituting m1 = 3 into (1) and solving for d we end up to answer (D).

this was really a nice and conceptual question. thanks!!

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: Three NEW questions for futher practice

physics_auth wrote:
EXTRA QUESTION 3:
Infrared electromagnetic radiation of broad range (it covers near and far infrared) is sent to pass through a gaseous mixture which consists amongst others of the following diatomic molecules

H_2, O_2, CO, HCl, N_2, HF, HI

Which of the above molecules will absorb the incident radiation?

(A) All of them
(B) HCl, HF, HI and O_2 only
(C) H_2, O_2 and N_2 only
(D) CO, HCl, HF and HI only
(E) None of the above

what is the principle used in this question?

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: Three NEW questions for futher practice

what is the principle used in this question?

Brief answer: As you may have noticed, the question pertains to diatomic molecules. The difference between these molecules is that some of them are homonuclear molecules whereas the rest of them aren't. The theory for diatomic molecules (if we ignore electronic transitions) says that the spectrum is composed of two components: (1) the vibrational component, whose spectrum looks like the energy levels of a quantum mechanical harmonic oscillator, and which obeys the selection rule Δn = {+1, -1}, where n as in equation E_n = (n + 1/2) * hbar*ω, and (2) the rotational component, whose spectrum is composed of a series of very closely situated -but non-equidistant- energy levels, and which obeys the selection rule Δl = {+1, -1}, where l is the quantum number of angular momentum. For in general the rotational energy is much smaller than the vibrational energy (about 1000 times smaller -in eV-) it comes out that to each vibrational level there correspond several rotational levels. In a typical diatomic spectrum, for instance, we have a vibrational level upon which sits a sequence of rotational levels, then at a greater energy height there is the next vibrational level upon which sits another sequence of rotational levels and so on. Under normal cisrcumstances, a molecule lies in the lowest vibrational level (though, it can occupy any rotational level of the sequence that sits upon the fundamental vibrational level). Keep in mind that allowed transitions are only those which conform with both of the selection rules mentioned above (one for each component). The above behavior is valid for the lower energy states, for higher enough states the situation is different.

For diatomic molecules, the rotational spectrum corresponds usually to the far infrared region, the vibrational spectrum corresponds usually to the near infrared region and the electronic spectrum is further, corresponding to the unltraviolet region or beyond. Since, the radiation employed covers infrared region (near to far), electronic transitions are indifferent to our case. Now, the essential point of the questions is this: For either a vibrational or a rotational transition to occur, either in emission or absorption, the diatomic molecule must have a permanent electric dipole moment so that it can behave as a rotating or oscillating electric dipole which, according to the classical electromagnetic theory, will radiate (and amongst others be able to come back to its fundamental energy level after it has been excited in some way). Homonuclear molecules H_2, O_2, N_2 do NOT have permanent electric dipole moment and do not show the spectrum discussed above, i.e. they do not absorb the incident infrared radiation. On the other hand, heteronuclear molecules such as CO, HCl, HF and HI have permanent electric dipole moment and show strong such spectrums, which means that they absorb the incident infrared radiation. To see why these molecules have permanent electric moment remember from basic chemistry how the electronegativity series develops ... with the hydrogen being the least electronegative element ... . Thus, the correct answer is (D).

sravanskarri
Posts: 58
Joined: Sat Jun 14, 2008 10:19 pm

### Re: ==> Sticky: More ETS and User-Created Sample Questions

Can you pls explain the solution for extra question 5. I think we need to apply rocket eq but I could not get to the answer. Was this on the sample GRE Qs ?

Thanks for the previous posts

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: ==> Sticky: More ETS and User-Created Sample Questions

sravanskarri wrote:Can you pls explain the solution for extra question 5. I think we need to apply rocket eq but I could not get to the answer. Was this on the sample GRE Qs ?

