3. Consider an ideal gas is initially confined to part of a thermally insulated box with a thin membrane. When the membrane is punctured, the gas rapidly expands to fill the whole box. Compare the initial and final states of the system. Which ones of the following quantities are not varied?
(A) temperature of the gas
(B) internal energy of the gas
(C) pressure of the gas
(D) entropy of the gas
(E) entropy of the box

1. As shown in Fig. 1, a solid rod is hanged by a wire attached to its right. The left of the rod contacts the wall with force of friction. If the coefficient of static friction is μ_s, what is the maximum value of θ that the rod can keep stable? (A) θ = tan⁻¹ μ_s (B) θ = cot⁻¹ μ_s (C) θ = sin⁻¹ μ_s (D) θ = cos⁻¹ μ_s (E) θ = sec⁻¹ μ_s

2. As shown in Fig. 2, a thin square plate with mass m and sides of length L is lain on the x-y plane. The center of the plate is put on the origin. Find the moment of inertia along the x-axis. (A) (B) (C) (D) (E)

3. Continued from question 2, consider the plate rotates with another axis lain on the x-y plane as shown in Fig. 3. The angle between the axis and x-axis is 30°. The angular frequency of rotation is ω. What is the magnitude of the angular momentum? (A)  (B) (C) (D) (E)

4. What is the correct form of the 1-dimensional wave equation?_______ where f is dynamic variable, x is position, t is time, and v is wave velocity. (A)(B) (C) (D) (E) 

5. In general, the resistivity of a conductor increases as the temperature increases. However, the resistivity of a pure semiconductor may decreases as the temperature increases. What is the possible reason of this unusual behavior of semiconductor? (A) The collisions between free electrons and atoms are reduced as the temperature increases. (B) The collisions between free electrons and atoms are enhanced as the temperature increases. (C) The drift velocity of electrons is increased as the temperature increases. (D) The electron density is decreased as the temperature increases. (E) The electron density is increased as the temperature increases.

6. A radio station broadcasts electromagnetic waves with a power of 2000 W. Assume the station acts as a point source. What is the amplitude of the electric field at a position 860-m away from the station? (A) 0.8 V/m (B) 0.7 V/m (C) 0.6 V/m (D) 0.5 V/m (E) 0.4 V/m

7. A parallel plate capacitor has circular plates of radius r = 2 cm separate by a distance d = 1 mm. If the potential difference between the plates changes at 10⁴ (volt/sec), what is its displacement current? (A) 4.0 × 10⁻¹⁰ amp (B) 2.0 × 10⁻⁹ amp (C) 1.0 × 10⁻⁸ amp (D) 5.0 × 10⁻⁸ amp (E) 2.5 × 10⁻⁷ amp

8. An observer A stands on the ground with clock CA and an observer B sits on a train with clock CB. The train moves with a velocity v with respect to the ground. Consider the relativistic time dilation effect, which one of the following descriptions is correct? (A) Both A and B find that CA counts slower than CB. (B) Both A and B find that CA counts as fast as CB. (C) Both A and B find that CA counts faster than CB. (D) The observer A finds that CA counts slower than CB, but the observer B finds that CB counts slower than CA. (E) The observer A finds that CA counts faster than CB, but the observer B finds that CB counts faster than CA.

9. The circuit in Fig. 4 has reached steady-state condition. Find the potential difference across the first resistor R₁. Take V = 12 volt, R₁ = 3 Ω, R₂ = 1 Ω, and C = 1 μF. (A) 3 volt (B) 6 volt (C) 9 volt (D) 10 volt (E) 12 volt

10. A positron collides head on with an electron and both are annihilated. Each particle had a kinetic energy of 1.5 MeV. What is the wavelength of the resulting photons? (A) 3.09 × 10⁻¹³ m (B) 6.18 × 10⁻¹³ m (C) 1.24 × 10⁻¹² m (D) 2.48 × 10⁻¹² m (E) 1.24 × 10⁻¹¹ m

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