GRE Physics Test Practice Book

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PHYSICS TEST. PRACTICE BOOK. Purpose of the. GRE Subject Tests. The GRE Subject Tests are designed to help graduate school admission committees ...

GRE  Physics Test ®

Practice Book This practice book contains n one actual, full-length GRE® Physics Test n test-taking strategies

Become familiar with n test structure and content n test instructions and answering procedures

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

www.ets.org/gre

Table of Contents Overview.....................................................................................................................................3 Test Content...............................................................................................................................3 Preparing for the Test..................................................................................................................4 Test-Taking Strategies.................................................................................................................4 What Your Scores Mean.............................................................................................................5 Taking the Practice Test.............................................................................................................5 Scoring the Practice Test............................................................................................................5 Evaluating Your Performance.....................................................................................................5 Practice Test................................................................................................................................7 Worksheet for Scoring the Practice Test..................................................................................87 Score Conversion Table............................................................................................................88 Answer Sheet............................................................................................................................89

Test takers with disabilities or health-related needs who need test preparation materials in an alternate format should contact the ETS Office of Disability Services at [email protected] For additional information, visit www.ets.org/gre/disabilities

Copyright © 2017 by Educational Testing Service. All rights reserved. ETS, the ETS logo, MEASURING THE POWER OF LEARNING, GRADUATE RECORD EXAMINATIONS, and GRE are registered trademarks of Educational Testing Service (ETS) in the United States and other countries.

Overview The GRE® Physics Test consists of about 100 multiple-choice questions. Testing time is 2 hours and 50 minutes; there are no separatelytimed sections. This publication provides a comprehensive overview of the GRE Physics Test to help you get ready for test day. It is designed to help you: • Understand what is being tested • Gain familiarity with the question types • Review test-taking strategies • Understand scoring • Practice taking the test To learn more about the GRE Subject Tests, visit www.ets.org/gre.

Test Content The test consists of approximately 100 fivechoice questions, some of which are based on such materials as diagrams, graphs, experimental data and descriptions of physical situations. The aim of the test is to determine the extent of the test takers’ grasp of fundamental principles and their ability to apply these principles in the solution of problems. Most test questions can be answered on the basis of a mastery of the first three years of undergraduate 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 used predominantly in the test. A table of information representing various physical constants and a few conversion factors among SI units is presented in the test book. Whenever necessary, additional values of physical constants are printed with the text of the question. The approximate percentages of the test on the major content topics have been set by the committee of examiners, with input

GRE ® Physics Test Practice Book

from a nationwide survey of undergraduate physics curricula. The percentages reflect the committee’s determination of the relative emphasis placed on each topic in a typical undergraduate program. These percentages are given below along with the major subtopics included in each content category. Nearly all the questions in the test will relate to material in this listing; however, there may be occasional questions on other topics not explicitly listed here. I.

Classical Mechanics (20%) (such as kinematics, Newton’s laws, work and energy, oscillatory motion, rotational motion about a fixed axis, dynamics of systems of particles, central forces and celestial mechanics, three-dimensional particle dynamics, Lagrangian and Hamiltonian formalism, non-inertial reference frames, elementary topics in fluid dynamics)

II. Electromagnetism (18%) (such as 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) III. Optics and Wave Phenomena (9%) (such as wave properties, superposition, interference, diffraction, geometrical optics, polarization, Doppler effect) IV. Thermodynamics and Statistical Mechanics (10%) (such as the laws of thermodynamics, thermodynamic processes, equations of state, ideal gases, kinetic theory, ensembles, statistical concepts and calculation of thermodynamic quantities, thermal expansion and heat transfer) V. Quantum Mechanics (12%) (such as fundamental concepts, solutions of the Schrödinger equation [including square wells, harmonic oscillators and hydrogenic atoms], spin, angular

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momentum, wave function symmetry, elementary perturbation theory) VI. Atomic Physics (10%) (such as properties of electrons, Bohr model, energy quantization, atomic structure, atomic spectra, selection rules, black-body radiation, x-rays, atoms in electric and magnetic fields) VII. Special Relativity (6%) (such as introductory concepts, time dilation, length contraction, simultaneity, energy and momentum, four-vectors and Lorentz transformation, velocity addition) VIII. Laboratory Methods (6%) (such as 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) IX. Specialized Topics (9%) Nuclear and Particle physics (such as nuclear properties, radioactive decay, fission and fusion, reactions, fundamental properties of elementary particles), Condensed Matter (such as crystal structure, x-ray diffraction, thermal properties, electron theory of metals, semiconductors, superconductors), Miscellaneous (such as astrophysics, mathematical methods, computer applications)

Preparing for the Test GRE Subject Test questions are designed to measure skills and knowledge gained over a long period of time. Although you might increase your scores to some extent through preparation a few weeks or months before you take the test, last minute cramming is unlikely to be of further help. The following information may be helpful. • A general review of your college courses is probably the best preparation for the

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test. However, the test covers a broad range of subject matter, and no one is expected to be familiar with the content of every question. • Become familiar with the types of questions in the GRE Physics Test, paying special attention to the directions. If you thoroughly understand the directions before you take the test, you will have more time during the test to focus on the questions themselves.

Test-Taking Strategies The questions in the practice test illustrate the types of multiple-choice questions in the test. When you take the actual test, you will mark your answers on a separate machine-scorable answer sheet. The 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 quickly, 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 corresponding to your desired answer. • Your score will be determined by the number of questions you answer correctly. Questions you answer incorrectly or for which you mark no answer or more than one answer are counted as incorrect. Nothing is subtracted from a score if you answer a question incorrectly. Therefore, to maximize your score it is better for you

GRE ® Physics Test Practice Book

to guess at an answer than not to respond at all. • Record all answers on your answer sheet. Answers recorded in your test book will not be counted. • Do not wait until the last few minutes of a testing session to record answers on your answer sheet.

What Your Scores Mean The number of questions you answered correctly on the whole test (total correct score) is converted to the total reported scaled score. This conversion ensures that a scaled score reported for any edition of a GRE Physics Test is comparable to the same scaled score earned on any other edition of the test. Thus, equal scaled scores on a particular test indicate essentially equal levels of performance regardless of the test edition taken. GRE Physics Test total scores are reported on a 200 to 990 score scale in ten-point increments. Test scores should be compared only with other scores on the Physics Test. For example, a 780 on the Physics Test is not equivalent to a 780 on the Chemistry Test.

Taking the Practice Test The practice test begins on page 7. The total time that you should allow for this practice test is 2 hours and 50 minutes. An answer sheet is provided for you to mark your answers to the test questions. It is best to take this practice test under timed conditions. Find a quiet place to take the test and make sure you have a minimum of 2 hours and 50 minutes available. To simulate how the administration will be conducted at the test center, print the answer sheet (pages 89 and 90). Then go to the back cover of the test book (page 86) and follow the instructions for completing the identification areas of the answer sheet. When you are ready to begin the test, note the time and begin marking your

GRE ® Physics Test Practice Book

answers on the answer sheet. Stop working on the test when 2 hours and 50 minutes have elapsed.

Scoring the Practice Test The worksheet on page 87 lists the correct answers to the questions. The “Correct Response” columns are provided for you to mark those questions for which you chose the correct answer. Mark each question that you answer correctly. Then, add up your correct answers and enter your total number of correct answers in the space labeled “Total Correct” at the bottom of the page. Next, use the “Total Score” conversion tables on page 88 to find the corresponding scaled score. For example, suppose you chose the correct answers to 67 of the questions on the test. The “Total Correct” entry in the conversion table of 67 shows that your total scaled score is 820.

Evaluating Your Performance Now that you have scored your test, you may wish to compare your performance with the performance of others who took this test. The data in the worksheet on page 87 are based on the performance of a sample of the test takers who took the GRE Physics Test in the United States. The numbers in the column labeled “P+” on the worksheet indicate the percentages of examinees in this sample who answered each question correctly. You may use these numbers as a guide for evaluating your performance on each test question. Interpretive data based on the scores earned by a recent cohort of test takers are available on the GRE website at www.ets.org/gre/subject/ scores/understand. The interpretive data show, for selected scaled score, the percentage of test takers who received lower scores. To compare yourself with this population, look at the percentage next to the scaled score you earned on the practice test. Note that these interpretive data are updated annually and reported on GRE score reports.

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It is important to realize that the conditions under which you tested yourself were not exactly the same as those you will encounter at a test center. It is impossible to predict how different test-taking conditions will affect test performance, and this is only one factor that may account for differences between your practice test scores and your actual test scores.

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By comparing your performance on this practice test with the performance of other individuals who took GRE Physics Test, however, you will be able to determine your strengths and weaknesses and can then plan a program of study to prepare yourself for taking the GRE Physics Test under standard conditions.

GRE ® Physics Test Practice Book

FORM GR1777

77 GRADUATE RECORD EXAMINATIONS®

PHYSICS TEST

Copyright © 2013 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.

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TABLE OF INFORMATION me = 9.11 × 10−31 kg

Rest mass of the electron

e = 1.60 × 10−19 C

Magnitude of the electron charge

NA = 6.02 × 1023

Avogadro’s number

R = 8.31 J/(mol ∑ K)

Universal gas constant

k = 1.38 × 10−23 J/K

Boltzmann’s constant

c = 3.00 × 108 m/s

Speed of light

h = 6.63 × 10−34 J ∑ s = 4.14 × 10−15 eV ∑ s

Planck’s constant

j = h/2 p hc = 1240 eV ∑ nm

 0 = 8.85 × 10−12 C 2/(N ∑ m 2)

Vacuum permittivity

m 0 = 4 p × 10−7 T ∑ m/A

Vacuum permeability

G = 6.67 × 10−11 m 3/(kg ∑ s 2)

Universal gravitational constant

g = 9.80 m/s 2

Acceleration due to gravity 1 atmosphere pressure

1 atm = 1.0 × 105 N/m 2 = 1.0 × 105 Pa 1Å = 1 × 10−10 m = 0.1 nm

1 angstrom

Rotational inertia about center of mass

Prefixes for Powers of 10 10−15

femto

f

10−12

pico

p

10− 9

nano

n

10− 6

micro

m

10−3

milli

m

10−2

centi

c

10 3

kilo

k

10 6

mega

M

10 9

giga

G

1012

tera

T

1015

peta

P

8 -2-

Rod

1 MA 2 12

Disc

1 MR 2 2

Sphere

2 MR 2 5

Thistest teststarts startson onpage page10. 4. This

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PHYSICS TEST Time— 170 minutes PHYSICS TEST 100 Questions 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. 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. A net force FA acts on object A, and a net force FBnet acts on object B.on The mass A, of object B force is object and a net 1. A force FA acts twice the mass of object A, and the acceleration F B acts on object B. The mass of object B is of object B is twice that A, of object Which of twice the mass of object and theA.acceleration theobject following true of forces FA and FB ? of of B isistwice that of object A. Which the following 1 is true of forces FA and FB ? (A) FB = FA 4 1 (A) FB = 1 FA (B) FB = 4 FA 2 1 (B) FB = FA 2A (C) FB = F