Thanks for the previous posts

I did it in this way:
since the thread is pulled at constant rate 10cm/s, thus the spool is rotating at a constant rate of v/r (since there is no slipping) any element of the thread in contact with the spool is also rotating at this constant angular velocity, thus it has only centrifugal acceleration (in non inertial frame) v^2/r , now as each segment leaves the cylinder, the only change in acceleration is from v^2/r to 0 (0 acceleration when it leaves the spool contact) thus the answer is v^2/r=0.01/0.05 = 0.2 m/s^2.

sravanskarri
Posts: 58
Joined: Sat Jun 14, 2008 10:19 pm

### Re: ==> Sticky: More ETS and User-Created Sample Questions

Thanks for the reply. But isn't the change in magnitude of acceleration of the "string" zero; when it is in contact with the cylinder it has a_radial = v^2/r and a_tangential =0 => total magnitude is a_radial and when the string comes off the cylinder it is a_tangential = v^2/r and a_radial = 0 leaving the magnitude constant.

I thought there will be some change in velocity due to some mass leaving the cylinder + string system...giving it some acceleration.May be I overdid it.

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: ==> Sticky: More ETS and User-Created Sample Questions

sravanskarri wrote: when the string comes off the cylinder it is a_tangential = v^2/r and a_radial = 0 leaving the magnitude constant.

no since the thread is being pulled at a constant rate ie 10cm/s there is no tangential acceleration.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: More ETS and User-Created Sample Questions

sravanskarri wrote:Thanks for the reply. But isn't the change in magnitude of acceleration of the "string" zero; when it is in contact with the cylinder it has a_radial = v^2/r and a_tangential =0 => total magnitude is a_radial and when the string comes off the cylinder it is a_tangential = v^2/r and a_radial = 0 leaving the magnitude constant.

I thought there will be some change in velocity due to some mass leaving the cylinder + string system...giving it some acceleration.May be I overdid it.

The solution given by blackcat007 is absolutely correct. It is a simple exercise in kinematics. Simply focus on what is going with the acceleration, which changes from υ^2 / R (centripetal only) to zero because the thread leaves the cylinder with a contant velocity thus zero acceleration. Please, do not make very complex thoughts, since the questions must be answered in at most 2 to 3 minutes. The questions I post in this thread are not ETS questions, but noone knows if they have ever been included in the real physics test (or even if a similar concept has appeared in the real test). Anyway, the underlying intention of my posted questions is simply to emphasize some details that may be helpful somehow for one's preparation. Furthermore, though it is highly improbable for you to meet a question in the real test that will be facsimile of the above questions, it is very probable to apply some of the strategies you used to solve some of the sample questions in the solution of your real test questions. This is also an aspect of success. I think so. By the way, if anyone of you want to see harder questions, let me know (send a message or sth, but i am not going to provide harder questions than those appeared in the 9677 real test!)

p.s.: ETS sample questions are in a pdf released archive. I describe how one can find it in some previous response in this thread. Know, in general that the questions in the real test are going to be a bit harder than the sample questions that ETS releases!

Physics_auth

sravanskarri
Posts: 58
Joined: Sat Jun 14, 2008 10:19 pm

### Re: ==> Sticky: More ETS and User-Created Sample Questions

My bad. Agree with the solution. As I mentioned earlier, I kind of mis-understood the Q, at this part

>>"As each small segment of string leaves the cylinder, by what amount does its acceleration change"

I never thought "its acceleration" implied "string acceleration" but "cylinder acceleration" which is a foolish mistake on my part. I did not mean to say the questions you had need to be from ETS. Please keep posting ,the questions are really good and helping me identify my shortcomings.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: More ETS and User-Created Sample Questions

sravanskarri wrote:My bad. Agree with the solution. As I mentioned earlier, I kind of mis-understood the Q, at this part

>>"As each small segment of string leaves the cylinder, by what amount does its acceleration change"

I never thought "its acceleration" implied "string acceleration" but "cylinder acceleration" which is a foolish mistake on my part. I did not mean to say the questions you had need to be from ETS. Please keep posting ,the questions are really good and helping me identify my shortcomings.

As you correctly found, it refers to the string acceleration. Keep in mind this: if in a question you make a more complex ratiocination than necessary -> by taking a quick look at the answer choices it may help you to "harness" your ratiocination. Keep also in mind that: (as I have observed) though ETS scarcely provides more information in a question than necessary to find its solution (maybe in a way to cause confusion to the candidate), they never provide questions deficient of data. All data necessary for the solution are given. If you think that sth is missed then you probably made a more complex ratiocination than required.

