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Official GRE Physics Exam
Which of the following best illustrates the acceleration of a pendulum bob at points a through e? correct answersThe pendulum sways back and forth with its acceleration pointing infinitely upwards toward the center of motion. Choice (C). The coefficient of static friction between a small coin and the surface of a turntable is 0.30. The turntable rotates at 33.3 revolutions per minute. What is the maximum distance from the center 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 correct answers33.3 rev/min = 33.32pi/60 rad/s = 1.11pi rad/s. u(v^2)/r = g (masses cancel out). r = u(v^2)/g = [(0.30)(1.11pi)^2]/(9.8 m/s^2) = 0.3012.3/9.8 = 0.30 *1.25 = 0.3 m, which is closest to choice (D). 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/ (E) proportional to R2 correct answersKepler's Third Law of Planetary Motion ==> R^3 = T^2, which implies the time for one revolution is proportional to R^(3/2). Choice (D).
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) 1/ (C) 1/ (D) 1/ (E) 2/3 correct answersInitial Momentum: 2m(v) + m(0) = 2mv Final Momentum is also 2mv but different mass of 3m. The kinetic energy is KE = (p^2)/(2m), so the ratio is (p,f^2)/(p,i^2) = m,i/m,f = 2m/3m = 2/3. So 1 - 2/3 = 1/3 is the fraction of kinetic energy lost. Choice (C). A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. The average total energy of the oscillator is (A) (1/2)kT (B) kT (C) (3/2)kT (D) 3kT (E) 6kT correct answersA three-dimensional oscillator at thermal equilibrium has kT average total energy for each degree of freedom, which is represented by choice (D). An ideal monatomic gas expands quasi-statically to twice its volume. If the process is isothermal, the work done by the gas is Wi
. If the process
(D) -Q
(E) -2Q correct answersThe positive charge induces a negative coulomb charge on the plate which is -Q. Choice (D). 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? ( ) k = 1 4p 0 (A) 0 (B) kq r (C) 5 2 kq r (D) ( / ) cos / kq r2 a f 2 5 p (E) ( / ) cos / 5 25 2 kq r a f correct answersAnytime all similar charges are arranged in circle and are symmetrically distributed, the net electric field becomes zero due to total cancellation. Choice (A). A 3-microfarad capacitor is connected in series with a 6-microfarad capacitor. When a 300-volt potential difference is applied across this combination, the total energy stored in the two capacitors is (A) 0.09 J (B) 0.18 J (C) 0.27 J (D) 0.41 J (E) 0.81 J correct answersThe equivalent capacitance is 1/3 + 1/6 = 1/2, which gives a capacitance of 2 uF. The total energy is E = (1/2)CV^2 = (1/2)(2E-6 F)(300 V)^2 = 0.09 J. Choice (A). 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 correct answersWhen two converging lenses are put together they only make the image smaller and smaller, so the image put to the right of the second lens should be significantly smaller than the focal lengths and the distance between the lenses. Choice (A). 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 (D) IV (E) V correct answersSince the object is within the focal point, then the image will appear behind the lenses, which is only the last choice. Choice (E). 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.) (A) 1 mm (B) 2.5 cm (C) 10 cm (D) 2.5 m (E) 10 m correct answersThe diffraction formula does the trick: 1.226E-7 = 3E-5d ==> d = 0.025 m = 2. cm. Choice (C).
(A) 80 s (B) 160 s (C) 2,000 s (D) 5,000 s (E) 6,400 s correct answersNo idea. The ground state electron configuration for phosphorus, which has 15 electrons, is (A) 1s2 2s2 2p6 3s1 3p (B) 1s2 2s2 2p6 3s2 3p (C) 1s2 2s2 2p6 3s2 3d (D) 1s2 2s2 2p6 3s1 3d (E) 1s2 2s2 2p6 3p2 3d3 correct answersSimple chemistry and a bit of counting. Choice (B). 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)? (A) 24.6 eV (B) 39.5 eV (C) 51.8 eV (D) 54.4 eV (E) 65.4 eV correct answers(79.0 eV)/(2^2) = 20.0 eV, which is approximately choice (A). The primary source of the Sun's energy is a series of thermonuclear reactions in which the energy produced is c^2 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 correct answersRemember this and remember it well that there are 4 hydrogen atoms and 1 helium atom in the system of thermonuclear reactions. Choice (B). In the production of X rays, the term "bremsstrahlung" refers to which of the following? (A) The cut-off wavelength, lmin , 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 correct answers"Bremstrahlung" tends to involve a metal and the smooth, continuous X-ray spectra produced by decelerating electrons. Choice (E). 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/ (B) 5/ (C) 1/
ignored, which of the velocity versus time graphs shown above best represents x u versus t and y u versus t, respectively? ux vs. t uy vs. t (A) I IV (B) II I (C) II III (D) II V (E) IV V correct answersThe horizontal velocity does not change, while the vertical velocity decreases linearly. Choice (C). 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? (A) (7/2) mr (B) (13/2) mr (C) (29/2) mr (D) (49/2) mr (E) (55/2) mr2 correct answersThe 6 outer pennies cause a moment of inertia of (1/2)mr^2 each and the pennies altogether create a total of (7^2)mr^2/2 moments of inertia. So (6/2)mr^2 + (49/2)mr^2 = (55/2)mr^2. Choice (E). 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? (A) sqrt(1/3 gL (B) sqrt(gL (C) sqrt(3gL (D) sqrt(12gL (E) sqrt(12 gL correct answersWhen it comes to rods, we have a moment of inertia at the edges as (1/3)Mr^2, which gives us ample speed at the end of the fall, which is choice (C).
