94年 - 學士後西醫普通物理學94普通物理學#85579

1. Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities v_A and v_B of the bodies at the end of distance D are related by (A) (B) (C) (D) (E)

2. A solid sphere, spherical shell, solid cylinder and a cylindrical shell all have the same mass m and radius R. If they are all released from rest at the same elevation and roll without slipping, which reaches the bottom of an inclined plane first? (A) solid sphere (B) spherical shell (C) solid cylinder (D) cylindrical shell (E) all take the same time

3. Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is (A) 2.5 mg (B) 3 mg (C) 4.5 mg (D) 6 mg (E) 9 mg

4. An ideal gas is allowed to undergo a free expansion. If its initial volume is V₁ and its final volume isV₂ , the change in entropy is (A) nR ln ( V₂ /V₁ ) (B) nRT ln ( V₂ /V₁ ) (C) nk ln ( V₂ /V₁ ) (D) 0 (E) nR

5. A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them. When it is connected to a battery of voltage V₀ , it has charge of magnitude Q₀ on its plates. While it is connected to the battery, the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitude of the charge on the plates and the potential difference between them are (A) (B) (C) (D) (E)

6. To decrease the intensity of the sound you are hearing from your speaker system by a factor of 36, you can (A) reduce the amplitude by a factor of 18 and increase your distance from the speaker by a factor of 2. (B) reduce the amplitude by a factor of 4 and increase your distance from the speaker by a factor of 3. (C) reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3. (D) reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 12. (E) reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 4.

7. If an R = 1 kΩ resistor, a C = 1 µF capacitor, and an L = 0.2 H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source? (A) 0.007 A (B) 27 mA (C) 54 mA (D)0.0308mA(E)0.34A

8. In which process will the internal energy of the system NOT change? (A) An adiabatic expansion of an ideal gas. (B) The evaporation of a quantity of a liquid at its boiling point. (C) An isothermal compression of an ideal gas. (D) An isobaric expansion of an ideal gas. (E) The freezing of a quantity of liquid at its melting point.

9. Two balls, projected at different times so they don’t collide, have trajectories A and B, as shown below. Which statement is correct? (A) v _0B must be greater than v _0A. (B) Ball B is in the air for a longer time than ball A. (C) Ball A is in the air for a longer time than ball B. (D) Ball B has a greater acceleration than ball A. (E) Ball A has a greater acceleration than ball B.

10. A binary star system in the constellation Orion has an angular separation between the two stars of 1.2 × 10^-5radians. If λ = 5 × 10^–7 m, what is the smallest aperture (diameter) telescope that may be used to resolve the two stars? (A) 10 cm (B) 5 cm (C) 50 cm (D) 1 m (E) 4 m

11. We wish to coat flat glass (n=1.5) with a transparent material (n=1.25) so that reflection of light at wavelength 600 nm is eliminated by interference. What minimum thickness can the coating have to do this? (A) 30 nm (B) 100 nm (C) 120 nm (D) 400 nm (E) 480 nm

12. The figure shows a circuit that contains three identical resistors with resistance R=9.0Ω, two identical inductors with inductance L=4.0 mH, and an ideal battery with emf ξ=36 V. IA is the current just after the switch is closed, and IB is the current through the battery long after the switch has been closed. What is the current ratio I_A/I_B? (A) 1/3 (B) 1/2 (C) 1 (D) 2 (E) 3

13. A long cylindrical wire (radius = 2.0 cm) carries a current of 40 A that is uniformly distributed over a cross section of the wire. What is the magnitude of the magnetic field at a point which is 1.5 cm from the axis of the wire? (A) 0.53 mT (B) 28 mT (C) 0.30 mT (D) 40 mT (E) 1.9 mT

14. The average position, or expectation value, of a particle whose wave function ψ(x) depends only on the value of x, is given by ＜ x＞ = ? (A) (B) (C) (D) (E)

15. A company that produces pulsed gas heaters claims their efficiency is approximately 90%. If an engine operates between 250 °C and 25 °C, what is its maximum thermodynamic efficiency? (A) 43% (B) 56% (C) 65% (D) 83% (E) 90%

16. A quantum particle (A) can be localized in space. (B) can be represented by an infinitely long wave having a single frequency. (C) can be represented by a wave packet. (D) travels at the phase speed of the infinitely long wave having the highest frequency. (E) has the highest probability of being present in those regions of space where its component waves interfere destructively.

17. An electron is in a state with l =3. What is the smallest value of the semiclassical angle θ between the direction of ? (A) 0^。 (B) 30 ^。 (C) 60 ^。 (D) cos^-1(1/3) (E) 90 ^。

18. A charged capacitor connected to a resistor and a switch, which is open for t＜0. After the switch is closed at t=0, the capacitor C is discharged through the resistor R. The energy stored in the capacitor decreases with time as it discharges. After how many time constants is this stored energy one eighth of its initial value? (ln2=0.693) (A) 0.347 RC (B) 0.693 RC (C) 1.040 RC (D) 1.386 RC (E) 2.079 RC

19. Water enters a house through a pipe with an inside diameter of 2.0 cm at an absolute pressure of 4.0×10⁵ Pa. A 1.0 cm-diameter pipe leads to the second-floor bathroom 5.0 m above. When the flow speed at the inlet pipe is 1.5 m/s, find the water pressure in the bathroom. (ρ_water=1000 kg/m³ ) (A) 0.17×10⁵ Pa (B) 0.32×10⁵ Pa (C) 0.49×10⁵ Pa (D) 0.66×10⁵ Pa (E) 3.3×10⁵ Pa

20. A cart with mass 450 g moving on a frictionless linear air track at an initial speed of 1.5 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision, the first cart continues in its original direction at 0.70 m/s. What is the mass of the second cart? (A) 0.16 kg (B) 0.47 kg (C) 1.24 kg (D) 2.14 kg (E) 3.40 kg

21. The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 2.5 s. Assuming R=0.5 m and m=2.0 kg, calculate the structure’s rotational inertial about the axis of rotation.

(A) (B) (C) (D) (E)

22. What is the de Broglie wavelength of an electron with a kinetic energy of 1.822×10^-16 J? ( ) (A) 0.3639 pm (B) 3.639 pm (C) 36.39 pm (D) 363.9 pm (E) 3639.0 pm

23. An LED is constructed from a p-n junction based on a certain Ga-As-P semiconducting material whose energy gap is 1.9 eV. What is the wavelength of the emitted light? (h=6.63×10^-34 J•s, c=3.00 ×10⁸ m) (A) 10.47 nm (B) 16.75 nm (C) 37.79 nm (D) 113.37 nm (E) 654.28 nm

24. An electron moves through a uniform magnetic field given by . At a particular instant, the electron has velocity m/s and the magnetic force acting on it is (6.4×10^-19 N) . Find Bx. (A) -1.6×10^-19 T (B) -3.2×10^-19 T (C) -0.22T (D) -1.0T (E) -2.0T

25.The potential energy of a diatomic molecule (a two-atom system like H₂ or O₂) is given by U= where r is the separation of the two atoms of the molecule and A and B are positive constants. This potential energy is associated with the force that binds the two atoms together. The force that one atom exerts on the other is: (A) (B) (C) (D) (E)

94年 - 學士後西醫普通物理學94普通物理學#85579

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