2. Two objects sliding on a frictionless surface, as represented above, collide and stick together. 2. Two objects sliding on a frictionless surface, How much kinetic energy is converted to heat as represented above, collide and stick together. during the collision? How much kinetic energy is converted to heat during 1 the collision? (A) J 9 1 (A) 1 J (B) 9 J 6 1 (B) 1 J (C) 6 J 2 1 (C) 3 J (D) 2 J 4 3 (D) 5 J (E) 4 J 6 5 (E) J 6

(C) FB = FA (D) FB = 2 FA (D) FB = 2 FA (E) FB = 4 FA (E) FB = 4 FA

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3. Two simple pendulums A and B consist of identical suspended strings 3. Two simplemasses pendulums A andfrom B consist of length L and L , respectively. The two B of identical Amasses suspended from strings pendulums in equal gravitational fields. of length Loscillate A and LB , respectively. The two If the periodoscillate of pendulum B gravitational is twice the period pendulums in equal fields. of pendulum A, which of the following is true If the period of pendulum B is twice the period of lengths A, of the twoofpendulums? of the pendulum which the following is true

6. The electric field of a plane electromagnetic wave number angular frequency wwave is 6. of Thewave electric field kofand a plane electromagnetic + eyangular ) sin(kz wt). Which given bynumber E = E0(ekx and of wave frequency w of is the following the associated + eydirection ) sin(kz -ofwt) given by E = gives . Which of E0(ex the magnetic fieldgives B ? the direction of the associated the following (A) ez field B ? magnetic (B) -e (A) ez x + ey - eey (C) -e -exx + (B) y (D) x x--ezey (C) e-e - eez (E) eey (D)

of the lengths 1 of the two pendulums? (A) LB = L 4 A 1 (A) LB = L 14 A LA (B) LB = 2 1

L (B) LB = 2 A (C) LB = LA

x

z

(E) ey - ez 7. Which of the following is true about any system that undergoes a reversible thermodynamic 7. Which of the following is true about any system process? that undergoes a reversible thermodynamic (A) There are no changes in the internal energy process? of the system. (A) There are no changes in the internal energy (B) The temperature of the system remains of the system. constant during the process. (B) The temperature of the system remains

(C) The entropy of the system and its constant during the process.

environment remains unchanged. (C) The entropy of the system and its

(D) The entropy of the system and its environment remains unchanged.

environment must increase. (D) The entropy of the system and its

(E) The net work done by the system is zero. environment must increase.

(E) The net work done by the system is zero. 8. For which of the following thermodynamic processes is the increase in the internal energy 8. For which of the following thermodynamic of an ideal gas equal to the heat added to the gas? processes is the increase in the internal energy (A) of anConstant ideal gastemperature equal to the heat added to the gas? (B) Constant volume (A) Constant temperature (C) Constant pressure (B) Constant volume (D) Adiabatic (C) Constant pressure (E) Cyclic (D) Adiabatic (E) Cyclic

(C) LB = LA (D) LB = 2LA (D) LB = 2LA (E) LB = 4LA (E) LB = 4LA

4. For the circuit shown in the figure above, what is the current i through the 2 W resistor? 4. For the circuit shown in the figure above, what is (A) 2 A i through the 2 W resistor? the current (B) 4 A (A) 2 A (C) 5 A (B) 4 A (D) 10 A (C) 5 A (E) 20 A (D) 10 A (E) 20 A 5. By definition, the electric displacement current through a surface S is proportional to the 5. By definition, the electric displacement current (A) magnetic flux Sthrough S through a surface is proportional to the (B) rate of change of the magnetic flux through S (A) magnetic flux through S (C) time integral of the magnetic flux through S (B) rate of change of the magnetic flux through S (D) electric flux through S (C) time integral of the magnetic flux through S (E) rate of change of the electric flux through S (D) electric flux through S (E) rate of change of the electric flux through S

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12. A single-electron atom has the electron in the A = 2 state. The number of allowed values of 12. A single-electron atom has the electron in the the quantum number mA is A = 2 state. The number of allowed values of the number mA is (A) quantum 1 (B) 2 (A) (C) 13 (B) (D) 24 (C) (E) 53 (D) 4 (E)particle 5 13. A of mass m is confined inside a

9. The root-mean-square speed of molecules in an ideal gas of molar mass M at temperature T is 9. The root-mean-square speed of molecules in an

(A) 0 of molar mass M at temperature T is

ideal gas (A) (B)

0 RT M RT (B) M RT (C) M RT (C) M 3RT (D) M 3RT (D) M 3RT (E) M 3RT (E) M variable frequency n shines on the metal 10. Light of surface of a photoelectric tube. Einstein’s theory variable frequency the metal n shines 10. Light of the of photoelectric effect predicts thatonthe surface of a photoelectric tube. Einstein’s theory (A)thework function of the metal is proportional of photoelectric effect predicts that the to the frequency (A) work function function of of the the metal metal is is proportional proportional (B) work to the frequency to the wavelength (B) work function of the is function proportional (C) current in the tube is metal a linear of to the wavelength the wavelength (C) current indifference the tube isnecessary a linear function of (D) potential to stop the the wavelength emitted electrons is a linear function of (D) potential difference necessary to stop the the frequency above the threshold frequency emitted electrons is a linear function of (E) potential difference necessary to stop the the frequency above the threshold frequency emitted electrons is equal to the work (E) potential functiondifference necessary to stop the emitted electrons is equal to the work function X rays, appearing as sharp lines 11. Characteristic

one-dimensional box (infinite square well) of 13. A particle of mass m is ground confined inside a is length a. The particle’s state energy one-dimensional box (infinite square well) of which of the following? length a. The particle’s ground state energy is = which (A) of the following? 8ma = (A) =2 8ma (B) 2 8ma =2 (B) 2 2

= (C) 8ma

2 ma =2 (C) 2 2 2 = p (D) ma 2 2ma =2 p 2 (D) 2 22

= a (E) 2ma 2 2 2 2=mc a (E) 2mc 2 length is the only combination of 14. The Planck the factors G (Newton’s gravitational constant), 14. The Planck length is the combination of of = (Planck’s constant / 2πonly ), and c (the speed the factors G (Newton’s gravitational constant), light) that has units of length. Which of the = (Planck’s constant / 2π ), and c (the speed of following gives the Planck length? light) that has units of length. Which of the 1/ 2 following =G gives the Planck length? (A) ÊÁ 3 ˆ˜ Ë c ¯ 1/ 2 =G (A) ÊÁ=G3 ˆ˜ Ë (B) 3c ¯ c =G (B) 32 G (C) c =c G2 (C) =c (D) =cG

on a continuous background, are produced 11. Characteristic X rays, appearing as sharp lines when high-energy electrons bombard a metal on a continuous background, are produced target. Which of the following processes results when in the high-energy characteristicelectrons X rays? bombard a metal target. Which of the following processes results (A)theElectrons producing Čerenkov radiation in characteristic X rays? (B) Electrons colliding with phonons in the metal (A) Electrons Electrons filling producing radiation (C) innerČerenkov shell vacancies that are (B) Electrons colliding with phonons in the metal created in the metal atoms (C) innerwith shellprotons vacancies that are (D) Electrons Electrons filling combining to form created in the metal atoms neutrons (D) protons to form (E) Electrons Electrons combining undergoingwith Coulomb scattering neutrons with nuclei (E) Electrons undergoing Coulomb scattering with nuclei

(D) =cG =G (E) c =G (E) c

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18. Two identical satellites, A and B, are in circular orbits around Earth. The orbital radius of A is 18. Two identical satellites, A and B, are in circular twice that of B. Which of the following gives orbits around Earth. The orbital radius of A is the ratio of the angular momentum of A to the twice that of B. Which of the following gives angular momentum of B ? the ratio of the angular momentum of A to the angular (A) 4 momentum of B ?

15. The speed of light inside of a nonmagnetic dielectric material with a dielectric constant 15. The speed of light inside of a nonmagnetic of 4.0 is dielectric material with a dielectric constant of is ¥ 109 m/s (A)4.01.2 8 (B) m/s (A) 3.0 1.2 ¥ ¥ 10 109 m/s 8 (C) m/s (B) 1.5 3.0 ¥ ¥ 10 108 m/s 8 (D) 1.0 ¥ 10 8 m/s (C) 1.5 ¥ 10 m/s 7 (E) m/s (D) 7.5 1.0 ¥ ¥ 10 108 m/s

(E) 7.5 ¥ 107 m/s 16. Fermat’s principle of ray optics states, “A ray of light follows the path between two points which 16. Fermat’s principle of ray optics states, “A ray of requires the least time.” This principle can be light follows the path between two points which used to derive which of the following? requires the least time.” This principle can be I. to Snell’s of refraction used derivelaw which of the following? II. The law of reflection I. Snell’s law of refraction III. Rayleigh’s criterion for resolution II. The law of reflection III. IRayleigh’s criterion for resolution (A) only

(A) (B)

4 2

(B) (C)

2 2

(C) (D)

19. 19.

(B) II only (A) I only (C) III only (B) II only (D) I and II (C) III only (E) II and III (D) I and II (E) II and III 17. Consider two identical systems, 1 and 2, each consisting of a planet in circular orbit about a 17. Consider two identical systems, 1 and 2, each much heavier star. For system 1 the radius of consisting of a planet in circular orbit about a the orbit is a, and for system 2 the radius of much heavier star. For system 1 the radius of the orbit is 4a. Which of the following gives the orbit is a, and for system 2 the radius of T the orbit of theoffollowing ratio, is 14a. , ofWhich the period system 1 gives to the TT2 1 the ratio, , of 2the period of system ? period of system 1 to the T

20.