Sorry, if i misunderstood your answer but I usually visit the site deep in the night and sometimes it is possible to miss sth ... . You know.

Physics_auth

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: ==> Sticky: More ETS and User-Created Sample Questions

yeah physics_auth please keep posting your questions they are very helpful.. the only prob i am facing is knowing the the topics widely. i have found that the topics which i know like EM, mechanics etc ;i am able to answer almost all, but topics like particle physics and stuffs, really are keeping me low sravanskarri
Posts: 58
Joined: Sat Jun 14, 2008 10:19 pm

### Re: ==> Sticky: More ETS and User-Created Sample Questions

Thanks for the Questions.. they are pretty clear ..I am feeling a little better now betelgeuse1
Posts: 116
Joined: Sat May 09, 2009 10:14 am

### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

small problem with problem 16: The Idea is to integrate 2/L * Sin^2(n pi x/L) from 5L/6 to L/2
I obtain Integral(1/2-Cos(2 n pi x/L)/2)dx and that gives (1/2)x from L/2 to 5L/6 minus a term depending on Sin(2 n pi x/L) from L/2 to 5L/6.
Now if the last term (the one depending on Sin) is zero the I obtain the probability for the particle to be there as 1/3 and the prob of not being there as 2/3 i.e. answer A but the problem is that Sin (2 n pi x/L) for n=2 and x=5L/6 is not zero as it is for x=L/2 so the Sine term is not zero so you won't get 2/3.
Do I make a mistake here?

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

betelgeuse1 wrote:small problem with problem 16: The Idea is to integrate 2/L * Sin^2(n pi x/L) from 5L/6 to L/2
I obtain Integral(1/2-Cos(2 n pi x/L)/2)dx and that gives (1/2)x from L/2 to 5L/6 minus a term depending on Sin(2 n pi x/L) from L/2 to 5L/6.
Now if the last term (the one depending on Sin) is zero the I obtain the probability for the particle to be there as 1/3 and the prob of not being there as 2/3 i.e. answer A but the problem is that Sin (2 n pi x/L) for n=2 and x=5L/6 is not zero as it is for x=L/2 so the Sine term is not zero so you won't get 2/3.
Do I make a mistake here?

Try to solve the problem using single geometry related to the probability density. For example the prob. density partitions into three sections from [0, L/3], [L/3, 2L/3] ... . See where the midpoints of these intervals are and use simple geometric thoughts to find the asked probability (don't forget to subtract your result from 1). For example the probability of finding the particle in [L/3, 2L/3] = 1/3, use that kind of geometrical manipulations. This method is quicker ... .

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

betelgeuse1 wrote:small problem with problem 16: The Idea is to integrate 2/L * Sin^2(n pi x/L) from 5L/6 to L/2
I obtain Integral(1/2-Cos(2 n pi x/L)/2)dx and that gives (1/2)x from L/2 to 5L/6 minus a term depending on Sin(2 n pi x/L) from L/2 to 5L/6.
Now if the last term (the one depending on Sin) is zero the I obtain the probability for the particle to be there as 1/3 and the prob of not being there as 2/3 i.e. answer A but the problem is that Sin (2 n pi x/L) for n=2 and x=5L/6 is not zero as it is for x=L/2 so the Sine term is not zero so you won't get 2/3.
Do I make a mistake here?

apart from the method mentioned by Physics_auth here is another one: 2nd excited means n=3, (n=1 is ground state) and the probability of not finding the particle in between L/2 and 5L/6 is (1- Probability of finding the particle between L/2 and 5L/6 )

betelgeuse1
Posts: 116
Joined: Sat May 09, 2009 10:14 am

### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

UPS! It's a bad idea to start solving problems when you are ILL like me now... so the second EXCITED state, not the second state: n=3 ok!

betelgeuse1
Posts: 116
Joined: Sat May 09, 2009 10:14 am

### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

physics_auth: Nice method! any other nice tricks you may write about?

betelgeuse1
Posts: 116
Joined: Sat May 09, 2009 10:14 am

### problem 30, particle alert!

what if the interaction is weak? As I know you should specify something about the life time of the stable initial state, otherwise you could choose D too if strangeness is not conserved... I agree with the conservation of barion number though betelgeuse1
Posts: 116
Joined: Sat May 09, 2009 10:14 am

### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

me again : problem 34: I don't have any idea about it now... some hlp! I guess quantum tunneling is not the solution...

