114年 - [非官方正解]114 台灣聯合大學系統_學士班轉學生考試試題：普通物理#128198

1. A particle of mass m slides down a smooth surface described by y = ax² from a height H. What is the magnitude of the normal force at the lowest point? (A) mg (B) mg + 2aHm (C) mg + mv²/R (D) mv²/a (E) (mg² + 4aHmg)¹/²

2. A simple spring-mass system consists of a block of mass m attached to a spring with spring constant k. What is the speed of the block as it passes through the equilibrium position x₀, given that the initial displacement is A? (A) A(kx₀²/m)¹/² (B) A(k/m)¹/² (C) 1/2(kx₀²) (D) (2gA)¹/² (E) kx₀

3. For the potential energy function V(x) = -kx + λx³, what is the nature of the equilibrium point(s)? (A) Stable (B) Unstable (C) Neutral (D) No equilibrium (E) Two stable and one unstable point

4. A satellite of mass m is mounted on a rocket that is initially at rest on the surface of the Earth. If the Earth has mass M, what is the total energy the rocket must provide in order for the satellite to orbit at an altitude equal to Rₑ above the Earth's surface? (A) GMm/Rₑ (B) 1/2(GMm/Rₑ) (C) 3/4(GMm/Rₑ) (D) 1/2(GMm/Rₑ²) (E) Rₑ/GMm

5. A disk with a momentum of inertia I and initial angular velocity ω₀ is slowed down by a constant torque τ. What is the stopping time? (A) ω₀/τ (B) Iω₀/τ (C) τ/ω₀ (D) ω₀²/2τ (E) ω₀I / τ²

6. An ideal gas undergoes a closed isobaric cycle with a triangular P-V diagram. If the base is ΔV and the height is P, what is the net work done? (A) PΔV (B) PΔV/2 (C) 3PΔV/2 (D) 0 (E) 2PΔV

7. The electric field is given by E(x) = . What is the potential difference from x = 0 to ∞? (A) ∞ (B) E₀λ (C) -E₀λ (D) 0 (E) λ²E₀

8. Four point charges of +0.500 μC, +1.50 μC, -1.00 μC, and -0.500 μC are randomly distributed on a ring. If the electric potential at the center of the ring due to the +0.500 μC charge alone is 4.5 × 10⁴ V, what is the total electric potential at the center due to all four charges?(A) 0(B) -4.5 × 10⁴ V(C) 4.5 × 10⁴ V(D) 9.0 × 10⁴ V(E) 18.0 × 10⁴ V

9. A charged particle with mass m and charge q enters a magnetic field B at angle θ with velocity v. What is the radius of the helical trajectory? (A) mv/(qB) (B) mvsinθ/(qB) (C) mvcosθ/(qB) (D) qB/(mv) (E) λ/(2π)

10. An infinitely large, thin conducting sheet carries a uniform current density J. What is the magnetic field at a distance r perpendicular to the surface of the sheet? (A) 1/2 μ₀ J (B) 1/2 μ₀ Jr (C) μ₀ J (D) μ₀ Jr (E) 1/2 μ₀ J²

11. The magnetic flux varies with time as Φ(t) = Φ₀e⁻ᵇᵗ. What is the maximum induced emf? (A) bΦ₀ (B) Φ₀/b (C) 0 (D) Φ₀²b (E) Φ₀/b²

12. What is the relationship between the power P emitted by a blackbody and its temperature T? (A) P ∝ T (B) P ∝ T² (C) P ∝ T³ (D) P ∝ T⁴ (E) P ∝ T⁵

13. In the photoelectric effect, which equation relates stopping voltage U₀ and wavelength λ? (A) hc/(eλ) = U₀ (B) eU₀ = hc/λ (C) U₀ = hc /(eλ) – φ (D) U₀ = φ – hc /(eλ) (E) φ = U₀

14. In a hydrogen atom, what is the energy difference between n = 3 and n = 2? (A) 13.6 eV (B) 1.89 eV (C) 3.4 eV (D) 10.2 eV (E) 12.1 eV

15. An observer measures a clock moving at speed v = 0.6c. What is the time dilation factor γ? (A) 1.0 (B) 1.15 (C) 1.25 (D) 1.50 (E) 2.0

16. What is the energy density ratio of electric and magnetic fields in an electromagnetic wave? (A) Equal (B) Electric is twice magnetic (C) Magnetic is twice electric (D) Cannot be compared (E) Depends on frequency

17. A radio station requires a coaxial cable to connect the transmitter to the antenna. The cable consists of an inner conductor with a diameter of 0.2 mm and an outer conductor with a diameter of 2.0 mm, whose thickness is negligible. If the maximum safe potential difference between the conductors is 2.3 kV, what is the maximum charge density the conductors can carry under this safety constraint? (A) 45 μC (B) 50 μC (C) 55 μC (D) 60μC (E) 65 μC

18. A spreading wave packet increases in width over time due to which principle? (A) Second Law of Thermodynamics (B) Conservation of Energy (C) Relativistic Effect (D) Uncertainty Principle (E) Momentum Conservation

19. A particle moves in a non-conservative field but its total energy remains conserved. What is the likely form of the external force? (A) Constant force (B) Position-dependent (C) Velocity-dependent (D) Perpendicular to displacement (E) Time-dependent

20. When a photon undergoes Compton scattering with an electron and is scattered at a 90° angle relative to its original direction, its energy after scattering is half of its original energy. What is the initial wavelength of the photon? (A) 1.33 nm (B) 2.43 nm (C) 1.33 pm (D) 2.43 pm (E) None of the above