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

1. Which one of the following physical quantities is a pseudo-vector? (A) position (B) velocity (C) electric field (D) kinetic energy (E) angular momentum

2. A hanged ball moves in a horizontal circle, as shown in the right figure. The length of the string is L, and the gravitational acceleration is g. What is the period of this circular motion? (A) (B) (C)(D)(E)

3. What is the work-energy theorem in particle kinematics? (A) The net work done on a particle is equal to the resulting change in its kinetic energy. (B) The net work done on a particle is equal to the resulting change in its potential energy. (C) The net work done on a particle is equal to the resulting change in its total energy. (D) The change of kinetic energy of a particle results in a net work done on its surroundings. (E) The change of potential energy of a particle results in a net work done on its surroundings.

4. Consider a collision between two objects. Which one of the following statements is wrong? (A) If the collision is elastic, the total kinetic energy is conserved after the collision. (B) If the collision is elastic, the total momentum is conserved after the collision. (C) If the collision is inelastic, the internal energy of these two objects may increase. (D) If the collision is inelastic, the total momentum is not conserved after the collision. (E) If the collision is inelastic, the total kinetic energy is not conserved after the collision.

5. Consider a uniform solid sphere with radius R. The gravitational field strength f is determined by the distance r from the center. What is the correct dependence of r inside the sphere (r ＜ R)? (A) f ∝ 1/r² (B) f ∝ 1/r (C) f ∝ r⁰ (D) f ∝ r¹ (E) f ∝ r²

6. Consider a thermodynamic system and its surroundings. What is the correct description of a reversible process? (A) A reversible process must be a quasi-static process. (B) During a reversible process, the temperature of the system must keep constant. (C) During a reversible process, the temperature of its surroundings must keep constant. (D) During a reversible process, the entropy of the system must keep constant. (E) During a reversible process, the entropy of its surroundings must keep constant.

7. The equation of motion of a driven oscillator is written as where m is the mass of the oscillator, kx is the restoring force, F is the amplitude of the driven force, and ω is the angular frequency of the driven force. In what condition the oscillation becomes out of phase? (A) (B) (C) (D) (E)

8. The wave function of a transverse string wave is written as y(x, t) = y₀ sin(kx - ωt) where y₀, k, and ω are amplitude, wave number, and angular frequency, respectively. Consider the cycle-averaged power P transmitted by the wave. What is the correct relation between P and y₀? (A) P ∝ 1/y₀² (B) P ∝ 1/y₀ (C) P ∝ y₀⁰ (D) P ∝ y₀¹ (E) P ∝ y₀²

9. The pressure(P)-volume(V) diagram of a thermodynamic cycle is shown in the right figure (solid line). What area in the P-V diagram represents the work done by the system in each cycle?  (A) α (B) β (C) γ (D) α + β (E) β + γ

10. What is the microscopic interpretation of the temperature of an ideal gas? (A) average potential energy of the gas particles (B) average kinetic energy of the gas particles (C) average momentum of the gas particles (D) average angular momentum of the gas particles (E) average mass of the gas particles

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