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: problem 30, particle alert!

betelgeuse1 wrote:what if the interaction is weak? As I know you should specify something about the life time of the stable initial state, otherwise you could choose D too if strangeness is not conserved... I agree with the conservation of barion number though My intention in this question is to check if you know selection rules for strangeness. If the interaction is strong or electromagnetic then ΔS = 0, whereas if it is weak it holds that ΔS = +1 or -1 (but not zero). The answers are carefully selected so that there is only one answer that can cover all three cases. This is why I don't mention sth about the kind of interaction. Did you get my point?

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

betelgeuse1 wrote:me again : problem 34: I don't have any idea about it now... some hlp! I guess quantum tunneling is not the solution...

Simply use the formula about the reflection coefficient for the one-dimensional scattering in a potential step. If you don't remember it by heart, then try to work out this formula analytically. Then, check if you can make a mnemonics so as to remember it for the exam or invent a more quick way that will help you find the asked formula in the quickest possible time. Use your imagination in the latter case ... . You expect the formula for the reflection coefficient to depend on E and the step height amongst other possible things. And be carefull -> it is a step not a barrier.

physics_auth
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### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

blackcat007 wrote:
betelgeuse1 wrote:small problem with problem 16: The Idea is to integrate 2/L * Sin^2(n pi x/L) from 5L/6 to L/2
I obtain Integral(1/2-Cos(2 n pi x/L)/2)dx and that gives (1/2)x from L/2 to 5L/6 minus a term depending on Sin(2 n pi x/L) from L/2 to 5L/6.
Now if the last term (the one depending on Sin) is zero the I obtain the probability for the particle to be there as 1/3 and the prob of not being there as 2/3 i.e. answer A but the problem is that Sin (2 n pi x/L) for n=2 and x=5L/6 is not zero as it is for x=L/2 so the Sine term is not zero so you won't get 2/3.
Do I make a mistake here?

apart from the method mentioned by Physics_auth here is another one: 2nd excited means n=3, (n=1 is ground state) and the probability of not finding the particle in between L/2 and 5L/6 is (1- Probability of finding the particle between L/2 and 5L/6 )[/quote

Yeah man. It is impossible that ETS will ask you to use Bragg's formula for a non-simple cubic lattice, since in this case one needs to know things about Miller indices, and the edge of the cube also, in order to use a formula for the distance between lattice planes. At least me I have never met such question in PGRE. By the way what type of radiation do you think is used in practice to illustrate Bragg's law? Monochromatic or of continuous spectrum and why (give a possible explanation)?

physics_auth
Posts: 163
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### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

physics_auth wrote:
blackcat007 wrote:
betelgeuse1 wrote:small problem with problem 16: The Idea is to integrate 2/L * Sin^2(n pi x/L) from 5L/6 to L/2
I obtain Integral(1/2-Cos(2 n pi x/L)/2)dx and that gives (1/2)x from L/2 to 5L/6 minus a term depending on Sin(2 n pi x/L) from L/2 to 5L/6.
Now if the last term (the one depending on Sin) is zero the I obtain the probability for the particle to be there as 1/3 and the prob of not being there as 2/3 i.e. answer A but the problem is that Sin (2 n pi x/L) for n=2 and x=5L/6 is not zero as it is for x=L/2 so the Sine term is not zero so you won't get 2/3.
Do I make a mistake here?

apart from the method mentioned by Physics_auth here is another one: 2nd excited means n=3, (n=1 is ground state) and the probability of not finding the particle in between L/2 and 5L/6 is (1- Probability of finding the particle between L/2 and 5L/6 )[/quote

Yeah man. It is impossible that ETS will ask you to use Bragg's formula for a non-simple cubic lattice, since in this case one needs to know things about Miller indices, and the edge of the cube also, in order to use a formula for the distance between lattice planes. At least me I have never met such question in PGRE.

