103年 - [無官方正解]103 國立臺灣大學_轉學生招生考試：普通物理學(A)#138597

1. The Planck constant has the same SI unit as: (A) energy (B) momentum (C) power (D) angular momentum (E) torque

2. The ratio of the centripedal acceleration to the gravitational acceleration of a person standing on the earth surface around equator is about: (A) 0.003% (B) 0.03% (C) 0.3% (D) 3% (E) 30%

3. A particle with mass 1 kg is acted by a force F(x) = 3x²+x +1/2 along the x axis, where x is in meter and F in Newton. If the particle's speed is 0 at x=0, what is its speed at x = 1? (A) 0 (B) 2 m/s (C) 4 m/s (D) 6 m/s (E) 8 m/s

4. Which of the following is rolling down faster on a slanted surface assuming they have the same mass and outer radius? (A) solid sphere (B) hollow sphere (C) disk (D) tire (E) ring

5. Water is streaming downward from a faucet opening with an area of 5.0 × 10⁻⁴ m². The cross sectional area of the stream 0.2 m below shrinks to 3.0 × 10⁻⁴ m². What is the water speed in m/s at the faucet end? (A) 1.5 m/s (B) 3.0 m/s (C) 4.5 m/s (D) 6.0 m/s (E) 7.5 m/s

6. A sinusoidal wave, 0.01sin(0.2x-10t+π/2), is propagating on a string, where all terms are written in SI units. If the tension of this string is 10 N, what is the linear density of this string? (A) 0.0004 kg/m (B) 0.004 kg/m (C) 0.04 kg/m (D) 0.4 kg/m (E) 4. kg/m

7. For an ideal gas, the difference between the molar specific heat at constant pressure and constant volume, i.e. C_p − C_v, equals to: (A) −R (B) −1/2 R (C) 1/2 R (D) R (E) 3/2 R R is the universal gas constant.

8. A pump utilizing the geothermal energy is set up to operate between the ground and the underground heat source. Assuming the average ground temperature is 15 C° and the source end has a temperature 450 C°, approximately what is the best possible efficiency of this pump? (A) 20% (B) 30% (C) 40% (D) 50% (E) 60%

9. Estimate the pressure needed to make two deuterons fused into a helium nucleus assuming the Coulomb force to confine deuterons is uniformly distributed on the surface of a 2 fm radius sphere. (A) 5 × 10¹⁰ N/m² (B) 5 × 10¹⁵ N/m² (C) 5 × 10²⁰ N/m² (D) 5 × 10²⁵ N/m² (E) 5 × 10³⁰ N/m²

10. In an oscillating series RLC circuit with R = 50 Ω, L = 20 mH and C = 2.0 μF, the maximum charge is stored on the capacitor at t = 0. Find the time required for the charge on the capacitor falling to 37% of its initial value. (A) 1. × 10⁻⁴ s (B) 2. × 10⁻⁴ s (C) 4. × 10⁻⁴ s (D) 6. × 10⁻⁴ s (E) 8. × 10⁻⁴ s

11. A ball is held 50 cm in front of a plane mirror. The distance between the ball and its image is: (A) 100 cm (B) 200 cm (C) 25 cm (D) 10 cm (E) 500 cm

12. The phase difference between the two waves which give rise to a dark spot in a Young's double-slit experiment is (where m = integer): (A) 2πm+π/2 (B) 2πm+π/4 (C) 2πm+π/8 (D) zero (E) 2πm+π

13. The rainbow seen after a rain shower is caused by: (A) polarization (B) absorption (C) refraction (D) interference (E) diffraction

14. An astronaut travels to a hypothetical star located 30 light years from Earth in a spaceship at 0.6c. According to a clock located on the spaceship, how long does the trip take? (A) 10 years (B) 20 years (C) 30 years (D) 40 years (E) 50 years

15. The frequency of light beam A is twice that of light beam B. The ratio E_A/E_B of photon energies is: (A) 1/2 (B) 1/4 (C) 1/3 (D) 2 (E) 8

16. If the kinetic energy of a non-relativistic free electron doubles, the frequency of its wave function changes by the factor: (A) 1/2 (B) 4 (C) 3/2 (D) 3 (E) 2

17. The energy of a particle in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is proportional to (n = quantum number): (A) n (B) 2n (C) 1/n (D) 4n (E) n²

18. Possible values of the principal quantum number n for an electron in an atom are: (A) 0 and 1 (B) 2,4,6,... (C) 0,1,2,... (D) 1,3,5,... (E) 1,2,3,...

19. Two protons are about 10⁻¹⁰ m apart. Their relative motion is chiefly determined by: (A) nuclear forces (B) electrical forces (C) gravitational forces (D) torque from electrical dipole moments (E) magnetic forces

20. Nuclear fusion in the Sun is increasing its supply of: (A) neutrons (B) helium (C) positrons (D) hydrogen (E) nucleons

21. A current I is running uniformly toward the positive z direction on a long thin plate lying on the x-z plane with wider width w. Find out the magnetic field at a place very close to the center part of the plate (3 points). If this plate is bent to form a cylinder centering at the z axis with radius r = w/2π, what will be the magnetic field inside and outside this cylinder (3 points)? What is the pressure acting on this cylinder due to the magnetic force induced by the parallel current (4 points)?

22. What are the two basic postulates through which Einstein based his Special Theory of Relativity on (10 points)?