101年 - 101 國立中山大學轉學生招生考試試題_光電系學士班二年級：普通物理#139263

1. A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of: (A)(B)(1/2)mv² (C)(1/4)mv² (D)mv²/4k (E)

2. A block of mass m is placed on top of a light vertical spring of force constant k and pushed downward, so that the spring is compressed by x. After the block is released from rest it travels upward and then leaves the spring. To what maximum height above the point of release does it rise? (A)kx²/(mg) (B)2kx²/(mg) (C)kx²/(2mg) (D)kx²/(√2 mg) (E)√2 kx²/(mg)

3. A spherical shell has inner radius R₁, outer radius R₂, and mass M, distributed uniformly throughout the shell. The magnitude of the gravitational force exerted on the shell by a point particle of mass m located a distance d from the center, outside the inner radius and inside the outer radius, is: (A)0 (B)GMm/d² (C)GMm/(R₂²-R₁³) (D)GMm(d³-R₁³)/d²(R₂³-R₁³) (E)GMm/(d²-R₁²)

4. A simple pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g, and a is: (A)2π (B)2π(C)2π (D)2π (E)(1/2π)

5. What is the speed of transverse wave in a steel wire with a tensile stress of 2 × 10⁸ N/m². The density of steel is 7.8 g/cm³. (A)60 m/s (B)120 m/s (C)160 m/s (D)200 m/s (E)250 m/s

6. A point source emits sound waves with a power output of 100 watts. What is the sound level (in dB) at a distance of 10 m? (A)139 (B)119 (C)129 (D)109 (E)10

7. An ideal gas is allowed to expand adiabatically. Assume the process is reversible. The change in entropy is: (A)0 (B)nR ln(V₂/V₁) (C)nR ln(T₂/T₁) (D)kn ln(V₂/V₁) (E)kn ln(T₂/T₁)

8. The p-V diagram in Fig. 8 shows two paths along which a sample of gas can be taken from state a to state b, where V_b=3V₁. Path 1 requires that energy equal to 5 p₁V₁ be transferred to the gas as heat. Path 2 requires that energy equal to 5.5 p₁V₁ be transferred to the gas as heat. The ratio p₂/p₁ should be
(A)1.5 (B)2.0 (C)2.5 (D)3.0 (E)4.0

9. During an isothermal compression of 1 mol of ideal gas from a volume of 22.4 L at 0°C to a volume of 16.8 L, (Gas constant R=8.31 J/mol·K.) The work done by an external agent is (A)0 J (B)326 J (C)653 J (D)979 J (E)1306 J

10. Work done in an isobaric process by an ideal gas is
(A)nRT₂ ln(V₂/V₁) (B)nRT₂(1-V₁/V₂) (C)nRT₂ ln(V₁/V₂) (D)nRT₁(1-V₂/V₁) (E)nRT₁(1-V₁/V₂)

11. In Fig. 11, two tiny conducting balls of identical mass m and identical charge q hang from nonconducting threads of length L. Assume that θ is small, then the equilibrium separation x is approximately
(A)q²L/(4πε₀mg) (B)[q²L/(4πε₀mg)]^1/2 (C)2[q²L/(4πε₀mg)]^1/2(D)[q²L/(2πε₀mg)]^1/3 (E)3[q²L/(πε₀mg)]^1/3

12. Three particles, each with positive charge Q, form an equilateral triangle, with each side of length d. Then the magnitude of the electric field produced by the particles at the midpoint of any side is (A)Q/(4πε₀d²) (B)Q/(3πε₀d²) (C)2Q/(3πε₀d²) (D)Q/(πε₀d²) (E)4Q/(3πε₀d²)

13. Two conducting spheres have radii R₁ and R₂, with R₁ greater than R₂. If they are far apart the capacitance is proportional to: (A)R₁R₂/(R₁-R₂) (B)R₁²-R₂² (C)(R₁-R₂)/R₁R₂ (D)R₁²+R₂² (E)none of these

14. A 0.20 cm radius cylinder, 3.0 cm long, is wrapped with wire to form an inductor. At the interior is 5.0 mT the energy stored in the field is about: (A)0 (B)3.8×10⁻⁶ J (C)7.5×10⁻⁶ J (D)7.5×10⁻⁴ J (E)9.9 J

15. If an electron travels with speed v around a circle of radius r, then the magnitude of the orbital magnetic dipole moment is: (A)evr/2 (B)ev/r (C)ev/2πr (D)2πer/v (E)2πev/r

16. An LC circuit consists of a 1-μF capacitor and a 4 mH inductor. Its oscillation frequency is approximately: (A)0.025 Hz (B)25 Hz (C)60 Hz (D)2500 Hz (E)15800 Hz

17. A charge of +3.0 μC is distributed uniformly along the circumference of a circle with a radius of 20 cm. How much external energy is required to bring a charge of 25 μC from infinity to the center of the circle? (A)5.4 J (B)3.4 J (C)4.3 J (D)2.7 J (E)6.8 J

18. A proton is accelerated from rest through a potential difference of 2.5 kV and then moves perpendicularly through a uniform 0.60-T magnetic field. What is the radius of the resulting path? (A)15 mm (B)12 mm (C)18 mm (D)24 mm (E)8.5 mm

19. A dipole of dipole moment p is placed in a uniform electric field E. The maximum potential energy difference that can occur as the dipole is rotated is (A)0 (B)pE (C)2pE (D)πpE (E)pE/π

20. A 2-μF capacitor in series with a 2-kΩ resistor is connected to a 60-Hz ac source. Calculate the impedance of the circuit. (A)1500 ohms (B)1800 ohms (C)2100 ohms (D)2400 ohms (E)8600 ohms

21. A 30-μF capacitor is charged to 40 V and then connected across an initially uncharged 20-μF capacitor. What is the final potential difference across the 30-μF capacitor? (A)15 V (B)24 V (C)18 V (D)21 V (E)40 V

22. An electric field of approximately 100 V/m is often observed near the surface of Earth. If this were the field over the entire surface, what would be the electric potential of a point on the surface of Earth? (set V=0 at infinity) (A)0 (B)1.6×10⁸ V (C)3.2×10⁸ V (D)6.4×10⁸ V (E)1.28×10⁹ V

23. An inductance L, resistance R, and ideal battery of emf ε are wired in series. A switch in the circuit is closed at time 0, at which time the current is zero. At any later time t, the emf of the inductor is given by: (A)ε(1-e^-Lt/R) (B)εe^-Lt/R (C)ε(1+e^-Rt/L) (D)εe^-Rt/L (E)ε(1-e^-Rt/L)

24. A conductor of radius r, length l and resistivity ρ has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the length of the original conductor. The resistance of the new conductor is (A)(B)(C)R (D)4R (E)16R

25. A charged particle (m = 2.0 g, q = -50 μC) moves in a region of uniform field along a helical path (radius = 4.0 cm, pitch = 8.0 cm) as shown. What is the angle between the velocity of the particle and the magnetic field?
(A)27° (B)72° (C)63° (D)18° (E)58°

計算題（每題二十五分）
An electric field is directed out of the page within a circular region of radius R=3.00 cm. The magnitude of the electric field is given by E = (0.500 V/m·s)(1-r/R)t, where t is in seconds and r is the radial distance (r ≤ R). What is the magnitude of the induced magnetic field at radial distance (a) 2.00 cm and (b) 5.00 cm?