12. A person sits on a swing. When the person sits still, the swing oscillates back and forth at its natural frequency ω₀. If, instead, two people sit on the swing, the new natural frequency of the swing is
(A) 4ω₀.
(B) 3ω₀.
(C) 2ω₀.
(D) ω₀.
(E) ω₀/2.

1. A particle of mass m =100 g moves straight forward under an acceleration a(t) = 2 + t² (m/s²). If the particle starts at rest, what is the magnitudes of the momentum of the particle at t = 3 sec? (A) 0.2 kg-m/s (B) 0.5 kg-m/s (C) 1.1 kg-m/s (D) 1.5 kg-m/s (E) 2 kg-m/s

2. A circular object of mass m and of radius R rolls smoothly (without sliding) along a frictional incline, as shown in the right figure. In the following, which type of the object will roll with the highest acceleration? (A) A ring (Rotational inertia about the center of mass Icm = mR²) (B) A solid sphere (Icm = 2mR²/5) (C) A spherical shell (Icm = 2mR²/3) (D) A disk (Icm = mR²/2) (E) The same.

3. Peter ties a stone to the end of a thin string (1-meter long), and swings it with a period 2-seconds. The central acceleration of the stone is approximately (m/s²): (A) 10 (B) 20 (C) 30 (D) 40 (E) 50

4. A sinusoidal wave is traveling on a string with velocity 0.4 m/s along the x direction. The displacement of the particles of the string is found to vary with time in the y direction according to the equation y(x,t) = 0.05 sin(kx − 2πt) m where k is the angular wave number of the wave. What is the wave length in meter of this wave? (A) 0.05 (B) 0.4 (C) 1 (D) 2π (E) 5π

5. Following the science fiction, earth is a hollow shell, and there is a cavity in the center of the earth as the inner world. According to gravitation theory, what is the gravity field in that inner world? (A) same as on the surface of the earth (B) linear function as the distance from the center (C) very small (D) proportional to 1/r² (E) proportional to 1/r

6. A disk rolls down a 30-degree slope without slipping. Given the inertial moment of a disk (mass M and radius R) I = MR²/2, please find the frictional force for the disk during rolling down: (A) 1 Mg (B) 1/2 Mg (C) 1/3 Mg (D) 1/6 Mg (E) 2/3 Mg

7. Connect three disks as shown in the following figure. Their centers form a regular triangle. Each disk of mass M, radius R has an inertial moment I = MR²/2 when rotating about the disk center. Calculate the total inertial moment of the three disks when rotating about the center of triangle (in unit of MR²). (A) 1.5 (B) 2.5 (C) 3.5 (D) 4.5 (E) 5.5

8. The intensity from a sound source is I. If another identical but independent sound source is placed next to it, what will be the change of intensity level? (A) 2 dB (B) 3 dB (C) 4 dB (D) 5 dB (E) 6 dB

9. Which of the following is a consequence of (or is implied by) the second law of thermodynamics: (A) for all cyclic processes we have ΔQ/T ＜ 0 (B) work cannot be completely converted to heat energy (C) heat energy cannot be completely converted to work (D) the reason all heat engine efficiencies are less than 100% is friction, which is unavoidable (E) in the Carnot engine, ΔS ＞ 0 for each cycle

10. As shown in the following, two large insulating parallel plates carry positive charge of equal magnitude, one positive and the other negative, that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest. (A) 1, 2, 3, 4, 5 (B) 5, 4, 3, 2, 1 (C) 1= 4 = 5, 2 = 3 (D) 2 = 3, 1 = 4 = 5 (E) 2 = 3, 1, 4 = 5

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