Physics 2 Algebra-Based Exam 2024

Section I: Multiple-Choice Questions 1. The root-mean-square speed of the atoms of a monatomic ideal gas at a temperature of 200 K is vrms . At a later time, the root-mean-square speed of the atoms is 2vrms . What is the temperature of the gas at this later time? (A) 800 K (B) 400 K (C) 200 K (D) 50 K Observer A 10 m/s 10 m/s Truck Observer C (at rest) 2. Observer B 25 m/s Observer D (at rest) A truck is traveling to the east with a speed of 25 m/s relative to the road while emitting a loud sound with a single frequency. The figure shows four different observers and indicates their locations and velocities relative to the road. Which observer hears a sound with the highest frequency? (A) A (B) B (C) C (D) D 2024 κ Capacitor 1 3. κ d 2d κ Capacitor 2 The figures show two different capacitors made of identical parallel conducting plates. In Capacitor 1, the plates are separated by a distance d and a block of material with dielectric constant is inserted between the plates. In Capacitor 2, the plates are separated by a distance 2d and two identical blocks of material with dielectric constant are inserted between the plates. A student claims that the capacitance of Capacitor 2 is the same as that of Capacitor 1. Which of the following indicates whether the claim is correct or incorrect, and provides a valid justification? (A) Correct, because the effects of doubling the distance between the plates and doubling the volume of the dielectric cancel each other. (B) Correct, because the capacitance is a property of the plates and the plates have not changed. (C) Incorrect, because doubling the thickness of the dielectric material will cause the capacitance to double. (D) Incorrect, because doubling the distance between the plates will reduce the capacitance by half. 4. At time t = 0 , a sample of radioactive material with decay constant has N 0 nuclei. At time t = t1 , there are N1 nuclei remaining. At a later time t = t 2 , there are N 2 nuclei remaining. Which of the following correctly relates N 2 to N1? (A) (B) (C) (D) 2024 5. A student places a lens 40 cm from an object and observes an enlarged image on a screen on the opposite side of the lens. Which of the following could be the type of lens and the focal length of the lens? (A) A diverging lens with a focal length of 30 cm (B) A diverging lens with a focal length of 50 cm (C) A converging lens with a focal length of 30 cm (D) A converging lens with a focal length of 50 cm –30 V –20 V –10 V 0V –40 V +10 V –50 V A 6. B x The figure shows equipotential lines in a particular region. The value of the potential along each line is indicated. Two points, A and B, lie along the x-axis.   The electric field at Point A is EA and the electric field at Point B is EB. Which   of the following correctly compares the magnitudes of EA and EB, and indicates whether the vectors are in the same or opposite direction? A B C D Magnitudes E A < EB E A < EB E A > EB E A > EB Directions Same direction Opposite directions Same direction Opposite directions (A) A (B) B (C) C (D) D 2024 Questions 7 and 8 refer to the following. C R1 = 2R R2 = 2R R3 = R The circuit shown consists of an ideal battery of emf , three resistors with the resistances indicated, a capacitor of capacitance C, and a switch. The capacitor is initially uncharged and the switch is initially open. 7. When the switch is open, which of the following correctly compares the powers P1 , P2 , and P3 dissipated by the resistors with resistances R1, R2 , and R3 , respectively? (A) P1 = P2 = P3 (B) P3 > ( P1 = P2 ) (C) ( P1 = P2 ) > P3 > 0 (D) ( P1 = P2 ) > ( P3 = 0) 8. The switch is closed at time t = t1 . A long time later, at t = t 2 , the circuit reaches steady state conditions. Which of the following correctly indicates how the current I s in the switch and the magnitude of the potential difference VC across the capacitor change between t1 and t 2 ? Is VC A Increases Increases B Increases Decreases C Decreases Increases D Decreases Decreases (A) A (B) B (C) C (D) D 2024 9. A 0.050 kg piece of an unknown metal is initially at a temperature of 373 K. The metal is then quickly moved into an insulated container with 0.100 kg of water at a temperature of 295 K. The water and the metal come to equilibrium at a temperature of 300 K. The specific heat of water is 4184 J/(kg K) . What is the specific heat of the unknown metal? (A) 287 J/(kg K) (B) 573 J/(kg K) (C) 2090 J/(kg K) (D) 6620 J/(kg K) 4I 3d A d I 10. Two long parallel wires, each in the plane of the page, are separated by a distance 3d, as shown. The top wire carries current 4I directed to the right, and the bottom wire carries current I directed to the left. Point A is also in the plane of the page, located a distance d above the bottom wire. Which of the following correctly represents the magnitude of the magnetic field due to the wires at Point A ? (A) (B) (C) (D) 2024 11. A blackbody of temperature T0 emits a spectrum of light with a peak wavelength 0 . The rate at which energy is emitted by the blackbody is P0 . The temperature of the blackbody is then changed so that the new peak wavelength emitted by the blackbody is 0 . Which of the following correctly indicates the 2 rate at which energy is emitted by the blackbody at this new temperature? P0 (A) 2 (B) P0 16 (C) 2P0 (D) 16P0 × × × × × × × × × × B × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × xi xf Top View 12. A metal bar of mass M and resistance R is pushed to the right at a constant speed along two horizontal, parallel, conducting rails, as shown in the top view diagram. The rails are separated by a distance , and are connected at the left end by a wire. The rails and wire have negligible resistance. The entire apparatus is in a uniform magnetic field of magnitude B that is directed into the page. At time ti the bar is at position xi , and a short time later at time t f the bar is at position x f . Which of the following expressions is equal to the average force exerted on the bar by the magnetic field between ti and t f ? (A) (B) (C) (D) 2024 Pair 1 Pair 2 0.04 Gauge Pressure (Pa) 0.04 0.02 Gauge Pressure (Pa) 0.00 –0.02 –0.04 0.00 0.05 0.10 0.15 0.20 0.25 Time (s) 0.02 0.00 –0.02 –0.04 0.00 0.05 0.10 0.15 0.20 0.25 Time (s) Pair 3 Pair 4 0.04 Gauge Pressure (Pa) 0.02 0.00 –0.02 –0.04 0.00 0.05 0.10 0.15 0.20 0.25 Time (s) 0.04 Gauge Pressure (Pa) 0.02 0.00 –0.02 –0.04 0.00 0.05 0.10 0.15 0.20 0.25 Time (s) 13. Pairs of tuning forks are struck near a microphone, which is connected to a computer that creates graphs of the resulting gauge pressure (the difference between the pressure and atmospheric pressure) as functions of time. The figure shows graphs for four pairs of tuning forks, where each pair consists of tuning forks that vibrate at different frequencies. Which pair of tuning forks has the greatest difference in frequencies? (A) Pair 1 (B) Pair 2 (C) Pair 3 (D) Pair 4 2024 10 V 14. A 10 V battery, resistors with resistances of 100 , 200 , and 400 , a 12 mF capacitor, and a switch are connected as shown. The capacitor is initially uncharged and the switch is initially open. What is the current in the battery immediately after the switch is closed? (A) Zero (B) 14 mA (C) 25 mA (D) 33 mA Observer Diver 15. A diver is swimming underwater in a pool filled with water. An observer is standing at the edge of the pool, as shown. Will the observer always be able to see the diver no matter where the diver is in the pool? Why or why not? (A) Yes, because there will always be a light ray originating from the diver that will refract toward the observer and reach the observer. (B) Yes, because for every position of the diver, there is a straight-line path connecting the diver and the observer. (C) No, because light passing from a medium with high index of refraction to low index of refraction will always totally reflect at the boundary between the two media. (D) No, because for some positions of the diver some of the light rays from the diver will totally reflect at the water-air boundary. 2024