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This practice book contains䡲 one actual full-length GRE Physics Test 䡲 test-taking strategies Become familiar with 䡲 test structure and content 䡲 test instructions and answering procedur

This practice book contains

䡲 one actual full-length GRE Physics Test

䡲 test-taking strategies

Become familiar with

䡲 test structure and content

䡲 test instructions and answering procedures

Compare your practice test results with the performance of those who took the test at a GRE administration.

Visit GRE Online at www.gre.org

This book is provided FREE with test registration by the Graduate Record Examinations Board.

PHYSICS TEST

PRACTICE BOOK

Purpose of the GRE

Subject Tests

The GRE Subject Tests are designed to help graduate

school admission committees and fellowship sponsors

assess the qualifications of applicants in specific fields

of study The tests also provide you with an assessment

of your own qualifications

Scores on the tests are intended to indicate

knowl-edge of the subject matter emphasized in many

under-graduate programs as preparation for under-graduate study

Because past achievement is usually a good indicator of

future performance, the scores are helpful in predicting

success in graduate study Because the tests are

stan-dardized, the test scores permit comparison of students

from different institutions with different undergraduate

programs For some Subject Tests, subscores are

pro-vided in addition to the total score; these subscores

indicate the strengths and weaknesses of your

prepara-tion, and they may help you plan future studies

The GRE Board recommends that scores on the

Subject Tests be considered in conjunction with other

relevant information about applicants Because

numer-ous factors influence success in graduate school,

reliance on a single measure to predict success is not

advisable Other indicators of competence typically

include undergraduate transcripts showing courses

taken and grades earned, letters of recommendation,

the GRE Writing Assessment score, and GRE General Test scores For information about the appropriate use

of GRE scores, write to GRE Program, Educational Testing Service, Mail Stop 57-L, Princeton, NJ 08541,

or visit our Web site at www.gre.org/codelst.html

Development of the Subject Tests

Each new edition of a Subject Test is developed by a committee of examiners composed of professors in the subject who are on undergraduate and graduate facul-ties in different types of institutions and in different regions of the United States and Canada In selecting members for each committee, the GRE Program seeks the advice of the appropriate professional associations

in the subject

The content and scope of each test are specified and reviewed periodically by the committee of examin-ers Test questions are written by the committee and by other faculty who are also subject-matter specialists and by subject-matter specialists at ETS All questions proposed for the test are reviewed by the committee and revised as necessary The accepted questions are assembled into a test in accordance with the content specifications developed by the committee to ensure adequate coverage of the various aspects of the field and, at the same time, to prevent overemphasis on any single topic The entire test is then reviewed and approved by the committee

Subject-matter and measurement specialists on the ETS staff assist the committee, providing information and advice about methods of test construction and helping to prepare the questions and assemble the test

In addition, each test question is reviewed to eliminate language, symbols, or content considered potentially offensive, inappropriate for major subgroups of the test-taking population, or likely to perpetuate any negative attitude that may be conveyed to these subgroups The test as a whole is also reviewed to ensure that the test questions, where applicable, include an appropriate balance of people in different groups and different roles Because of the diversity of undergraduate curricula,

it is not possible for a single test to cover all the material you may have studied The examiners,