Blackcat -> By the way what type of radiation do you think is used in practice to illustrate Bragg's law? Monochromatic or of continuous spectrum and why (give a possible explanation)?

blackcat007
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### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

Blackcat -> By the way what type of radiation do you think is used in practice to illustrate Bragg's law? Monochromatic or of continuous spectrum and why (give a possible explanation)?

well i think it should be monochromatic, because if its a continuous spectrum, then for a given lattice spacing, the final pattern of diffraction will be very cumbersome.. there will resolution problem (Rayleigh's Criterion), ie difficult to resolve, since dispersion d(theta)/d(lambda) will be very large and thus overlapping will prevent proper identification of the angle diffreacted.
The wavelength is continuous, so in 2*d*sin(theta)=n*(lambda), since lambda is continuous we will get a continuous pattern and thus difficult to differentiate.

physics_auth
Posts: 163
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### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

blackcat007 wrote:
Blackcat -> By the way what type of radiation do you think is used in practice to illustrate Bragg's law? Monochromatic or of continuous spectrum and why (give a possible explanation)?

well i think it should be monochromatic, because if its a continuous spectrum, then for a given lattice spacing, the final pattern of diffraction will be very cumbersome.. there will resolution problem (Rayleigh's Criterion), ie difficult to resolve, since dispersion d(theta)/d(lambda) will be very large and thus overlapping will prevent proper identification of the angle diffreacted.
The wavelength is continuous, so in 2*d*sin(theta)=n*(lambda), since lambda is continuous we will get a continuous pattern and thus difficult to differentiate.

Good attempt, but we use radiation of continuous spectrum. In fact, it is difficult to find the correct direction of the incident ray -assuming it is monochromatic- for which it can lead to Bragg diffraction. Besides the detector assumes only a small solid angle in space - detectors of solid angle of 4π are only very rarely used due their high cost (and probably other factors that I miss... for the time being). By using a continuous radiation, Bragg diffraction picks automatically out all these wavelengths that satisfy Bragg's law and in the pattern in the output we see well resolved peaks sitting upon an almost flat background. The peaks do correspond to Bragg reflections (or diffractions) and then we try to find out which possible groups of lattice planes could give a specific peak (this is done by the formula that connects d -the distance between consecutive planes in a group- with the Miller indices and the dimensions of the cell.) The point is that we don't know in advance which group of planes (i.e. the d) has given a specific Bragg reflection ... .

blackcat007
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### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

physics_auth wrote:
blackcat007 wrote:
Blackcat -> By the way what type of radiation do you think is used in practice to illustrate Bragg's law? Monochromatic or of continuous spectrum and why (give a possible explanation)?

well i think it should be monochromatic, because if its a continuous spectrum, then for a given lattice spacing, the final pattern of diffraction will be very cumbersome.. there will resolution problem (Rayleigh's Criterion), ie difficult to resolve, since dispersion d(theta)/d(lambda) will be very large and thus overlapping will prevent proper identification of the angle diffreacted.
The wavelength is continuous, so in 2*d*sin(theta)=n*(lambda), since lambda is continuous we will get a continuous pattern and thus difficult to differentiate.

Good attempt, but we use radiation of continuous spectrum. In fact, it is difficult to find the correct direction of the incident ray -assuming it is monochromatic- for which it can lead to Bragg diffraction. Besides the detector assumes only a small solid angle in space - detectors of solid angle of 4π are only very rarely used due their high cost (and probably other factors that I miss... for the time being). By using a continuous radiation, Bragg diffraction picks automatically out all these wavelengths that satisfy Bragg's law and in the pattern in the output we see well resolved peaks sitting upon an almost flat background. The peaks do correspond to Bragg reflections (or diffractions) and then we try to find out which possible groups of lattice planes could give a specific peak (this is done by the formula that connects d -the distance between consecutive planes in a group- with the Miller indices and the dimensions of the cell.) The point is that we don't know in advance which group of planes (i.e. the d) has given a specific Bragg reflection ... .

but then how do we know which was the wavelength that actually created the diffraction pattern that the detector is detecting? suppose i use lambda varying from say 5-6 nm, and we want to find the plane spacing d, we know theta, and as you said, we try to see which plane was responsible for the diffraction.. then which value of wavelength we use?

blackcat007
Posts: 378
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### Re: ==> Sticky: More ETS and 41 "active" Sample Questions

blackcat007 wrote:
physics_auth wrote:Blackcat -> By the way what type of radiation do you think is used in practice to illustrate Bragg's law? Monochromatic or of continuous spectrum and why (give a possible explanation)?

well i think it should be monochromatic, because if its a continuous spectrum, then for a given lattice spacing, the final pattern of diffraction will be very cumbersome.. there will resolution problem (Rayleigh's Criterion), ie difficult to resolve, since dispersion d(theta)/d(lambda) will be very large and thus overlapping will prevent proper identification of the angle diffreacted.
The wavelength is continuous, so in 2*d*sin(theta)=n*(lambda), since lambda is continuous we will get a continuous pattern and thus difficult to differentiate.

