20. The lifetime of a muon is 2.2 μs. Suppose that a muon is generated at a height of 15 km above Earth's surface. In order to be detected on the ground, the velocity of the muon must be at least (c = 3 × 10⁸ m/s²)
(A) 0.9 c
(B) 0.99 c
(C) 0.999 c
(D) 0.9999 c.

1. The position of a simple harmonic oscillator (SHO) as a function of time is given by x = 20 cos( + ), where t is in seconds and x in meters. Find the maximum speed in unit of m/s: (A) 12.57 (B) 15.71 (C) 18.85 (D) 20.

2. A rocket whose initial mass is 800 kg consumes fuel at the rate R = 2.8 kg/s. The speed of the exhaust gases relative to the rocket engine is 2400 m/s. The initial acceleration of the rocket is (in unit of m/s²): (A) 0.9 (B) 1.1 (C) 3.0 (D) 8.4.

3. A rectangular block of mass 1 kg rests on a 30°-wedge-shaped block of mass 3 kg, as shown in the figure. Neglecting all the frictions between the contact surfaces, find the magnitude of the horizontal force F that must be applied to the wedge in order that the rectangular block does not slide along the wedge: (A) 19.60 N (B) 22.63 N (C) 27.72 N (D) 33.95 N.

4. What will be the speed of a solid ring of mass M and radius R when it reaches the bottom of an incline if it starts from rest at a vertical height h and rolls without slipping? Ignore losses due to dissipative forces. (g: gravitational acceleration) (A)(B) (C) (D)

5. A vertical force applied tangentially to a uniform cylinder of weight 100 N as shown in the figure. The coefficient of static friction between the cylinder and all surfaces is 0.4. Find the magnitude of the maximum force F that can be applied without causing the cylinder to rotate: (A) 12.29 N (B) 24.57 N (C) 32.57 N (D) 48.86 N.

6. As a longitudinal wave, sound induces compressions and expansion in air. In terms of displacement, which of the illustrations is correct? (A) A (B) B (C) C (D) D

7. When we blow across the mouth of a bottle, we can cause a standing wave in the air inside the bottle, which makes a musical sound. Blowing harder can give a higher musical pitch, but that takes practice. Assume that, for any liquid height in the bottle, we can reliably obtain only the fundamental (first harmonic) and the next higher harmonic frequency by blowing. Consider a beverage bottle 25 cm in length, with an original liquid height of 20 cm inside (before we drink any of the beverage). Given that the speed of sound in air is 343 m/s, what range of frequencies can you obtain as you slowly sip the liquid in the bottle? (Choose the closest match.) (A) 20 – 20000 Hz. (B) 80 – 13500 Hz. (C) 350 – 5000 Hz. (D) 1200 – 3600 Hz.

8. Consider four paths on a P-V diagram, through which a gas can be taken from state i to state f. States i and f are at the same temperature. Rank the paths according to the magnitude of the energy transferred as heat ΔQ between the gas and its environment (high to low). (A) 1234. (B) 4321. (C) 1324. (D) 2413.

9. In a model gasoline engine, the air-gasoline mixture can be treated approximately with a thermodynamic cycle known as the Otto cycle. In the first process (1→2), the gas undergoes an isentropic compression (the engine's compression stroke), during which the temperature rises from 300 K to 600 K. The next process (2→3) is an isochoric pressure increase, and the gas temperature reaches 1500 K as the gasoline burns. Next (3→4), the gas undergoes isentropic expansion (the engine's power stroke) during which its temperature drops to 800 K. Finally (4→1), the gas experiences an isochoric pressure decrease during which its temperature drops back to 300 K. Please estimate the efficiency of this model engine. (A) 10%~20% (B) 20%~30% (C) 30%~40% (D) 40%~50%.

10. A sample of a monatomic ideal gas containing 6.00 × 10²³ atoms in a volume of 8.00 × 10⁻³ m³ is initially in thermal equilibrium with its surroundings at 300 K. The gas is made to expand until the final volume is 6.40 × 10⁻² m³, and the final temperature is 50 K. The change in entropy of the gas should be (A) positive (B) negative (C) zero (D) undetermined.

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