2

20.

periodT of system 2 ? (A) 1 = 1 TT2 (A) T1 = 1 1 (B) T12 = TT2 2 1 (B) T1 = 1 T 2 12 = (C) TT2 4 1 (C) T1 = 1 (D) T12 = 4 TT2 8 1 (D) T1 = 1 (E) T21 = 8 TT2 16 1 (E) 1 = T2 16

12 12 (D) 1 (E) 2 2 1 (E) 2 A 10 kg box slides horizontally without friction at a speed of 1 m/s. At one point, a constant A 10 kg box slides horizontally without friction force is applied to the box in the direction of its at a speed of 1 m/s. At one point, a constant motion. The box travels 5 m with the constant force is applied to the box in the direction of its force applied. The force is then removed, leaving motion. The box travels 5 m with the constant the box with a speed of 2 m/s. Which of the force applied. The force is then removed, leaving following gives the magnitude of the applied the box with a speed of 2 m/s. Which of the force? following gives the magnitude of the applied (A) 1 N force? (B) 2 N (A) 1 N (C) 3 N (B) 2 N (D) 4 N (C) 3 N (E) 5 N (D) 4 N (E) 5 N What is the magnitude of the magnetic field at the center of a circular conducting loop of radius a What is the magnitude of the magnetic field at the that is carrying current I ? center of a circular conducting loop of radius a that carrying Ia 2 current I ? (A) is4 pm 0

(A) 4pm0 Ia 2 (B) m0 Ia (B) m0 Ia (C) 0 (C) 0mo I (D) m2 aI (D) mo I o (E) 2a

4mp aI 2 (E) o 2

4pa

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24. Which of the following gives the total spin quantum number of the electrons in the ground 24. Which of the following gives the total spin state of neutral nitrogen (Z = 7) ? quantum number of the electrons in the ground state 1of neutral nitrogen (Z = 7) ? (A) 2 1 (A) (B) 21

21. Let w p , wd , and wa be the cyclotron frequencies and alpha 21. Let w p , wdof, protons, and wa deuterons, be the cyclotron particles, respectively, the same and magnetic frequencies of protons,in deuterons, alpha field. Therespectively, frequencies are related which particles, in the samebymagnetic of the The following? (Assume that thebyparticle field. frequencies are related which masses are in the ratio 1 : 2that : 4.)the particle of the following? (Assume

3 (B) (C) 1 2 3 (C) 25 (D) 2 5 (D) 27 (E) 2 7 (E) 2 25. Consider a Hermitian operator Aˆ with the property aAˆ 4Hermitian of the Aˆfollowing = 1 . Which 25. Consider operator with the 4 is an allowed eigenvalues of Aˆ ? property Which of the following Aˆ =pair 1 . of (A)an0,allowed 1 is pair of eigenvalues of Aˆ ? (B) (A) 1, 0, -1 1 (C) 1, i (B) 1, -1 (D) (C) 1, 1, -i i (E) (D) 11,+-ii, 1 - i

masses in 1 : 2 : 4.) w= = (A) p are w d thewratio a (B) w= (A) w= d > wa p (C) w= wd < wa (B) d > p (D) w= (C) < wa p < wdd = (E) w p > wa (D) w d = wa 22. The emission spectrum of the doubly ionized lithium atom spectrum Li++ (Z =of 3, the A =doubly 7) is identical 22. The emission ionized to that of a hydrogen atom in which all the ++ lithium atom Li (Z = 3, A = 7) is identical wavelengths are to that of a hydrogen atom in which all the (A) decreased wavelengths areby a factor of 9 (B) decreased by a factor of 49 (A) decreased by a factor of 9 (C) decreased by a factor of 81 (B) decreased by a factor of 49 (D) increased by a factor of 9 (C) decreased by a factor of 81 (E) increased by a factor of 81 (D) increased by a factor of 9 (E) increased by a factor of 81 23. In an atom of hydrogen, the electron is bound to a proton. In an atom of positronium, the electron 23. In an atom of hydrogen, the electron is bound to is bound to a positron instead of a proton. Which a proton. In an atom of positronium, the electron of the following gives the approximate Rydberg is bound to a positron instead of a proton. Which constant for positronium? (For a nucleus of of the following gives the approximate Rydberg 4 me e(For constant for positronium? a nucleus of .) infinite mass, R• = 2 43 8 em0e ech .)

infinite mass, R• = 8 e0 2 ch 3 (A) 0.0005R

(E) 1 + i, 1 - i

pˆ 2 Tˆ ∫ 2 2pˆm Tˆ pˆ∫2 2m Hˆ ∫ + V ( xˆ ) 2 2pˆm Hˆ ∫ + V ( xˆ ) 2m 26. Consider the kinetic energy operator Tˆ and the Hamiltonian Which Hˆ above. 26. Consider the operator kinetic energy operator Tˆ and the of the following pairs ofHˆ observables can be Hamiltonian operator above. Which measured simultaneously with no restriction of the following pairs of observables can be on their precision? measured simultaneously with no restriction



(B) (A) 0.5R 0.0005R • • (C) 0.999R (B) 0.5R• • (D) 0.999R (C) 2R • • 1880R (E) (D) 2R •

on precision? (A)their xˆ and pˆ (B) (A) xˆ and Tpˆˆ



(E) 1880R•

ˆ pˆ andT

(C) xˆˆ and (B) H (D) (C) Hˆˆ and Tpˆˆ ˆˆ and ˆˆ

(E) (D) TH and pT (E) Tˆ and pˆ

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27. Electromagnetic radiation emitted from a nucleus is most likely to be in the form of 27. Electromagnetic radiation emitted from a nucleus (A)most gamma is likelyrays to be in the form of (B) microwaves (A) gamma rays (C) ultraviolet radiation (B) microwaves (D) visible light (C) ultraviolet radiation (E) infrared radiation (D) visible light (E) infrared radiation

28. A sample of nitrogen gas undergoes the cyclic thermodynamic process shown above. Which of the 28. A sample of nitrogen gas undergoes the cyclic following gives the net heat transferred to the system thermodynamic process shown above. Which of the in one complete cycle Æ 2transferred Æ 3 Æ 1 ?to the system following gives the net1heat in one complete cycle 1 Æ 2 Æ 3 Æ 1 ? (A) -80 J (B) -80 -40 JJ (A) (C) 40 J (B) -40 J (D) 80 J (C) 40 J (E) 180 J (D) 80 J (E) 180 J

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29. For an ideal gas, consider the three thermodynamic processes— labeled 1, 2, and 3 —shown in the PV diagram 29. For an ideal gas, consider the three thermodynamic above. Each process has the same initial state and the same processes— labeled 1, 2, and 3 —shown in the PV diagram final volume. One process is adiabatic, one is isobaric, and above. Each process has the same initial state and the same one is isothermal. Which of the following correctly identifies final volume. One process is adiabatic, one is isobaric, and the three processes? one is isothermal. Which of the following correctly identifies Adiabatic Isothermal the three processes? Isobaric (A) 1 2 3 Adiabatic Isobaric Isothermal (B) 2 1 3 (A) 1 2 3 (C) 2 3 1 (B) 2 1 3 (D) 3 1 2 (C) 2 3 1 (E) 3 2 1 (D) 3 1 2 3 2 1 (E)

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34. A rod measures 1.00 m in its rest system. How fast must an observer move parallel to the rod 34. A rod measures 1.00 m in its rest system. How to measure its length to be 0.80 m? fast must an observer move parallel to the rod (A)measure 0.50c its length to be 0.80 m? to (B) 0.60c (A) 0.50c (C) 0.70c (B) 0.60c (D) 0.80c (C) 0.70c (E) 0.90c (D) 0.80c (E) 0.90c 35. A particle decays in 2.0 ms in its rest frame. If the same particle moves at u = 0.60c in the lab 35. A particle decays in 2.0 ms in its rest frame. If frame, how far will it travel in the lab before the same particle moves at u = 0.60c in the lab decaying? frame, how far will it travel in the lab before (A) 150 m decaying? (B) 288 m (A) 150 m (C) 360 m (B) 288 m (D) 450 m (C) 360 m (E) 750 m (D) 450 m (E) 750 m 36. The rest mass of a particle with total energy 5.0 GeV and momentum 4.9 GeV/c is 36. The rest mass of a particle with total energy approximately 5.0 GeV and momentum 4.9 GeV/c is

approximately (A) 0.1 GeV/c2

2 (B) (A) 0.2 0.1 GeV/c GeV/c22 (C) 0.5 GeV/c GeV/c2 (B) 0.2 (D) 1.0 GeV/c22 (C) 0.5 GeV/c (E) 1.5 GeV/c GeV/c22 (D) 1.0

30. The driver of a police car hears an echo of the car’s siren from a wall toward which the car is 30. The driver of a police car hears an echo of the moving with a speed of 3.5 m/s. If the speed of car’s siren from a wall toward which the car is sound is 350 m/s and the frequency of the siren is moving with a speed of 3.5 m/s. If the speed of 600 Hz, the driver hears the echo at a frequency sound is 350 m/s and the frequency of the siren is nearest to which of the following? 600 Hz, the driver hears the echo at a frequency (A) 588toHz nearest which of the following? (B) 594 Hz (A) 588 Hz (C) 600 Hz (B) 594 Hz (D) 606 Hz (C) 600 Hz (E) 612 Hz (D) 606 Hz (E) 612 Hz 31. The first five harmonics produced by an organ pipe open at both ends are 50 Hz, 100 Hz, 150 Hz, 31. The first five harmonics produced by an organ 200 Hz, and 250 Hz. Which of the harmonics, pipe open at both ends are 50 Hz, 100 Hz, 150 Hz, if any, will survive once the pipe is closed at 200 Hz, and 250 Hz. Which of the harmonics, one end? if any, will survive once the pipe is closed at (A) end? 50 Hz, 150 Hz, and 250 Hz only one (B) 100 Hz and 200 Hz only (A) 50 Hz, 150 Hz, and 250 Hz only (C) 150 Hz and 250 Hz only (B) 100 Hz and 200 Hz only (D) 200 Hz only (C) 150 Hz and 250 Hz only (E) None (D) 200 Hz only (E) None 32. A refracting telescope consists of two converging lenses separated by 100 cm. The eye-piece lens 32. A refracting telescope consists of two converging has a focal length of 20 cm. The angular lenses separated by 100 cm. The eye-piece lens magnification of the telescope is has a focal length of 20 cm. The angular (A) 4 magnification of the telescope is (B) 5 4 (A) (C) 6 (B) 5 (D) 20 (C) 6 (E) 100 (D) 20 (E) 100 33. The best type of laser with which to do spectroscopy over a range of visible 33. The best type of laser with which to wavelengths is do spectroscopy over a range of visible (A) a dye laser wavelengths is (B) a helium-neon laser (A) a dye laser (C) an excimer laser (B) a helium-neon laser (D) a ruby laser (C) an excimer laser (E) a neodymium-YAG laser (D) a ruby laser (E) a neodymium-YAG laser

(E) 1.5 GeV/c2 37. If charge +Q is located in space at the point (x = 1 m, y = 10 m, z = 5 m), what is the total 37. If charge +Q is located in space at the point electric flux that passes through the yz-plane? (x = 1 m, y = 10 m, z = 5 m), what is the total (A) • flux that passes through the yz-plane? electric (A) 1• (B)