The eigenvalues of a Hermitian operator are always (A) real (B) imaginary (C) degenerate (D) linear (E) positive correct answersDefinition: The eigenvalues of a Hermitian operator are always real. Choice (A) y1 =-+ 51> 32> 2*3> y2 =- + 1 52 3 x
- 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) - (E) -10 correct answersThis is similar to a dot product, which gives us 5*1 + (-3)(-5) + 2x = 0, so 2x = - and x = -10. Choice (E). The state ww w w = ++ − 1 6 1 2 1 3 112
(D) 13.6 eV (E) 24.2 eV correct answersPositronium has a base ground energy of 6.8 eV and the transition gives us: 6.8 eV(1/(1^2) - 1/(3^2)) = 6.8 eV(1 - 1/9) = 6.0 eV. Choice (A). 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 (A) mc/ (B) mc / 2 (C) mc (D) 3mc (E) 2mc correct answersPythagorean Question: sqrt(2^2 - 1^2) = sqrt(4 - 1) = sqrt(3). So we have sqrt(3)*mc. Choice (D). 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 correct answersThis is pretty damn close to the speed of light just by inspection and 2.98E8 m/s should fit the details and we have choice (D). 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 /DtΩ< c (C) Only if ΩDx /DtΩ> c (D) Only if ΩDx /DtΩ= c (E) Under no condition correct answersTimelike events occur when the light acts as x/t = c. Choice (D). 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. (B) Decreases by a factor of 9. (C) Increases by a factor of 9. (D) Increases by a factor of 27. (E) Increases by a factor of 81. correct answersWien's Law gives us, the 3^4 = 81 as the factor of energy radiated per second per unit area due to the temperature tripling. Choice (E). 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 of state f. (C) The change of internal energy of the gas is - z PdV. (D) The mechanical work done by the gas is PdV z. (E) The temperature of the gas remains constant. correct answersDuring a quasi-"static" expansion, we should expect the temperature of the gas to remain constant throughout its expansion. Choice (E). 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
inductor, as seen on an oscilloscope? correct answersThe voltage quickly drops and we get choice (D). 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 be changed? I. ∇ = E r/ o II. ∇ = B 0 III. ∇× = − ∂ ∂ E B t IV. ∇× = + ∂ ∂ B J E μ μ o oo t (A) I only (B) II only (C) III only (D) I and IV (E) II and III correct answersThe Maxwell's Equations involving the divergence and time derivative of the magnetic field vector will be changed. Choice (E). 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 correct answersA reversed current is induced in the front loop, while the back loop gets an induced current in the same direction as the velocity v of the loops. Choice (C). The components of the orbital angular momentum operator L = (Lx , Ly , Lz) satisfy the following commutation relations. [Lx , Ly] = i = Lz , [Ly , Lz] = i = Lx , [Lz , Lx] = i = Ly. What is the value of the commutator [LxLy , Lz]? (A) 2i = Lx L y (B) i = L L x y 2 2 e + j (C) -i = L L x y 2 2 e + j (D) i = L L x y 2 2 e - j (E) -i = L L x y
3 of the eigenstates, what is the expectation value of the energy operator in this ensemble state? (A) 102 14 =w (B) 43 14 =w (C) 23 14 =w (D) 17 14 =w (E) 7 14 =w correct answersFrom the last question we got 36/14 and from this question we get half of 14 is 7 and so we get 36 + 7 = 43. Choice (B). 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? (A) l (1 + E/V) (B) l (1 - V/E) (C) l (1 - E/V)^- (D) l (1 + V/E)^1/
(E) l (1 - V/E)^-1/2 correct answersAs the potential energy increases, then them more the wavelength should increase as well. Choice (E) is the only choice which is capable of this. 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 container 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? (A) 2nR ln (B) nR ln (C) 1 2 nR ln (D) -nR ln (E) -2nR ln2 correct answersTake the number of moles and the universal gas constant and the change in entropy formula and we get nR*ln(2) which is choice (B). 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 u rms rms ( ) ( ) N O