Good attempt, but we use radiation of continuous spectrum. In fact, it is difficult to find the correct direction of the incident ray -assuming it is monochromatic- for which it can lead to Bragg diffraction. Besides the detector assumes only a small solid angle in space - detectors of solid angle of 4π are only very rarely used due their high cost (and probably other factors that I miss... for the time being). By using a continuous radiation, Bragg diffraction picks automatically out all these wavelengths that satisfy Bragg's law and in the pattern in the output we see well resolved peaks sitting upon an almost flat background. The peaks do correspond to Bragg reflections (or diffractions) and then we try to find out which possible groups of lattice planes could give a specific peak (this is done by the formula that connects d -the distance between consecutive planes in a group- with the Miller indices and the dimensions of the cell.) The point is that we don't know in advance which group of planes (i.e. the d) has given a specific Bragg reflection ... .

hehehe somehow in experimental physics things turn out the opposite of what i think.. !!! thats a clue.. i will answer whatever seems wrong to me in experimental physics questions betelgeuse1
Posts: 116
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

Now that I jumped into the pool and came out in a poor condition but still alive I would like to see the other pool... you said something about harder problems. Where are they?

physics_auth
Posts: 163
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

betelgeuse1 wrote:Now that I jumped into the pool and came out in a poor condition but still alive I would like to see the other pool... you said something about harder problems. Where are they?

I will NOT post this other pool that is mentioned in this thread. However, I can send it via an e-mail upon "private" request (it is a pdf archive and a pdf with solutions). It is a small pool of 60 questions with brief answers only. I have already sent it to blackcat007. You can ask for his opinion as well.

Don't worry if my pool "brought to light" possible weaknesses... it is your responsibility to find out your weak points and re-read the pertinent piece of material to see if you missed any essential detail. I will be glad to hear that this pool helped you -even a bit- to answer correctly one, two or more questions in the real test.

betelgeuse1
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

First about problem 34: I don't understand how is it possible to solve this problem using R=(k1-k2)^2/(k1+k2)^2, k1~sqrt(E) and k2~sqrt(E-V) in 2 minutes. I am sure there may be a quicker solution but I don't get it.

physics_auth
Posts: 163
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

betelgeuse1 wrote:First about problem 34: I don't understand how is it possible to solve this problem using R=(k1-k2)^2/(k1+k2)^2, k1~sqrt(E) and k2~sqrt(E-V) in 2 minutes. I am sure there may be a quicker solution but I don't get it.

Who told you that all questions in PGRE are designed to be solved in 2 minutes? There are always questions that require >2 minutes. If you pinpoint such questions in the test you can avoid them in a first browsing, and return to them at a later time, given that there is sufficient time to do so! If you stick to such "time-consuming" questions then you will probably miss time to solve easier questions. From my experience, when the answers to a question are in the form of pure numbers then there is no trick to zero in on the correct result. You can only eliminate answers that are false according to your physics knowledge or intuition. But in such questions the test comittee want you to do some rough calculation and for this reason 2 or 3 answers can not be eliminated unless you have done some calculations in your scratch paper.

colonblow
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

hi, shouldn't the answer to #1 problem be letter D, which is 3g/L? If 3g/2L is the correct answer, can someone please tell me how it was solved? thanks thanks!

blackcat007
Posts: 378
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

colonblow wrote:hi, shouldn't the answer to #1 problem be letter D, which is 3g/L? If 3g/2L is the correct answer, can someone please tell me how it was solved? thanks thanks!

the only torque that is acting is that due to the weight of the beam. so mgl/2 =Ia
I=(ml^2)/3

equate and solve..

colonblow
Posts: 2
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

I was doing mgl=Ia... thanks again!

blackcat007
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

QUESTION 35: (Magnetism - CR question)
The magnetic dipole moment of a current-carrying loop of wire is in the positive z direction. The magnetic dipole is placed in space where there is a magnetic field B = B0*i + B0*j, where B0 = const. and i , j the unit vectors along directions x and y respectively. What is the direction of the magnetic torque on the loop?