Q (B) (C) 1 eQ0 (C) Q (D) e0 2Q e0 (D) (E) 02 e0 (E) 0

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38. A point charge Q is placed at the center of a hollow, conducting spherical shell of inner radius 38. A point charge Q is placed at the center of a a and outer radius b, as shown above. A net hollow, conducting spherical shell of inner radius charge q is placed on the conducting shell. If the a and outer radius b, as shown above. A net electric potential is assumed to be 0 at infinity, the charge q is placed on the conducting shell. If the magnitude of the electric potential at r, where electric potential is assumed to be 0 at infinity, the a < r < b, is magnitude of the electric potential at r, where (A) 0 a < r < b, is (B)

(C)

(D)

(E)

Q 4 pe0 r

Q+q 4 pe0 r Q 4 pe0 a

Q+q 4 pe0 b

(A) 0 (B)

Q 4 pe0 r

(C)

Q+q 4pe0 r

(D)

Q 4 pe0 a

(E)

Q+q 4pe0 b

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39. The figure above shows three arrangements of one electron (e) and two protons (p). Which of the 39. The figure above shows three arrangements of following is true about the magnitude F of the net one electron (e) and two protons (p). Which of the electrostatic force acting on the electron due to the following is true about the magnitude F of the net protons? electrostatic force acting on the electron due to the protons? (A) F1 > F2 > F3

= (B) (A) F 11 > F22 (C) > F32 = (B) F 11 (D) (C) F12 >> FF31

> F33 > F23 > F23

(E) (D) F22 > F13 > F31 (E) F2 > F3 > F1

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40. A series AC circuit with impedance Z consists of resistor R, inductor L, 40. andAcapacitor series ACC,circuit with impedance Z consists as shown above. The ideal emf source has R, inductor L, and capacitor C, of resistor

e as= shown emax sinabove. wt , The ideal emf source has and the current is given by I aI sinusoidal = f ). given by e = emax sin wt , output max sin( wt -

a sinusoidal output given by

What is the average power dissipated the and theincurrent is given by I I max sin( wt - f ). = What iscurrent.) the average power dissipated in the circuit? ( I rms is the root-mean-square 2 R (A) Irms

1 2 (B) I R 2 rms 1 2 (C) I Z 2 rms 1 2 (D) Irms R cos f 2 1 2 (E) I Z cos f 2 rms

circuit? ( I rms is the root-mean-square current.) 2 R (A) Irms

(B)

1 2 I R 2 rms

(C)

1 2 I Z 2 rms

(D)

1 2 I R cos f 2 rms

(E)

1 2 I Z cos f 2 rms

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41. The quantum efficiency of a photon detector is 0.1. If 100 photons are sent into the detector, one after the 41. The quantum efficiency of a photon detector is 0.1. other, the detector will detect photons If 100 photons are sent into the detector, one after the (A) 10 times other,exactly the detector will detect photons (B) an average of 10 times, with an rms deviation of (A) exactly 10 times about 0.1 (B) an average of 10 times, with an rms deviation of

(C) an average of 10 times, with an rms deviation of about 1 about 0.1

(D) an average of 10 times, with an rms deviation of about 2 (C) an average of 10 times, with an rms deviation of about 1

(E) an average of 10 times, with an rms deviation of about 3 (D) an average of 10 times, with an rms deviation of about 2

(E) an average of 10 times, with an rms deviation of about 3

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44. A particle in an infinite square well has as itsparticle initial wave an equal mixture 44. A in anfunction infinite square well has asof the first three states: its initial waveorthonormal function an stationary equal mixture of Y x ,0 = A y x + y x + y x . ( ) ( ) ( ) ( ) [ ] the first three orthonormal states: 1 2 stationary 3 The value of the normalization constant Y ( x,0 )= A [y1 ( x ) + y 2 ( x ) + y 3 ( x )] . A is equal to which the following?constant A is The value of theofnormalization

42. Two students perform an experiment in which they drop a ball from rest from a known height 42. Two students perform an experiment in which above the ground and measure the speed of they drop a ball from rest from a known height the ball just before it strikes the ground. From above the ground and measure the speed of repeated measurement, the students estimate the ball just before it strikes the ground. From the uncertainty in the measured speed of the repeated measurement, the students estimate ball to be 10 percent. Which of the following the uncertainty in the measured speed of the gives the uncertainty in the kinetic energy of ball to be 10 percent. Which of the following the ball? (Assume the uncertainty in the ball’s gives the uncertainty in the kinetic energy of mass is negligibly small.) the ball? (Assume the uncertainty in the ball’s (A) is 5% mass negligibly small.) (B) 10% (A) 5% (C) 15% (B) 10% (D) 20% (C) 15% (E) 40% (D) 20% (E) 40% 43. Which of the following wave functions represents a solution to the Schrödinger equation for an 43. Which of the following wave functions represents electron in the 2s state of a hydrogen atom? a solution to the Schrödinger equation for an ( c is a constant and a is the Bohr radius.) electron in the 2s state0 of a hydrogen atom? ( c iscacos constant and a0 is the Bohr radius.) q (A)

equal 1to which of the following? (A) 13 (A) 1 (B) 3

2 1

(B) (C) 1 2 (C) 1 (D) 2

(A) c cosq Ê r ˆ (B) c exp Á - ˜ Ë a0 ¯ Ê r ˆ (B) c exp Á - ˜ Ê Ë ra0ˆ¯ Ê r ˆ (C) c Á 1 exp Á Ë Ë 2 a0 ˜¯ 2 a0 ˜¯ r ˆ Ê Ê r ˆ (C) c Á 1 exp Á ˜ 2ra0 ˆ¯˜ ÊË ÊË 2 ra0 ˆ¯ (D) c Á 1 exp Á cos q ˜ ˜ Ë Ë 2 a0 ¯ 2 a0 ¯ r ˆ Ê r ˆ Ê (D) c Á 1 exp Á ˜ cos q ËÊ 2ra ˆ¯˜ ÊË 2 ra ˆ¯ (E) c Á 1 - 0 ˜ exp Á - 0 ˜ sin q exp ( ± i f ) Ë Ë 2 a0 ¯ 2 a0 ¯ r ˆ Ê Ê r ˆ (E) c Á 1 exp sin q exp ( ± i f ) ˜ Ë ËÁ 2 a0 ¯˜ 2 a0 ¯

(D) (E)

2 3

(E)

3

45. A matter wave of energy E > 0 and wave number k is incident from the left on a potential 45. A matter wave of energy E > 0 and wave well of width L and depth V . The top of the number k is incident from the0 left on a potential well zero energy and theV bottom of the well well is of at width L and depth 0. The top of the is at -V , as shown in the figure above. Thewell well is at0 zero energy and the bottom of the spatial of the wave function in region 3 has is at -Vpart 0, as shown in the figure above. The which theoffollowing (Ainisregion a constant.) spatial of part the wave forms? function 3 has which of ikx the following forms? (A is a constant.) (A) Ae (B) (A)

ikx A sin kx Ae

(C) (B)

A coskx Asin kx

(D) (C)

ik ¢x Ae (k ¢ < k ) Acos kx

(k¢ real < k) and positive) (D) (E) Aeik- k¢xx (k (E)

Ae - k x (k real and positive)

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48. A uniform solid disk starts from rest and rolls down an inclined plane without slipping. After 48. A uniform solid disk starts from rest and rolls some time, what fraction of the disk’s total kinetic down an inclined plane without slipping. After energy is rotational kinetic energy? some time, what fraction of the disk’s total kinetic energy 1 is rotational kinetic energy? (A) 4 1

(A) 1 (B) 4

3 1

(B) 1 (C) 3

2 1

(C) 2 (D) 2

3 2

(D) 3 (E) 3

4 3

(E) 4

49. Two projectiles are launched from ground level with the same initial speed. The maximum height 49. Two projectiles are launched from ground level h1 reached by initial projectile 1 isThe twice the maximum with the same speed. maximum height

46. Spring 1 has force constant k1 and spring 2 has force constant k2 ,constant where k 1k > and k2 . spring If the same 46. Spring 1 has force 2 has 1 external force is applied to both springs, which force constant k2 , where k1 > k2 . If the same of the following is true about the extensions external force is applied to both springs, which (ofDthe x1 and D x ) and theabout storedthe potential energies 2 is true following extensions (( U the two springs? 2 ) of Dx1 and andUDx ) and the stored potential energies 1

2

( U1 Extension and U 2 ) of the two springs? Stored Potential Energy

Dx1 < Dx2 (A) Extension

Stored Potential U < U Energy

Dx1 < Dx Dx2 (B) Dx (A)

> U2 U1


(D) (C) Dx1 =Dx2

= U2 U1
(D) =Dx2

U1 = U 2

(E) Dx1 > Dx2

U1 = U 2

1

2

h2 reached by projectile 2. If and θ 2 height h1 reached by projectile 1 is twice theθ1maximum denote the respective angles, h2 reached by launch projectile 2. If as θ1 measured and θ 2 height from thethehorizontal, angles satisfy which of denote respectivethese launch angles, as measured the following relationships? from the horizontal, these angles satisfy which of

47. A stone is glued to the top of a light wooden block that floats in a pool of water, as shown in 47. A stone is glued to the top of a light wooden Figure 1 above. Assume that exactly 50 percent block that floats in a pool of water, as shown in of the block is under water, and that the stone Figure 1 above. Assume that exactly 50 percent has half the weight of the block. If the block and of the block is under water, and that the stone stone are flipped over, as shown in Figure 2, and has half the weight of the block. If the block and replaced in the pool, the amount of the block stone are flipped over, as shown in Figure 2, and under water will be replaced in the pool, the amount of the block (A) less thanwill 50% under water be (B) still 50% (A) less than 50% (C) between 50% and 75% (B) still 50% (D) between 75% and 100% (C) between 50% and 75% (E) 100%, since the stone and block sink (D) between 75% and 100% (E) 100%, since the stone and block sink

the (A) following cos θ1 = relationships? 2 cos θ 2 (B) (A) (C) (B) (D) (C) (E) (D)

sin cosθθ11 == 22 sin cosθθ22 tanθ1 1 = 2 sin tanθθ2 2 sin sin θ 2θ 2 tanθθ11 == 2sin 2 tan cosθθ1 == 2sin 2cosθθ 2 sin 1

2

(E) cos θ1 = 2cos θ 2

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50. When an object is located 25 cm from lens 1, an inverted image is produced 100 cm from the lens, as shown in Figure 1 50. When an object is located 25 cm from lens 1, an inverted above. A second lens with a focal length of +20 cm is placed image is produced 100 cm from the lens, as shown in Figure 1 110 cm from the first lens, as shown in Figure 2 above. above. A second lens with a focal length of +20 cm is placed Which of the following is true of the image produced by 110 cm from the first lens, as shown in Figure 2 above. lens 2 ? Which of the following is true of the image produced by (A) It lens 2 ?is real and inverted relative to the object. (B) It is real and upright relative to the object. (A) It is real and inverted relative to the object. (C) It is virtual and inverted relative to the object. (B) It is real and upright relative to the object. (D) It is virtual and upright relative to the object. (C) It is virtual and inverted relative to the object. (E) An image cannot be produced in this situation. (D) It is virtual and upright relative to the object. (E) An image cannot be produced in this situation.