Table of Contents

Purpose of the GRE Subject Tests 3

Development of the Subject Tests 3

Content of the Physics Test 4

Preparing for a Subject Test 5

Test-Taking Strategies 6

What Your Scores Mean 6

Practice Physics Test 9

Scoring Your Subject Test 71

Evaluating Your Performance 74

Answer Sheet 75

study in the particular field The committee keeps the

test up-to-date by regularly developing new editions

and revising existing editions In this way, the test

content changes steadily but gradually, much like most

curricula In addition, curriculum surveys are conducted

periodically to ensure that the content of a test

reflects what is currently being taught in the

under-graduate curriculum

After a new edition of a Subject Test is first

admin-istered, examinees’ responses to each test question are

analyzed in a variety of ways to determine whether

each question functioned as expected These analyses

may reveal that a question is ambiguous, requires

knowledge beyond the scope of the test, or is

inappro-priate for the total group or a particular subgroup of

examinees taking the test Answers to such questions

are not used in computing scores

Following this analysis, the new test edition is

equated to an existing test edition In the equating

process, statistical methods are used to assess the

difficulty of the new test Then scores are adjusted so

that examinees who took a difficult edition of the test

are not penalized, and examinees who took an easier

edition of the test do not have an advantage

Varia-tions in the number of quesVaria-tions in the different

editions of the test are also taken into account in

this process

Scores on the Subject Tests are reported as three

digit scaled scores with the third digit always zero

The maximum possible range for all Subject Test total

scores is from 200 to 990 The actual range of scores for

a particular Subject Test, however, may be smaller The

maximum possible range of Subject Test subscores is

20 to 99; however, the actual range of subscores for any

test or test edition may be smaller Subject Test score

interpretive information is provided in Interpreting Your

GRE Scores, which you will receive with your GRE

score report, and on the GRE Web site at www.gre.org/

codelst.html

their ability to apply these principles in the solution

of problems Most test questions can be answered onthe basis of a mastery of the first three years of under-graduate physics The test questions are constructed

to simplify mathematical manipulations As a result, neither calculators nor tables of logarithms are needed

If the solution to a problem requires the use of logarithms,the necessary values are included with the question.The International System (SI) of units is usedpredominantly in the test A table of information (seepage 10) representing various physical constants and afew conversion factors among SI units is presented inthe test book Whenever necessary, additional values

of physical constants are printed with the text of the question

The approximate percentages of the test on themajor content topics have been set by the committee

of examiners, with input from a nationwide survey ofundergraduate physics curricula The percentagesreflect the committee’s determination of the relativeemphasis placed on each topic in a typical under-graduate program These percentages are given belowalong with the major subtopics included in each contentcategory Nearly all the questions in the test will

relate to material in this listing; however, there may beoccasional questions on other topics not explicitlylisted here

1 CLASSICAL MECHANICS (such as 20%kinematics, Newton’s laws, work and

energy, oscillatory motion, rotationalmotion about a fixed axis, dynamics ofsystems of particles, central forces andcelestial mechanics, three-dimensionalparticle dynamics, Lagrangian andHamiltonian formalism, noninertialreference frames, elementary topics influid dynamics)

PHYSICS TEST

PRACTICE BOOK

2 ELECTROMAGNETISM (such as 18%

electrostatics, currents and DC

circuits, magnetic fields in free space,

Lorentz force, induction, Maxwell’s

equations and their applications,

electromagnetic waves, AC circuits,

magnetic and electric fields in matter)

3 OPTICS AND WAVE PHENOMENA 9%

(such as wave properties, superposition,

interference, diffraction,

geometrical optics, polarization,

Doppler effect)

4 THERMODYNAMICS AND STA- 10%

TISTICAL MECHANICS (such as

the laws of thermodynamics,

thermo-dynamic processes, equations of state,

ideal gases, kinetic theory, ensembles,

statistical concepts and calculation of

thermodynamic quantities, thermal

expansion and heat transfer)

5 QUANTUM MECHANICS (such as 12%

fundamental concepts, solutions of

the Schrödinger equation (including

square wells, harmonic oscillators,

and hydrogenic atoms), spin, angular

momentum, wave function symmetry,

elementary perturbation theory)

6 ATOMIC PHYSICS (such as proper- 10%

ties of electrons, Bohr model, energy

quantization, atomic structure, atomic

spectra, selection rules, black-body

radiation, x-rays, atoms in electric and

magnetic fields)

7 SPECIAL RELATIVITY (such as 6%

introductory concepts, time dilation,

length contraction, simultaneity,

energy and momentum, four-vectors

and Lorentz transformation,

velocity addition)

8 LABORATORY METHODS (such as 6%

data and error analysis, electronics,

instrumentation, radiation detection,

counting statistics, interaction of

charged particles with matter, lasers

and optical interferometers, dimensional

analysis, fundamental applications

of probability and statistics)

Miscellaneous (e.g., astrophysics, cal methods, computer applications)

mathemati-Those taking the test should be familiar withcertain mathematical methods and their applications

in physics Such mathematical methods include singleand multivariate calculus, coordinate systems (rectan-gular, cylindrical, and spherical), vector algebra andvector differential operators, Fourier series, partialdifferential equations, boundary value problems,matrices and determinants, and functions of complexvariables These methods may appear in the test in thecontext of various content categories as well as occasion-

al questions concerning only mathematics in thespecialized topics category above

Preparing for a Subject Test

GRE Subject Test questions are designed to measureskills and knowledge gained over a long period of time.Although you might increase your scores to someextent through preparation a few weeks or monthsbefore you take the test, last-minute cramming isunlikely to be of further help The following informa-tion may be helpful

