4. A string with two ends fixed has 12 Hz, 30 Hz, 33 Hz, and 45 Hz as harmonic frequencies. Which of the following is a possible fundamental frequency (first harmonic) of the string?
(A) 2 Hz
(B) 3 Hz
(C) 5 Hz
(D) 12 Hz
(E) 18 Hz

1. Given a circuit in Fig. 1, which is composed of a battery of voltage V, six resistors of resistance R, and a voltmeter, what is the readout from the voltmeter? (A)(B)(C)(D)(E)

2. It is known that all mechanical quantities, including the universal constants G, c and ħ, can be expressed in terms of length, time, and mass. In SI units, where the base of unit of length is meter (m), time is second (s), and mass is kilogram (kg), the three universal constants are G = 6.67 × m³ ﹒s2﹒, c = 3.00 × 108 m. s¯¹, and ħ = 1.05 × m². . kg. In another unit system, the base units of length, time, and, mass are denoted as lp, tp, and mp, respectively, so that G = , c = . mp. What is lp in SI units? (A) (B)(C)(D)(E)

3. A sound source emits a sound wave of frequency f. If the source is moving toward a stationary observer at one third (i.e., 1/3) of the speed of sound, what frequency does the observer observe? (A) 3f (B)(C) f (D)(E)

5. Two blocks with masses ma and me are attached to two identical springs. The block with mass ma oscillates with amplitude and frequency , while the block with mass me oscillates with amplitude and frequency . What is the ratio between ma and me, i.e., ? (A)(B)(C)(D)(E)

6. Two 5-kg objects with velocities in the unit of m/s collide and stick together. How much energy is lost in the process? (A) 5 J (B) 24 J (C) 78 J (D) 132 J (E) 247 J

7. On July 16, 1945, in the Manhattan Project led by Robert Oppenheimer, a physicist named Richard Feynman was observing the nuclear test. After the bomb was detonated (引爆), Feynman saw the flash of the bomb explosion roughly 40 seconds before he heard the sound of the explosion. Given the speed of light is 3.0 × 108 m/s and the speed of sound is 3.4 × 102 m/s, estimate the distance between Feynman and the place of detonation. (A) 1.6 km (B) 1.4 x 10 km (C) 3.1 × 102 km (D) 7.0 × 102 km (E) 1.2 × 107 km

8. According to the second law of thermodynamics, which of the statements below is correct? (A) Heat can never pass from a colder to a warmer body. (B) Heat cannot be converted into work. (C) Heat can flow spontaneously from hotter to colder regions. (D) It is derived from the first law of thermodynamics. (E) The entropy of a closed system always remains unchanged.

9. Two identical satellites, A and B, are circling around Earth in circular orbits. Given the orbital radius of A is twice that of B, what is the ratio of the speed of A to the speed of B? (A) 1 (B) √2 (C) 1/√2 (D) 2 (E) 1/2

10. If the period of a simple pendulum on Earth is T what would be the period of the same pendulum on the Moon, where the gravitational acceleration is 1/6 of that on Earth? (A) √6T (B) √3T (C) T (D) T/√3 (E) T/√6

11. Two spherical shells, A and B, surround an isolated charged point particle. Given that the radius of shell A is twice that of the radius of shell B, what is the ratio between the electric flux through shell A and the electric flux through shell B? (A) 4 (B) 2 (C) 1 (D) 1/2 (E) 1/4

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