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53. A microwave line has a laboratory wavelength of l mm. If the Hubble constant H ª 75wavelength (km/s)/Mpc, 53. A microwave line has a laboratory of the observed wavelength for the line from a l mm. If the Hubble constant H ª 75 (km/s)/Mpc, galaxy 100 Mpc distant is about the observed wavelength for the line from a (A) 250100 nmMpc shorter galaxy distant is about (B) 25 nm shorter (A) 250 nm shorter (C) the same (B) 25 nm shorter (D) 25 nm longer (C) the same (E) 250 nm longer (D) 25 nm longer (E) 250 nm longer

51. A grating spectrometer can just barely resolve two wavelengths of 500 nm and 502 nm, 51. A grating spectrometer can just barely resolve respectively. Which of the following gives two wavelengths of 500 nm and 502 nm, the resolving power of the spectrometer? respectively. Which of the following gives (A) resolving 2 power of the spectrometer? the (B) 250 (A) 2 (C) 5,000 (B) 250 (D) 10,000 (C) 5,000 (E) 250,000 (D) 10,000 (E) 250,000 52. A gas cell with an optical path length of 10 cm is placed in one arm of a Michelson interferometer. 52. A gas cell with an optical path length of 10 cm is If the light source for the interferometer is a laser placed in one arm of a Michelson interferometer. with wavelength l = 632.2 nm, then 100 fringes If the light source for the interferometer is a laser are counted as the gas cell is evacuated. What is with wavelength l = 632.2 nm, then 100 fringes the index of refraction of the original gas? are counted as the gas cell is evacuated. What is (A) 1.00063 the index of refraction of the original gas? (B) 1.00032 (A) 1.00063 (C) 1.00016 (B) 1.00032 (D) 0.99968 (C) 1.00016 (E) -1.00016 (D) 0.99968 (E) -1.00016

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54. The AC circuit shown above contains an ideal rectifying diode. If the function generator supplies e (t )AC = Vcircuit t , which of the following describes the voltage the resistor? 0 sin wshown 54. The above contains an ideal rectifying diode.across If the function generator supplies

e (t ) = V0 sin wt , which of the following describes the voltage across the resistor? (A) (A) (B) (B) (C) (C) (D) (D) (E)

(E)

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55. The Fourier series expansion of a function f ( x ) that is periodic withseries period 2p is of a function f ( x ) that is 55. The Fourier expansion • • awith periodic 2p nx is) + 0 + period f ( x) = an cos( bn sin(nx ). a20 n•1=n•1 = + f ( x) = a cos( nx ) + bn sin(nx ). which of the following If f ( x ) is2 given byn the graph above, = n 1= n 1 statements about by thethe coefficients is true? graph above, which of the following If f ( x ) is given

 Â

 Â

for allthe n coefficients is true? (A) an = 0 about statements (B) = 00 for for all all nn (A) bann = (C) ban = 0 for even n only (B) n = 0 for all n = only (D) b (C) ann = 00 for for even even nn only (E) ban = foreven all n n only (D) = b0nfor n

(E) an = bn for all n

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57. Which of the following statements is (are) true for a Maxwell-Boltzmann description of an ideal gas 57. Which of the following statements is (are) true for of atoms in equilibrium at temperature T ? a Maxwell-Boltzmann description of an ideal gas I. Thein average velocity of the atoms Tis ?zero. of atoms equilibrium at temperature II. The distribution of the speeds of the atoms I. The average velocity of the atoms is zero. has a maximum at u = 0. II. The distribution of the speeds of the atoms III. The probability of finding an atom with zero has a maximum at u = 0. kinetic energy is zero. III. The probability of finding an atom with zero (A) Ikinetic only energy is zero. (B) II only (A) I only (C) I and II (B) II only (D) I and III (C) I and II (E) II and III (D) I and III (E) II and III 58. A monatomic ideal gas changes from an initial state (Pi , Vi , ideal Ti, ngas a final from state an (Pfinitial , Vf , i) to 58. A monatomic changes T , n ), where P < P , V = V , T < T f f(P , V , T , i n ) fto a ifinalf state i (Pf , and state i i i i f Vf , of the following gives the nTi ,= nnf ),. Which where Pi < Pf , Vi = Vf , Ti < Tf change and f f in entropy of the gas? n = n . Which of the following gives the change

56. A sample of N molecules has the distribution of speeds shown the figure has above. P (u ) du is an 56. A sample of Ninmolecules the distribution of estimate of the number of molecules with speeds speeds shown in the figure above. P (u ) du is an between u the andnumber u + duof , and this number estimate of molecules with is speeds nonzero only up to 3u , where u is constant. 0 between u and u + du0 , and this number is Which of the following gives the value of a? nonzero only up to 3u , where u is constant. 0

0

Which of the N following gives the value of a ? (A) a = 3u0 N (A) a = N (B) a = 3u0 2u0 N (B) a = N 2 (C) a = u0 u0 N (C) a = 3N (D) a = u0 2u0 3N (D) a = 2 (E) a = Nu0

i

f

in entropy ofÊ the T f ˆgas? 3 (A) nR ln Á ˜ 2 ÊË TTif ˆ¯ 3 (A) nR ln Á ˜ 23 ÊË T ˆ¯ (B) nR ln Á i ˜ 2 ËÊ TTf ˆ¯ 3 (B) nR ln Á i ˜ 25 ËÊ T ¯ˆ (C) nR ln Á f ˜ 2 ÊË TTif ˆ¯ 5 (C) nR ln Á ˜ 25 ÊË T ˆ¯ (D) nR ln Á i ˜ 2 ËÊ TTf ˆ¯ 5 (D) nR ln Á i ˜ 2 Ë Tf ¯ (E) 0

(E) a = N

(E) 0

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59. Low-energy electrons are accelerated between electrodes in a tube filled with a gas in the Franck-Hertz apparatus represented above. A plot of current collected versus accelerating voltage is also shown. The 59. Low-energy electrons are accelerated between electrodes in a tube filled with a gas in the Franck-Hertz data provide evidence for which of the following? apparatus represented above. A plot of current collected versus accelerating voltage is also shown. The (A) energy for losses dueofonly elastic collisions data Electronic provide evidence which the to following? (B) Excitation energies of the gas atoms of 4.9, 9.8, and 14.7 eV (A) Electronic energy losses due only to elastic collisions (C) Excitation energy of the gas atoms of 4.9 eV only (B) Excitation energies of the gas atoms of 4.9, 9.8, and 14.7 eV (D) energy levels of -4.9, -9.8,ofand eV (C) Atomic Excitation energy of the gas atoms 4.9-14.7 eV only (E) Atomic energy levels of -4.9 and -9.8 eV only (D) Atomic energy levels of -4.9, -9.8, and -14.7 eV (E) Atomic energy levels of -4.9 and -9.8 eV only

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63. The operators for the total angular momentum and its three projections areangular Jˆ and momentum Jˆ x , Jˆ y , Jˆz , 63. The operators for the total respectively. The commutator and its three projections are Jˆ between and Jˆ x , two Jˆ y , Jˆz , ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ is ÈÎ A, B ˘˚ between operators A and ∫ AB - BA respectively. The B commutator two. ˆ true? ˆ ˆ - BA ˆ ˆ. Which of the following Bˆ is ÈÎis A, Bˆ ˚˘ ∫ AB operators Aˆ and 2 the Which is true? =0 (A) ÈÎ Jˆ of , Jˆ z ˘˚ following (A) ÈÈÎ Jˆˆ 22 , Jˆˆ z ˘˚˘ = 0 ˆ (B) Î J , J z ˚ = i=J y ˆ 2 , Jˆ ˘ = i=Jˆ (B) ÈÎÈ J ˆ ˆz y J (C) Î x , J y ˚˚˘ = 0 (C) ÈÎÈ Jˆˆ x , Jˆˆ y ˘˚˘ = 0 ˆ (D) Î J x , J z ˚ = i=J z ˆ Ȉ ˆ ˘ (D) (E) ÎÈÎ JJˆ xx , +J ziJ˚ˆ y=, Jˆiz=˘˚J z= 0 0 (E) ÈÎ Jˆ x + iJˆ y , Jˆz ˘˚ = 64. The suspension cable of a 1,000 kg elevator snaps, sending the elevator moving downward 64. The suspension cable of a 1,000 kg elevator through its shaft. The emergency brakes of snaps, sending the elevator moving downward the elevator stop the elevator shortly before it through its shaft. The emergency brakes of reaches the bottom of the shaft. If the elevator the elevator stop the elevator shortly before it fell a distance of 100 m starting from rest, the reaches the bottom of the shaft. If the elevator heat that the brakes must dissipate to bring the fell a distance of 100 m starting from rest, the elevator safely to rest is heat that the brakes must dissipate to bring the (A) 100 to J rest is elevator safely (B) 1,000 J (A) 100 J (C) 10,000 J (B) 1,000 J (D) 100,000 J (C) 10,000 J (E) 1,000,000 J (D) 100,000 J (E) 1,000,000 J

60. A photon of wavelength l is scattered from an electron through an angle q . 60. A photon of wavelength l is scattered Which of the following correctly gives the from an electron through an angle q . wavelength l¢ of the scattered photon? Which of the following correctly gives the wavelength l¢ hof the scattered photon? (A) l ¢ = l+ (1 - cos q ) mc h (A) l¢ = l + h (1 - cos q ) (B) l ¢ = l + mc (1 + cos q ) mc h (B) l¢ = l + h (1 + cos q ) mc (C) l ¢ = l(1 - cos q ) mc h (C) l¢ = l - h (1 - cos q ) (D) l ¢ = l - mc (1 + cos q ) mc h (D) l¢ = lh(1 + cos q ) (E)= l¢ (1mc- cos q ) mc h (E)= l¢ (1 - cos q ) mc 61. Excited states of the helium atom can be characterized as para- (antiparallel electron 61. Excited states of the helium atom can be spins) and ortho- (parallel electron spins). characterized as para- (antiparallel electron The observation that an ortho- state has lower spins) and ortho- (parallel electron spins). energy than the corresponding para- state can be The observation that an ortho- state has lower understood in terms of which of the following? energy than the corresponding para- state can be (A) The Heisenberg uncertainty principle understood in terms of which of the following? (B) The Pauli exclusion principle (A) The Heisenberg uncertainty principle (C) The Bohr model of the atom (B) The Pauli exclusion principle (D) Nuclear hyperfine coupling (C) The Bohr model of the atom (E) Maxwell-Boltzmann statistics (D) Nuclear hyperfine coupling (E) Maxwell-Boltzmann statistics 62. A particle of mass m and spin zero is in a 62. A particle of mass isotropic m and spin is in a three-dimensional wellzero described

