110年 - 110 國立臺灣大學_碩士班招生考試_大氣科學研究所乙組:普通物理學#103053

1. What isis natural fequency?(A)(B)(C)(D)

2. Following the previous question, what is the Lagrangian of the simple harmonic oscillator?(A)(B) (C) (D) (E) L=mv²+kx

複選題

3. Which of the following is correct?(A) Given physical quantities A and B of the same dimension (e.g. they are both the lengths of something), and quantities C and D of the same dimension, if D is uniquely determined by A, B, and C, there must be some num nerical constants k and n (of no dimension) such that D = kC(A/B)ⁿ. (B) The moon is orbiting around the earth with roughly the samne period as that for its spinning around its own axis. (C) The gravitational potential energy for N point masses is the distance between particle i and particle j, and G is the Newton constant. (D) As the kinetic energy is given by a diffcrent formula, the total energy of an isolated system is not conserved in special relativity. (E) The friction is a conservative force. GMMI

4. What is the center-of-mass velocity of the system? (A)

5. What is the moment of inertia I of the system around its center-of-mass? (A) (B) (C)I= (D)(E)

6. What is the magnitude of the total angular momentum of the system around its center of mass?(A)(B) (C) (D) (E)

7. Which of the following is wrong?
(A) Divide a uniform spring of spring constant k into two identical halves. The spring constant of each half is 2k. (B) Fix one endpoint of a rope on the edge of a cliff, and release the other endpoint from equal height. At the moment when the free endpoint falls a distance h below the other endpoint, its velocity v is smaller than for any h ＞ 0. (See Fig. B above.)(C) Newton'slaw is necessary for the momentum conservation of physical systems.(D) Given arbitrary 3-dimensional vectors A, B, and C, the following identity bolds: A X(BXC = B(AㆍC) - C(AㆍB)(E) The angular momentum of a point mass in linear motion at constant velocity can be non-zero.

8. The change in entropy for an ideal gas over a reversible isothermal process at the temperature T from the initial pressure P and volume V to the final pressure P/2 and volume 2Vis(A) PVlog(1/2)(B) PVlog(2) (C) PVlog(1/2)T (D) PV 10g(2)/T (E) 2PVlog(2)/T

9. Which of the following statement is correct?(A) The law of thermodynamics states that two systems in thermal contact always reach thermal equilibrium in the end. (B) The entropy of any macroscopic system never decreases over time. (C) The entropy of an idcal gas is doubled if its volume is doubled at the same temperature. (D) Any irreversible engine always has a smaller efficiency than any reversible engine. (E) By choosing a suitable definition of Kelvin, the Boltzmann constant has an exact value that does not have to be determined by experiments.

10. For a string of length L with one fixed end and one open end, the oscillation wave on the string travels at the speed v. What are the standing wave frequencies?(A)f=v/L, v/2L, v/3L, (B) f= v/L, 2v/L, 3vIL, ... (C) f= 2v/L, v/L. 3v/2L,.. . (D) f= v/2L, 3v/2L, 5v/2L, (E) f= v/4L, 3v/4L, 5v/4L.

11. Which of the following describes "no existence of magnetic monopole."? (A)(B) (C) (D) (E) nonc of above

12. Capacitance( C ):(A)2πε₀a (B) πε₀a (C) 4πε₀a (D)8πε₀a (E)πε₀a/2

13. Potential energy saved in this system (Ue): (A) (B) (C) (D) (E) none of above.

14. What is the electric field at a distance r from an infinitely long string uniformly charged with linear charge density λ ? (A) (B)(C) (D) (E) none of above.