A general review of your college courses isprobably the best preparation for the test How-ever, the test covers a broad range of subjectmatter, and no one is expected to be familiarwith the content of every question

Use this practice book to become familiarwith the types of questions in the GRE PhysicsTest, paying special attention to the directions Ifyou thoroughly understand the directions beforeyou take the test, you will have more time duringthe test to focus on the questions themselves

9 SPECIALIZED TOPICS: Nuclear 9%and Particle physics (e.g., nuclear

properties, radioactive decay, fissionand fusion, reactions, fundamentalproperties of elementary particles),Condensed Matter (e.g., crystalstructure, x-ray diffraction, thermalproperties, electron theory of metals,semiconductors, superconductors),

The questions in the practice test in this book

illus-trate the types of multiple-choice questions in the test

When you take the test, you will mark your answers on

a separate machine-scorable answer sheet Total testing

time is two hours and fifty minutes; there are no

separately timed sections Following are some general

test-taking strategies you may want to consider

 Read the test directions carefully, and work as

rapidly as you can without being careless For

each question, choose the best answer from the

available options

 All questions are of equal value; do not waste

time pondering individual questions you find

extremely difficult or unfamiliar

 You may want to work through the test quite

rapidly, first answering only the questions about

which you feel confident, then going back and

answering questions that require more thought,

and concluding with the most difficult questions

if there is time

 If you decide to change an answer, make sure you

completely erase it and fill in the oval

corre-sponding to your desired answer

 Questions for which you mark no answer or more

than one answer are not counted in scoring

 As a correction for haphazard guessing,

one-fourth of the number of questions you answer

incorrectly is subtracted from the number of

questions you answer correctly It is improbable

that mere guessing will improve your score

significantly; it may even lower your score

If, however, you are not certain of the correct

answer but have some knowledge of the question

and are able to eliminate one or more of the

Your raw score — that is, the number of questions youanswered correctly minus one-fourth of the numberyou answered incorrectly — is converted to the scaledscore that is reported This conversion ensures that ascaled score reported for any edition of a Subject Test

is comparable to the same scaled score earned on anyother edition of the same test Thus, equal scaledscores on a particular Subject Test indicate essentiallyequal levels of performance regardless of the testedition taken Test scores should be compared onlywith other scores on the same Subject Test (Forexample, a 680 on the Computer Science Test is notequivalent to a 680 on the Mathematics Test.)Before taking the test, you may find it useful toknow approximately what raw scores would be required

to obtain a certain scaled score Several factors ence the conversion of your raw score to your scaledscore, such as the difficulty of the test edition and thenumber of test questions included in the computation

influ-of your raw score Based on recent editions influ-of thePhysics Test, the table on the next page gives the range

of raw scores associated with selected scaled scores forthree different test editions (Note that when thenumber of scored questions for a given test is greaterthan the number of possible scaled scores, it is likely thattwo or more raw scores will convert to the same scaledscore.) The three test editions in the table that followswere selected to reflect varying degrees of difficulty.Examinees should note that future test editions may besomewhat more or less difficult than the test editionsillustrated in the table

PHYSICS TEST

PRACTICE BOOK

Range of Raw Scores* Needed to Earn

Selected Scaled Scores on Three

Physics Test Editions That

*Raw Score = Number of correct answers minus one-fourth the

number of incorrect answers, rounded to the nearest integer

For a particular test edition, there are many ways to

earn the same raw score For example, on the edition

listed above as “Form A,” a raw score of 44 would earn

a scaled score of 700 Below are a few of the possible

ways in which a scaled score of 700 could be earned on

that edition

Examples of Ways to Earn

a Scaled Score of 700 on the

Edition Labeled As “Form A”

Number ofQuestions Questions Questions Questions Used

Answered Answered Not to Compute

Raw Score Correctly Incorrectly Answered Raw Score

To become familiar with how the administration will be conducted at the test center, first remove theanswer sheet (pages 75 and 76) Then go to the back cover of the test book (page 70) and follow theinstructions for completing the identification areas of the answer sheet When you are ready to begin thetest, note the time and begin marking your answers on the answer sheet.

Copyright © 2001 by Educational Testing Service All rights reserved.

GRE, GRADUATE RECORD EXAMINATIONS, ETS, EDUCATIONAL TESTING

SERVICE and the ETS logos are registered trademarks of Educational Testing Service

FORM GR0177

THIS TEST BOOK MUST NOT BE TAKEN FROM THE ROOM.