(A) It is along the negative z direction.
(B) It is along the line y = -x in the forth quadrant.
(C) It is along the line y = x, in the third quadrant.
(D) It is along the line y = -x, in the second quadrant.
(E) It is along the line x = y = z towards positive x,y and z.

I think B0>0 should be mentioned for avoiding any ambiguity between B and D option

QUESTION 40: (Cosmology - CR question)
Which of the following facts could be a remnant of the Big Bang theory for the evolution of the universe from a space-time singularity?

I. Uniform distribution of microwave background radiation.
II. Uniform distribution of background electrons.
III. Uniform distribution of background neutrinos.
IV. Uniform distribution of gluons and quarks.

(A) I and II only
(B) I, II and III only
(C) I and III only
(D) I, III and IV only
(E) II and III only

but the recent WMAP found anisotropy in the cosmic background of the order of micro kelvins and astrophysicists (esp Smoot and Fire) have made some prediction of structure formations from these anisotropy.

physics_auth
Posts: 163
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

blackcat007 wrote:
QUESTION 35: (Magnetism - CR question)
The magnetic dipole moment of a current-carrying loop of wire is in the positive z direction. The magnetic dipole is placed in space where there is a magnetic field B = B0*i + B0*j, where B0 = const. and i , j the unit vectors along directions x and y respectively. What is the direction of the magnetic torque on the loop?

(A) It is along the negative z direction.
(B) It is along the line y = -x in the forth quadrant.
(C) It is along the line y = x, in the third quadrant.
(D) It is along the line y = -x, in the second quadrant.
(E) It is along the line x = y = z towards positive x,y and z.

I think B0>0 should be mentioned for avoiding any ambiguity between B and D option.

B0 is supposed to represent the magnitude of magnetic field component which is always a non-zero quantity. To avoid confusion with the direction in space I used the unit vectors i and j. If I said B0 *(-i) this means that the i-th component of the magnetic induction is towards negative x-direction. Anyway, I corrected it to avoid ambiguity as you said ... . Thanks!

QUESTION 40: (Cosmology - CR question)
Which of the following facts could be a remnant of the Big Bang theory for the evolution of the universe from a space-time singularity?

I. Uniform distribution of microwave background radiation.
II. Uniform distribution of background electrons.
III. Uniform distribution of background neutrinos.
IV. Uniform distribution of gluons and quarks.

(A) I and II only
(B) I, II and III only
(C) I and III only
(D) I, III and IV only
(E) II and III only

but the recent WMAP found anisotropy in the cosmic background of the order of micro kelvins and astrophysicists (esp Smoot and Fire) have made some prediction of structure formations from these anisotropy.

Well, PGRE candidates are not supposed to have such specific knowledge ... answer according to your undergraduate school knowledge.

noospace
Posts: 46
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

Where did there questions come from? Are they really official ETS? If so how come they're not available on the website?

What's going on here?

physics_auth
Posts: 163
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### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

noospace wrote:Where did there questions come from? Are they really official ETS? If so how come they're not available on the website?

What's going on here?

It is a bit irritating to have to apologize again ... but I will do it once and for all ... . Questions 1-42 in this post are not ETS official questions, but questions that imitate those of the real PGRE test. Above all, to post ETS questions is plagiarism! Furthermore, I give directions (in green color somewhere in the 1st page) in this post how to find a pdf archive with ETS questions (about 30 questions with their brief solutions). The pdf mentioned contains ETS official questions. Is that clear? For those of you who want to practise only on ETS official questions there are directions on how to do this (the pdf I mentioned... the 4 practice tests etc.), the questions I post here periodically are for those who want to practise on PGRE questions beyond the official material. Ok?
Last edited by physics_auth on Sun Sep 27, 2009 12:46 pm, edited 1 time in total.

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