1 three-dimensional 2 , wherewell r2 =described x2 + y2 + z2. by V (r ) = mw 2 risotropic 2 1 by V (r ) = mw 2 r 2 , where r2 7= x2 + y2 + z2. 2 How many states have energy =w ? 2 7

How many states have energy =w ? (A) 1 2 (B) 2 (A) 1 (C) 4 (B) 2 (D) 6 (C) 4 (E) 8 (D) 6 (E) 8

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65. A uniform rod of length L and mass M is released from rest at q = 0 and rotates about a 65. A uniform rod of length L and mass M is horizontal axis through its base, as shown in the released from rest at q = 0 and rotates about a figure above. What is the angular acceleration of horizontal axis through its base, as shown in the the rod as a function of q ? (Ignore the effects of figure above. What is the angular acceleration of friction and air resistance.) the rod as a function of q ? (Ignore the effects of friction g and air resistance.) (A) 2gL (A) g q (B) 2L

L g

(B) 6 gq (C) L cos q L 6g

(C) 3g cos q (D) L sin q 23g L (D) 12 gsin q (E) 2L sin q L 12g

(E) sin q L

66. Two identical, ideal springs, each with force constant k, are attached in series and hung 66. Two identical, ideal springs, each with force vertically. When a block of mass m is attached constant k, are attached in series and hung to the two-spring system, the block moves down vertically. When a block of mass m is attached a distance x from the relaxed state, as shown in to the two-spring system, the block moves down the figure above. Which of the following gives the a distance x from the relaxed state, as shown in angular frequency of the block when it oscillates the figure above. Which of the following gives the vertically? angular frequency of the block when it oscillates vertically? 2k (A) m 2k (A) km (B) m k (B) mk (C) 2m k (C) 2mk (D) 2 p x k (D) 2 p 2xk (E) 2 p x 2k (E) 2 p x 67. A block attached to a spring is moving along the x-axis on a frictionless horizontal surface. What is 67. A block attached to a spring is moving along the the Hamiltonian for the block? x-axis on a frictionless horizontal surface. What is H =0 (A) Hamiltonian the for the block? (A) H = 0 (B) H = - kx (B) H = - kx k (C) H = x 2 2 k (C) H = p 2x 2 2 (D) = H 2pm 2 (D) = H p2 (E) = H 2m + 2pm 2 (E) = H + 2m

k 2 x 2 k 2 x 2k x 2 2 k 2 x 2

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68. A conducting sphere is solid except for three spherical cavities inside. Cavity A contains a point charge of +2q, 68. A conducting sphere is solid except for three spherical cavity Binside. contains a point charge ofa point -4q, charge and cavity C is cavities Cavity A contains of +2q, empty, as shown above. What charges are induced on the cavity B contains a point charge of -4q, and cavity C is inner surfaces of the spherical cavities? empty, as shown above. What charges are induced on the B cavities? Cavity C A of the Cavity innerCavity surfaces spherical (A) Cavity -2q A (B) -2q -2q (A) (C) -2q (B) -2q (D) -2q +2q (C) (E) +2q (D) +2q (E) +2q

Cavity +4q B +4q +4q +4q +4q -4q +4q +2q -4q +2q

Cavity 0 C 0-2q -6q -2q 0 -6q +2q 0 +2q

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71. Consider the Pauli spin matrices sx , sy , and sz. The product sx spin sy ismatrices equal to swhich of the 71. Consider the Pauli x , sy , and following? s . The product s s is equal to which of the

69. A magnetic field is directed perpendicular to the plane of a circular of area 0.2 m2 and 250 69. A magnetic field iscoil directed perpendicular to the turns. of If the magnetic is increased from plane a circular coilfield of area 0.2 m2 and 250 0.01 0.06 T during a time interval of 0.25 s, turns.TIftothe magnetic field is increased from the induced EMF in theinterval coil is of 0.25 s, 0.01average T to 0.06 T during a time

z

x

y

(A) 0 following? (B) s (A) 0z (C) -s (B) s z

(A) average 0.04 Vinduced EMF in the coil is the (B) 0.1 V (A) 0.04 V (C) 2.5 V (B) 0.1 V (D) 10 V (C) 2.5 V (E) 50 V (D) 10 V (E) 50 V

z

(D) -s sy zsx (C) (E) s -syssx (D) y

x

(E) -sy sx 72. The binding energy per nucleon is greatest for which of the following nuclei? 72. The binding energy per nucleon is greatest for which of the following nuclei? (A) 3 He 2 (A) 2423 He (B) 4 (B) 56 Fe (C) 2 He

26 56

Fe (C) (D) 235 26 92 U 238 U (D) 235 (E) 92 92 U 238 (E) 92 U

70. The figure above depicts a step potential with U ( x )above = 0, depicts for xa £step 0 potential (region 1), 70. The figure with UU = > 00 (region ( x()x ) �U = 0,0 , for for xx £ (region 2). 1), A beam incident U ( xof) particles for xE>>00 is �U 0 , with = (region 2). from the left. The momentum of the particle in each A beam of particles with E > 0 is incident from region has the form =k . The reflection coefficient the left. The momentum of the particle in each R for the interface at x = 0 is region has the form =k . The reflection coefficient = 0interface at x = 0 is (A) R forRthe

73. The negative muon, m-, has properties most similar to which of the following? 73. The negative muon, m-, has properties (A) mostQuark similar to which of the following? (B) Boson (A) Quark (C) Photon (B) Boson (D) Meson (C) Photon (E) Electron (D) Meson (E) Electron

(A) R = 0 4 k1k2 (B) R = (k14k+1k22 )2 (B) R = (k1 + k2 ) 2

( k + k 2 )2 (C) R = 1 (k1 + - k2 )22 (k (C) R = 1 2 2

(k1 - k2 ) (k1 - k2 )2 (D) R = (k1 + k22 )22 (k (D) R = 1 (k1 + k2 )2

-4 k1k2 (E) R = (k-1 4k + 1kk22)2

(E) R = (k1 + k2 )2

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74. Which of the following correctly gives the quark and antiquark content of a lepton and a baryon? 74. Which of the following correctly gives the quark Baryon Lepton and antiquark content of a lepton and a baryon? Quarks Antiquarks Quarks Antiquarks Baryon Lepton (A) 0 0 3 0 Quarks Antiquarks Quarks Antiquarks (B) 0 0 1 1 (A) 0 0 3 0 (C) 1 0 1 1 (B) 0 0 1 1 (D) 1 1 2 0 (C) 1 0 1 1 (E) 1 1 3 0 (D) 1 1 2 0 (E) 1 1 3 0

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75. Under certain conditions, a beam of electrons impinging on a crystal surface will diffract and 75. Under certain conditions, a beam of electrons a scattering pattern of the beam can be obtained. impinging on a crystal surface will diffract and What is the approximate kinetic energy of the a scattering pattern of the beam can be obtained. electrons needed in order to see the pattern? What is the approximate kinetic energy of the (Assume the lattice spacing of the crystal to electrons needed in order to see the pattern? be 0.4 nm.) (Assume the lattice spacing of the crystal to (A) 0.1 eV be 0.4 nm.) (B) 1 eV (A) 0.1 eV (C) 10 eV (B) 1 eV (D) 100 eV (C) 10 eV (E) 1000 eV (D) 100 eV (E) 1000 eV

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76. A beam of positive ions is initially moving in the +x-direction with nonrelativistic velocity. The beam enters a velocity 76. A beam of positive ions is initially moving in the +x-direction selector in which the electric field E is oriented along the with nonrelativistic velocity. The beam enters a velocity +y-direction and the magnetic field B is oriented along the selector in which the electric field E is oriented along the +z-direction, as shown above. Which of the following gives +y-direction and the magnetic field B is oriented along the the critical speed uc at which the ion beam is not deflected +z-direction, as shown above. Which of the following gives as movesspeed through at velocity which theselector? ion beam is not deflected theitcritical u the c

as through the velocity selector? (A)it moves uc = EB (A) uc = EB 1 (B) uc = EB 1 (B) uc = B2 EB (C) uc = E B2 (C) uc = B (D) uc = E

E B

(D) uc = E (E) uc = E

B E

(E) uc = B

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77. Under ideal conditions, the electric and magnetic fields inside a superconductor 77. Under ideal conditions, the electric and are zero. Maxwell’s equations imply that magnetic fields inside a superconductor which of the following must be true just are zero. Maxwell’s equations imply that outside the surface of the superconductor? which of the following must be true just (A) B =the 0 surface of the superconductor? outside (B) B is perpendicular to the surface. (A) B = 0 (C) B is tangential to the surface. (B) B is perpendicular to the surface. (D) B is time independent. (C) B is tangential to the surface. (E) The magnetic flux is quantized. (D) B is time independent. (E) The magnetic flux is quantized.

79. A block with mass m1 that slides on a frictionless table is attached by m a massless string a 79. A block with mass that slides on over a frictionless massless, frictionless 1pulley to a hanging ball table is attached by a massless string over a with mass m2 , as shown in the figure above. massless, frictionless pulley to a hanging ball The tension string must with mass min ,the as shown in thebefigure above. 2

(A) tension equal toinmthe The 2 g string must be (B) greater than (A) equal to m2 gm2 g (C) thanthan m2 gm g (B) less greater 2 (D) equalthan to mm1gg (C) less 2 (E) equal greatertothan m gm1g (D)

78. A positive charge, +q, oscillates up and down, as represented in the figure above. What is the 78. A positive charge, +q, oscillates up and down, direction of the Poynting vector S at point P ? as represented in the figure above. What is the (Assume P is located far to the right of +q.) direction of the Poynting vector S at point P ? (A) Toward thelocated left far to the right of +q.) (Assume P is (B) Toward the right (A) Toward the left (C) Toward the top of the page (B) Toward the right (D) Toward the bottom of the page (C) Toward the top of the page (E) Into the page (D) Toward the bottom of the page (E) Into the page

1

(E) greater than m1g

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80. Two planets of mass m revolve around a star of 80. Two massofmradius revolve around a star of mass planets M in aofcircle r , as shown in the

82. As represented in the figure above, a light ray refracts from air into a rectangular block of plastic 82. As represented in the figure above, a light ray with an index of refraction n > 1. At a point on refracts from air into a rectangular block of plastic the side of the block, the ray partly reflects (at an with an index of refraction n > 1. At a point on angle of of 60∞) partly The value (at of the the side theand block, therefracts. ray partly reflects an angle a is angle of 60∞) and partly refracts. The value of the angle a is (A) 30∞

mass M in a The circletwo of planets radius rare , asalways shownon in the figure above. opposite sidesThe of the The are orbital period figure above. twostar. planets always on T of 3

r period T of opposite sides theform star. T The the planets is ofofthe = orbital 2p . GM 3 ¢ r the planets of the M ¢ ?T = 2 p GM ¢ . What is theisvalue ofform What is themvalue of M ¢ ?