Do not break the seal until you are told to do so.

The contents of this test are confidential.

Disclosure or reproduction of any portion

of it is prohibited.

PHYSICS TEST

77

9

TABLE OF INFORMATION

Rest mass of the electron m e = 9.11 × 10−31 kilogram = 9.11 × 10−28 gram

Magnitude of the electron charge e = 1.60 × 10−19 coulomb = 4.80 × 10−10 statcoulomb (esu)

Boltzmann’s constant k = 1.38 × 10−23 joule/K = 1.38 × 10−16 erg/K

Speed of light c = 3.00 × 108 m/s = 3.00 × 1010 cm/s

Planck’s constant h = 6.63 × 10−34 joule ∑ second = 4.14 × 10−15 eV ∑ second

j = h/2 p Vacuum permittivity ⑀0 = 8.85 × 10−12 coulomb2/(newton ∑ meter2) Vacuum permeability m0 = 4 p × 10−7 weber/(ampere ∑ meter)

Universal gravitational constant G = 6.67 × 10−11 meter3/(kilogram ∑ second2)

1 atmosphere pressure 1 atm = 1.0 × 105

newtons/meter2 = 1.0 × 105

pascals (Pa)

1 weber/m2 = 1 tesla = 104 gauss

Moments of inertia about center of mass

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This test starts on page 12

11

PHYSICS TEST

Time—170 minutes

100 Questions

Directions: Each of the questions or incomplete statements below is followed by five suggested answers or

completions Select the one that is best in each case and then fill in the corresponding space on the answer sheet

1 Which of the following best illustrates the

acceleration of a pendulum bob at points

of the turntable at which the coin will not slide? (A) 0.024 m

(B) 0.048 m (C) 0.121 m (D) 0.242 m (E) 0.484 m

3 A satellite of mass m orbits a planet of mass M

in a circular orbit of radius R The time required

for one revolution is

(A) independent of M (B) proportional to m (C) linear in R

(D) proportional to R3/2(E) proportional to R2

4 In a nonrelativistic, one-dimensional collision,

a particle of mass 2m collides with a particle of mass m at rest If the particles stick together after

the collision, what fraction of the initial kinetic energy is lost in the collision?

(A) 0

(B) 141

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5 A three-dimensional harmonic oscillator is in

thermal equilibrium with a temperature reservoir

at temperature T The average total energy of the

6 An ideal monatomic gas expands quasi-statically

to twice its volume If the process is isothermal,

the work done by the gas is W i If the process

is adiabatic, the work done by the gas is W a

Which of the following is true?

7 Two long, identical bar magnets are placed under

a horizontal piece of paper, as shown in the figure above The paper is covered with iron filings When the two north poles are a small distance apart and touching the paper, the iron filings move into a pattern that shows the magnetic field lines Which of the following best illustrates the pattern that results?

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8 A positive charge Q is located at a distance L

above an infinite grounded conducting plane,

as shown in the figure above What is the total

charge induced on the plane?

9 Five positive charges of magnitude q are

arranged symmetrically around the circumference

of a circle of radius r What is the magnitude of

the electric field at the center of the circle?

10 A 3-microfarad capacitor is connected in series

with a 6-microfarad capacitor When a 300-volt

potential difference is applied across this

com-bination, the total energy stored in the two

capacitors is

(A) 0.09 J

11 An object is located 40 centimeters from the first of two thin converging lenses of focal lengths

20 centimeters and 10 centimeters, respectively,

as shown in the figure above The lenses are separated by 30 centimeters The final image

formed by the two-lens system is located

(A) 5.0 cm to the right of the second lens (B) 13.3 cm to the right of the second lens (C) infinitely far to the right of the second lens (D) 13.3 cm to the left of the second lens (E) 100 cm to the left of the second lens

12 A spherical, concave mirror is shown in the figure

above The focal point F and the location of the object O are indicated At what point will the

image be located?

(A) I (B) II (C) III

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13 Two stars are separated by an angle of

3 ¥ 10-5 radians What is the diameter of the

smallest telescope that can resolve the two stars

using visible light (l @ 600 nanometers) ?

(Ignore any effects due to Earth’s atmosphere.)

NaI(Tl) detector detects gamma rays of a specific

energy from a point source of radioactivity When

the source is placed just next to the detector at

the center of the circular face, 50 percent of all

emitted gamma rays at that energy are detected

If the detector is moved to 1 meter away, the

fraction of detected gamma rays drops to

(B)

(C)

(D)

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19

16 A student makes 10 one-second measurements

of the disintegration of a sample of a long-lived

radioactive isotope and obtains the following

values

3, 0, 2, 1, 2, 4, 0, 1, 2, 5 How long should the student count to establish

the rate to an uncertainty of 1 percent?

17 The ground state electron configuration

for phosphorus, which has 15 electrons, is

18 The energy required to remove both electrons

from the helium atom in its ground state is

79.0 eV How much energy is required to ionize

helium (i.e., to remove one electron) ?

19 The primary source of the Sun’s energy is a series

of thermonuclear reactions in which the energy

produced is c2 times the mass difference between (A) two hydrogen atoms and one helium atom (B) four hydrogen atoms and one helium atom (C) six hydrogen atoms and two helium atoms (D) three helium atoms and one carbon atom (E) two hydrogen atoms plus two helium atoms and one carbon atom

20 In the production of X rays, the term

“bremsstrahlung” refers to which of the following?

(A) The cut-off wavelength, l min, of the X-ray tube

(B) The discrete X-ray lines emitted when an electron in an outer orbit fills a vacancy in

an inner orbit of the atoms in the target metal of the X-ray tube

(C) The discrete X-ray lines absorbed when an electron in an inner orbit fills a vacancy in

an outer orbit of the atoms in the target metal of the X-ray tube

(D) The smooth, continuous X-ray spectra produced by high-energy blackbody radiation from the X-ray tube (E) The smooth, continuous X-ray spectra produced by rapidly decelerating electrons

in the target metal of the X-ray tube

21 In the hydrogen spectrum, the ratio of the

wavelengths for Lyman-a radiation (n = 2 to

n = 1) to Balmer-a radiation (n = 3 to n = 2) is

(A) 5/48 (B) 5/27 (C) 1/3 (D) 3 (E) 27/5

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21

22 An astronomer observes a very small moon

orbiting a planet and measures the moon’s

minimum and maximum distances from the

planet’s center and the moon’s maximum orbital

speed Which of the following CANNOT be

calculated from these measurements?

(A) Mass of the moon

(B) Mass of the planet

(C) Minimum speed of the moon

(D) Period of the orbit

(E) Semimajor axis of the orbit

23 A particle is constrained to move in a circle with a 10-meter radius At one instant, the particle’s speed is 10 meters per second and is increasing at

a rate of 10 meters per second squared The angle between the particle’s velocity and acceleration vectors is

(A) 0∞ (B) 30∞ (C) 45∞ (D) 60∞ (E) 90∞

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23

t O

I

t O

II

t O

IV

t O

V

t O

III

u u

24 A stone is thrown at an angle of 45° above the horizontal x-axis in the +x-direction If air resistance is

ignored, which of the velocity versus time graphs shown above best represents u versus t and x u versus t, y

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25

25 Seven pennies are arranged in a hexagonal, planar

pattern so as to touch each neighbor, as shown in

the figure above Each penny is a uniform disk of

mass m and radius r What is the moment of

inertia of the system of seven pennies about an

axis that passes through the center of the central

penny and is normal to the plane of the pennies?

26 A thin uniform rod of mass M and length L is

positioned vertically above an anchored frictionless

pivot point, as shown above, and then allowed to

fall to the ground With what speed does the free

end of the rod strike the ground?

y1 = 5 1 - 3 2 + 2 3

y2 = 1 - 5 2 + x 3

28 The states 1 , 2 , and 3 are orthonormal

For what value of x are the states y1 and

y2 given above orthogonal?

(A) 10 (B) 5 (C) 0 (D) -5 (E) -10

6

12

13

1 1 2

is a linear combination of three orthonormal

eigenstates of the operator Ô corresponding

to eigenvalues -1, 1, and 2 What is the

expectation value of Ô for this state?

(A) 23

6(C) 1(D) 43

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27

30 Which of the following functions could represent

the radial wave function for an electron in an

atom? (r is the distance of the electron from

the nucleus; A and b are constants.)