(A) M 2 m (A) M - m (B) M - 2 4 m (B) M (C) 4 m (C) (D) M + 4 m

(D) M + m (E) M + 4 2 m (E) M + 2 81. White light is normally incident on a puddle of water (index of refraction 1.33). A thin (500 nm) 81. White light is normally incident on a puddle of layer of oil (index of refraction 1.5) floats on the water (index of refraction 1.33). A thin (500 nm) surface of the puddle. Of the following, the most layer of oil (index of refraction 1.5) floats on the strongly reflected wavelength is surface of the puddle. Of the following, the most (A) 500 reflected nm strongly wavelength is (B) 550 nm (A) 500 nm (C) 600 nm (B) 550 nm (D) 650 nm (C) 600 nm (E) 700 nm (D) 650 nm (E) 700 nm

(A) 30∞ (B) 60∞ (B) 60∞ -1 n (C) cos 2 n (C) cos--11 n 2 (D) sin 2 -1 n (D) sin-1 (E) tan n2 (E) tan-1 n 83. Assume that the solar flux at Earth’s surface 2 is 1,000 W/m that theatsunlight normal 83. Assume that theand solar flux Earth’s issurface to a completely reflecting surface with an area 2 is 1,000 2 W/m and that the sunlight is normal of m . What isreflecting the total radiation force to a3 completely surface with anexerted area on the 2surface? of 3 m . What is the total radiation force exerted on (A)the 2 ¥surface? 10-6 N -6 N (B) 21 ¥ ¥ 10 10-5 (A) N -5 -5 N (C) 2 ¥ 10 (B) 1 ¥ 10 N (D) N 10-5 N (C) 32 ¥ (E) (D) 63 N N (E) 6 N

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85. Protons used in cancer therapy are typically accelerated to about 0.6c . How much work must 85. Protons used in cancer therapy are typically be done on a particle of mass m in order for it to accelerated to about 0.6c . How much work must reach this speed, assuming it starts at rest? be done on a particle of mass m in order for it to 2 reach this speed, assuming it starts at rest? (A) 0.25mc

84. The hydrogen lines observed in the spectrum of the quasar 3C9 are shifted so far into the red that 84. The hydrogen lines observed in the spectrum of their wavelengths are three times as long as those the quasar 3C9 are shifted so far into the red that observed in the light from hydrogen atoms at rest their wavelengths are three times as long as those in a laboratory on Earth. If it is assumed that the observed in the light from hydrogen atoms at rest shift is entirely due to the relative motion of in a laboratory on Earth. If it is assumed that the 3C9 and Earth, the relative speed of the quasar is shift is entirely due to the relative motion of (A) 2c 3C9 and Earth, the relative speed of the quasar is (B) c (A) 2c (C) 0.8c (B) c (D) 0.5c (C) 0.8c (E) 0.3c (D) 0.5c (E) 0.3c

(B) (A) (C) (B)

2 0.60mc 0.25mc 2 2 0.67mc 0.60mc 2

2 (D) 1.25mc (C) 0.67mc 2 2 (E) (D) 1.60mc 1.25mc 2

(E) 1.60mc 2 86. The sign of the charge carriers in a doped semiconductor can be deduced by measuring 86. The sign of the charge carriers in a doped which of the following properties? semiconductor can be deduced by measuring (A) Specific heat which of the following properties? (B) Thermal conductivity (A) Specific heat (C) Electrical resistivity (B) Thermal conductivity (D) Magnetic susceptibility (C) Electrical resistivity (E) Hall coefficient (D) Magnetic susceptibility (E) Hall coefficient

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87. In the experimental setup above, two masses, m1 and m2 , arethe connected by a massless stringtwo over a massless pulley. 87. In experimental setup above, masses, m1 and m2 , Mass m slides on a frictionless surface. The values of the 1 are connected by a massless string over a massless pulley. two can be as well as the distance d and Massmasses m slides onmeasured, a frictionless surface. The values of the 1

the ofcan mass x1 asand at x2d. The twospeed masses be m measured, as well theagain distance and 1 as it passes experiment be m usedastoitdo whichx ofand the again following? the speed ofcan mass passes at x . The 1

1

2

I. Demonstrate conservation experiment can be momentum used to do which of the following? II. Demonstrate energy conservation I. Demonstrate momentum conservation III. Measure the value of the acceleration due to gravity II. Demonstrate energy conservation (A) only III. IMeasure the value of the acceleration due to gravity (B) II only (A) I only (C) III only (B) II only (D) I and II (C) III only (E) II and III (D) I and II (E) II and III

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89. Two balls, identical in every way except that one has twice the mass of the other, are dropped from 89. Two balls, identical in every way except that one rest from the same height so that they both reach has twice the mass of the other, are dropped from terminal speed before hitting the ground. If it is rest from the same height so that they both reach assumed that the drag force varies like the speed terminal speed before hitting the ground. If it is squared, what is the ratio of the terminal speeds assumed that the drag force varies like the speed of the balls? (Note: The subscripts h and l squared, what is the ratio of the terminal speeds denote the heavy and light masses, respectively.) of the balls? (Note: The subscripts h and l denote u the heavy and light masses, respectively.) (A) h = 1 uul (A) h = 1 u (B) hl = 2 uul (B) h = 2 u (C) hl = 2 uul (C) h = 2 u (D) hl = 2 2 uul (D) h = 2 2 u (E) hl = 4 uul (E) h = 4 ul

88. An airplane drops a payload while traveling due north, parallel to the ground, at a constant speed 88. An airplane drops a payload while traveling due of 100 m/s. If air resistance is neglected, what is north, parallel to the ground, at a constant speed the velocity of the payload relative to the plane of 100 m/s. If air resistance is neglected, what is 4.0 s after it is released? the velocity of the payload relative to the plane (A) s0after it is released? 4.0 (B) 40 m/s down (A) 0 (C) 80 m/s down (B) 40 m/s down (D) 100 m/s north and 40 m/s down (C) 80 m/s down (E) 100 m/s south and 40 m/s down (D) 100 m/s north and 40 m/s down (E) 100 m/s south and 40 m/s down

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90. One end of a horizontal, massless spring is attached to a wall. A mass of 0.30 kg is attached to the other end of the spring 90. One end of a horizontal, massless spring is attached to a wall. and rests on a table. The mass is displaced 0.030 m from its A mass of 0.30 kg is attached to the other end of the spring equilibrium position and released. It has a speed of 0.040 m/s and rests on a table. The mass is displaced 0.030 m from its as it passes through its equilibrium position. In the absence of equilibrium position and released. It has a speed of 0.040 m/s friction, what is the total mechanical energy of the system? as it passes through its equilibrium position. In the absence of (A) 0.24what mJ is the total mechanical energy of the system? friction, (B) 0.38 mJ (A) 0.24 mJ (C) 0.48 mJ (B) 0.38 mJ (D) 0.75 mJ (C) 0.48 mJ (E) 0.96 mJ (D) 0.75 mJ (E) 0.96 mJ

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93. An inertial reference frame S ¢ moves at constant speed with respect to frame a second reference S ¢ inertial moves at constant 93. An inertial reference frame S. An observer in S measures the energy speed with respect to a second inertial reference E, momentum p, and position x of a moving frame S. An observer in S measures the energy particle at time p, t for particularxevent. An E, momentum anda position of a moving observeratintime S ¢ measures energy Eevent. ¢ , momentum particle t for a particular An p¢ , and position x at time t for the same ¢ ¢ observer in S ¢ measures energy E ¢ , momentum moving of the p¢ , and particle positionatxthe time event. t ¢ forWhich the same ¢ atsame following is an expression a relativistic moving particle at the sameofevent. Which of the invariant for this event? following is an expression of a relativistic

91. The diagram above shows a Carnot cycle for an idealdiagram air conditioner, whicha is to cool a house on a 91. The above shows Carnot cycle for an hot day. The which air conditioner idealsummer air conditioner, is to coolabsorbs a househeat on a at the lower temperature inside and pumps it to hot summer day. The air conditioner absorbs heat the environment at the higher at the lower temperature insidetemperature and pumps outside. it to Which of the following gives the ratio of the heat the environment at the higher temperature outside. Q in the house (i.e., bc absorbed Which of the following gives thebetween ratio of points the heatb

invariant (A) x = for x ¢ this event? (B) (A) xp== xp¢¢ (C) tp== t p¢ ¢ (B) (D) tE== t ¢E ¢ (C)

E=2 -E( ¢pc ) =E ¢2 - ( p ¢c ) (E) (D) E 2

2

(E) E 2 - ( pc ) =E ¢2 - ( p ¢c ) 94. Consider three identical, ideal capacitors. The first capacitor three is charged to a voltage V0 and then The first 94. Consider identical, ideal capacitors. disconnected from the battery. The other two capacitor is charged to a voltage V0 and then capacitors, initially uncharged disconnected from the battery. and Theconnected other two in series, are then connected across theconnected first capacitors, initially uncharged and in capacitor. What is the final voltage on the first series, are then connected across the first capacitor? capacitor. What is the final voltage on the first 2

and c on the cycle) to the work done during the Q bc absorbed in the house (i.e., between points b cycle? and c on the cycle) to the work done during the (A) 0 cycle? (B) 0.033 (A) 0 (C) 0.97 (B) 0.033 (D) 1.0 (C) 0.97 (E) 30. (D) 1.0 (E) 30. 92. A particle in an infinite square well with walls at 9= 2 p 2 92. xA=particle squareE well 0 and in x =anLinfinite has energy = with2 walls . The at 2 2 92=mLp xprobability = 0 and xthat hasparticle energyisEbetween = Lthe = x .= The 0 and 2mL2 x = L/6 is that the particle is between x = 0 and probability

2

capacitor? V (A) 0 V5 (A) 0 V5 (B) 0 V3 (B) V0 3 (C) 0 2 V0 (C) 2V 2 0 (D) 3 2V

0 (D) (E) V03

1/36is x(A) = L/6 (B) 1/6 (A) 1/36 (C) 1/3 (B) 1/6 (D) 1/2 (C) 1/3 (E) 1 (D) 1/2 (E) 1