(D) I and III only

(E) I, II, and III

31 Positronium is an atom formed by an electron

and a positron (antielectron) It is similar to the

hydrogen atom, with the positron replacing the

proton If a positronium atom makes a transition

from the state with n = 3 to a state with n = 1,

the energy of the photon emitted in this transition

32 If the total energy of a particle of mass m is

equal to twice its rest energy, then the magnitude

of the particle’s relativistic momentum is

33 If a charged pion that decays in 10-8 second in

its own rest frame is to travel 30 meters in the laboratory before decaying, the pion’s speed must

be most nearly (A) 0.43 ¥ 108 m/s (B) 2.84 ¥ 108 m/s (C) 2.90 ¥ 108 m/s (D) 2.98 ¥ 108 m/s (E) 3.00 ¥ 108 m/s

34 In an inertial reference frame S, two events occur

on the x-axis separated in time by Dt and in space by Dx In another inertial reference frame

S ¢, moving in the x-direction relative to S, the two

events could occur at the same time under which,

if any, of the following conditions?

(A) For any values of Dx and Dt

(B) Only if ΩDx / Dt Ω< c

(C) Only if ΩDx / Dt Ω> c (D) Only if ΩDx / Dt Ω= c

(E) Under no condition

35 If the absolute temperature of a blackbody is increased by a factor of 3, the energy radiated per second per unit area does which of the following? (A) Decreases by a factor of 81

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29

36 Consider the quasi-static adiabatic expansion

of an ideal gas from an initial state i to a final

state f Which of the following statements is

NOT true?

(A) No heat flows into or out of the gas

(B) The entropy of state i equals the entropy

(E) The temperature of the gas remains constant

37 A constant amount of an ideal gas undergoes the

cyclic process ABCA in the PV diagram shown

above The path BC is isothermal The work

done by the gas during one complete cycle,

beginning and ending at A, is most nearly

38 An AC circuit consists of the elements shown

above, with R = 10,000 ohms, L = 25 millihenries, and C an adjustable capacitance The AC voltage

generator supplies a signal with an amplitude of

40 volts and angular frequency of 1,000 radians

per second For what value of C is the amplitude

of the current maximized?

(D) 40 mF (E) 400 mF

39 Which two of the following circuits are high-pass filters?

(A) I and II (B) I and III (C) I and IV (D) II and III

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31

40 In the circuit shown above, the switch S is closed at t = 0

Which of the following best represents the voltage across the inductor, as seen on an oscilloscope?

(E)

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33

41 Maxwell’s equations can be written in the form

shown below If magnetic charge exists and if it is

conserved, which of these equations will have to

(E) II and III

42 Three wire loops and an observer are positioned

as shown in the figure above From the observer’s

point of view, a current I flows counterclockwise

in the middle loop, which is moving towards the

observer with a velocity u Loops A and B are

stationary This same observer would notice that (A) clockwise currents are induced in loops

A and B

(B) counterclockwise currents are induced in

loops A and B (C) a clockwise current is induced in loop A, but

a counterclockwise current is induced in

loop B

(D) a counterclockwise current is induced in

loop A, but a clockwise current is induced

in loop B

(E) a counterclockwise current is induced in loop

A, but no current is induced in loop B

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35

43 The components of the orbital angular momentum

operator L = (L x , L y , L z) satisfy the following

44 The energy eigenstates for a particle of mass m

in a box of length L have wave functions

f n( )x = 2/L sin(n x L p / ) and energies

Which of the following is a possible result of a

measurement of energy for the state Y ?

46 A free particle with initial kinetic energy E and

de Broglie wavelength l enters a region in

which it has potential energy V What is the

particle’s new de Broglie wavelength?

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37

47 A sealed and thermally insulated container of total

volume V is divided into two equal volumes by

an impermeable wall The left half of the con-

tainer is initially occupied by n moles of an ideal

gas at temperature T Which of the following

gives the change in entropy of the system when

the wall is suddenly removed and the gas expands

to fill the entire volume?

48 A gaseous mixture of O2 (molecular mass 32 u)

and N2 (molecular mass 28 u) is maintained at

constant temperature What is the ratio u

49 In a Maxwell-Boltzmann system with two states

of energies
and 2
, respectively, and a

degeneracy of 2 for each state, the partition

function is

-
/kT

50 At 20∞C, a pipe open at both ends resonates at a frequency of 440 hertz At what frequency does the same pipe resonate on a particularly cold day when the speed of sound is 3 percent lower than

it would be at 20∞C ? (A) 414 Hz

(B) 427 Hz (C) 433 Hz (D) 440 Hz (E) 453 Hz

51 Unpolarized light of intensity I0 is incident on a series of three polarizing filters The axis of the second filter is oriented at 45° to that of the first filter, while the axis of the third filter is oriented

at 90° to that of the first filter What is the intensity

of the light transmitted through the third filter? (A) 0