(E) V0

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95. A charge of -5.0 µC is distributed uniformly around a ring 1.0 m in radius. A point charge of 95. A charge of -5.0 µC is distributed uniformly +3.0 µC is at the center of the ring. The work around a ring 1.0 m in radius. A point charge of required to move the point charge 1.0 m in a +3.0 µC is at the center of the ring. The work direction normal to the plane of the ring is most required to move the point charge 1.0 m in a nearly direction normal to the plane of the ring is most (A) 40 mJ nearly (B) 80 mJ (A) 40 mJ (C) 100 mJ (B) 80 mJ (D) 140 mJ (C) 100 mJ (E) 270 mJ (D) 140 mJ (E) 270 mJ

96. The magnetic field inside a long coil of wire (solenoid) has a certain magnitude and direction 96. The magnetic field inside a long coil of wire when the coil is air filled. If a diamagnetic (solenoid) has a certain magnitude and direction material is inserted in the coil, how do the when the coil is air filled. If a diamagnetic magnitude and direction of the magnetic field material is inserted in the coil, how do the change? magnitude and direction of the magnetic field Direction Magnitude change? (A) (B) (A) (C) (B) (D) (C) (E) (D) (E)

Increases Magnitude Increases Increases Decreases Increases Decreases Decreases No change Decreases No change

Same Direction Opposite Same Same Opposite Opposite Same Opposite Opposite Opposite

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SCRATCH WORK

79 -73-

97. The figure above shows two identical simple pendulums, each with mass m and suspended by a massless rod of length a. The pendulums are coupled by a massless spring of force constant k. The coordinates qi measure 97. The figure above shows two identical simple pendulums, each with mass m and suspended by a massless rod the angular displacements from vertical, as shown. Which of the following gives the Lagrangian for the system? of length a. The pendulums are coupled by a massless spring of force constant k. The coordinates qi measure (Assume small angular displacements qi .) the angular displacements from vertical, as shown. Which of the following gives the Lagrangian for the system? qi .) (Assume small displacements 1 2angular 1 1 L ma q 21 + q 22 - mga q 21 + q 22 - ka 2 (q2 - q1 )2 (A)= 2 2 2 1 1 1 L 1 ma 22 q 221 + q 22 - 1 mga q 221 + q 22 - 1 ka 22 (q2 - q1 )22 (A)= (B)= L 2 ma q 1 + q 2 + 2 mga q 1 + q 2 - 2 ka (q2 - q1 ) 2 2 2 1 1 1 L 1 ma 22 q 221 + q 22 + 1 mga q 221 + q 22 - 1 ka 22 (q2 - q1 )22 (B)= (C)= L 2 ma q 1 + q 2 - 2 mga q 1 + q 2 + 2 ka (q2 - q1 ) 2 2 2 1 1 1 L 1 ma 22 q 221 + q 22 - 1 mga q 221 + q 22 + ka 2 (q2 - q1 )2

(C)= 2 (D)= L 2 ma q 1 + q 2 + 2 mga q 1 + q 2 2 2 1 2 2  2 1 2 2 L 1 ma 2 q 21 + q 2 + 1 mga q +q (D)= (E)= L 2 ma q 1 + q 2 + 2 ka 2 (q2 1- q1 )22 2 2 1 1 2 2  2 L ma q 1 + q 2 + ka 2 (q2 - q1 )2

(E)= 2 2

( (( (( (( (( (

) )) )) )) )) )

( (( (( (( (

) )) )) )) )

GO ON TO THE NEXT PAGE.

80

-74-74-

GO ON TO THE NEXT PAGE.

SCRATCH WORK

81 -75-

= n 4, = A 1 state in 99. Consider an electron in the Which of the following final = n 4, = A 1states statecan in 99. hydrogen. Consider an electron in the NOT be reached by an allowed transition? hydrogen. Which of the following final states can

98. The spacing between the parallel Bragg planes in a certain crystal is d . Electrons of fixed energy, 98. The spacing between the parallel Bragg planes in corresponding to a given wavelength l , are a certain crystal is d . Electrons of fixed energy, incident on the crystal. Which of the following is corresponding to a given wavelength l , are the minimal condition for strong reflection for at incident on the crystal. Which of the following is least two different angles? the minimal condition for strong reflection for at (A) ltwo > ddifferent angles? least d (A) l > d

(B) 2 d

(B) l > (C) < 2d 2 d (D) (C) l < 2d d (D) (E) l < d

2 d

(E) l < 2

nbe reached 3, = A 2by an allowed transition? (A)= NOT (B)= nn 3, = = 3, = AA 12 (A) (C)= nn 3, = AA 10 (B) = 3, = (D) nn 3, 2, = (C)= = = AA 00 (E) = n 1, = A (D)= n 2, = A 00 (E)= n 1,= A 0

GO ON TO THE NEXT PAGE.

82

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GO ON TO THE NEXT PAGE.

SCRATCH WORK

83 -77-

100. A room-temperature Mössbauer absorption spectrum for the 14.4 keV gamma-ray transition of illustrated in the figure above. From the data, it can be deduced that the lifetime of the

57

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3 excited state is 2

approximately

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

100 ms 100 ms 100 ns 100 ps 100 fs

If you finish before time is called, you may check your work on this test.

84 -78-

Fe is

SCRATCH WORK

85 -79-

I

NOTE: To ensure prompt processing of test results, it is important that you fill in the blanks exactly as directed.

SUBJECT TEST A. Print and sign your full name in this box:

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Physics TEST NAME ___________________________________ GR1777 FORM CODE ___________________________________

GRADUATE RECORD EXAMINATIONS SUBJECT TEST B. The Subject Tests are intended to measure your achievement in a specialized field of study. Most of the questions are concerned with subject matter that is probably familiar to you, but some of the questions may refer to areas that you have not studied. Your score will be determined by the number of questions you answer correctly. Questions you answer incorrectly or for which you mark no answer or more than one answer are counted as incorrect. Nothing is subtracted from a score if you answer a question incorrectly. Therefore, to maximize your score, it is better for you to guess at an answer than not to respond at all. You are advised to use your time effectively and to work as rapidly as you can without losing accuracy. Do not spend too much time on questions that are too difficult for you. Go on to the other questions and come back to the difficult ones later if you can. YOU MUST INDICATE ALL YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. No credit will be given for anything written in this examination book, but you may write in the book as much as you wish to work out your answers. After you have decided on your response to a question, fill in the corresponding oval on the answer sheet. BE SURE THAT EACH MARK IS DARK AND COMPLETELY FILLS THE OVAL. Mark only one answer to each question. No credit will be given for multiple answers. Erase all stray marks. If you change an answer, be sure that all previous marks are erased completely. Incomplete erasures may be read as intended answers. Do not be concerned that the answer sheet provides spaces for more answers than there are questions in the test. Sample Answer

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Rome Paris London Cairo Oslo

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CORRECT ANSWER PROPERLY MARKED IMPROPER MARKS

DO NOT OPEN YOUR TEST BOOK UNTIL YOU ARE TOLD TO DO SO.

®

86

Educational Testing Service Princeton, New Jersey 08541

Worksheet for the GRE Physics Test, Form GR1777 Answer Key and Percentages* of Test Takers Answering Each Question Correctly QUESTION Number

Answer

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

E E E B E B C B D D C E D A C D D C C D E A B C B E A C D E E A A B D D D E C A E D C A A A A B B C

P+ 92 41 70 64 30 47 59 64 91 59 41 79 77 76 48 53 74 34 70 60 43 49 50 31 51 66 71 47 63 32 32 39 23 82 53 56 52 24 86 23 28 44 41 85 37 76 53 52 49 30

CORRECT RESPONSE

QUESTION Number

Answer

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

B B D B B B D A C A B D A E D C E A D D E C E A C E C B C D C D C C A E E B B A E B E D A C A D B C

P+

CORRECT RESPONSE

33 29 39 56 45 64 46 69 20 57 50 36 63 78 43 52 77 71 52 43 32 49 74 53 19 74 43 41 54 26 20 59 25 55 38 50 66 44 47 70 25 55 70 24 22 34 52 22 48 21

Total Correct: _____________ Total Scaled: _____________ * The numbers in the P+ column indicate the percentages of test takers in the United States who answer each question correctly.

GRE ® Physics Test Practice Book

87 | Page

Score Conversions for the GRE Physics Test, Form GR1777 TOTAL SCORE

88 | Page

Total Correct

Scaled Score

Total Correct

Scaled Score

84-100 83 82 81 80

990 980 970 960 950

43 42 41 40 38-39

590 580 570 560 550

79 78 77 76 75

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37 36 35 33-34 32

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340 330 320 310 300

54 53 52 51 50

690 680 670 660 650

6 5 4 1-3 0

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49 48 47 46 44-45

640 630 620 610 600

GRE ® Physics Test Practice Book

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Omit spaces, apostrophes, Jr., II., etc. Use only a pencil with soft, black lead (No. 2 or HB) to complete this answer sheet. Be sure to fill in completely the space that corresponds to your answer choice. Completely erase any errors or stray marks.

- SUBJECT TEST

2

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6. TITLE CODE

1 2 3 4

SIDE 1

SHADED AREA FOR ETS USE ONLY

8. TEST BOOK SERIAL NUMBER (number in upper right corner of front cover of your test book)

your test book)

FORM CODE (on back cover of

7. TEST NAME (on back cover of your test book)

Item responses continued on reverse side.

B C D E

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(from your admission ticket)

5. REGISTRATION NUMBER

66 A B C D E 67 A B C D E 68 A B C D E 69 A B C D E

61 A B C D E 62 A B C D E 63 A B C D E 64 A B C D E 65 A B C D E

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GRADUATE RECORD EXAMINATIONS ® -

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Enter your last name, first name initial (given name), and

1. NAME middle initial if you have one. Q3442/1-2/2 89176-02954 • TF212E70 Copyright ® 2012 by Educational Testing Service, Princeton, NJ 08541 All rights reserved. Printed in U.S.A. ®

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CERTIFICATION STATEMENT Please write the following statement below, DO NOT PRINT. “I certify that I am the person whose name appears on this answer sheet. I also agree not to disclose the contents of the test I am taking today to anyone.” Sign and date where indicated.

SUBJECT TEST

COMPLETE THE CERTIFICATION STATEMENT, THEN TURN ANSWER SHEET OVER TO SIDE 1. SIGNATURE:

DATE:

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B. Sign your full name here:

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B B

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A. Fill in both circles here . . .

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A A

Day

To cancel your scores from this test administration, you must:

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GRE ® Physics Test Practice Book

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