108年 - 台聯大轉學考 物理#99867

1. If we denote the dimension of length as [L], dimension of time as [T], and dimension of mass as [M], what is the dimension of the universal gravitational constant G?(A) (B)(C)(D)(E)

2. A small ball of mass m is suspended in an elevator by a string of length L. The string does not stretch and its mass can be ignored. If the elevator located at the surface of the Earth and moves upward with an acceleration a, what is the frequency of the ball's oscillatory motion?(A) m(g - a)/(2πL), (B) m(g +a)/(2πL),(C)(D)(E)Here g is the gravitational acceleration on Earth's surface.

6. A solid spherical marble starts from rest and rolls without slipping on the loop-the-loop track in fgure 1. What is the minimum starting height h from which the marble will remain on the track through the loop. Assume the marbles radius is small compared with R. (A) 2.5R； (B) 2.7R； (C)2.9R； (D) 3.1R； (E) 3.3R.
 (Note: the moment of inertial for a solid spherical object is, where m is the mass of the object and r is its radius.) Figure 1: Figure for problem 6. Figure 2: Figure for problem 7.

8. A thin circular disk of radius R carries a total charge Q uniformly distributed on its surface. Assuming symmetric electric field on the two sides of the disk, which of the following expressions is a good approximation of the electric feld strength at a distance r above the center of the disk, where r << R?(A) (B) (C) (D)(E)

9. Same setting as in prablem 8, but with r ＞＞ R. Which of the following is a good approximation of the electric field strength?(A) (B) (C) (D) (E)

10. A piston system containing 1 mole of ideal gas in a 10 liter volume initially. The system is put in thermal contact with the environment at 20℃ and 1 atm of pressure. The piston is then released and the volume expands slowly in a quasi-static manner. The temperature is maintained at 20℃ during the whole process. The expansion stops when the pressure inside the piston reaches 1 atm. What is the volume of the gas chamber after the expansion? (The universal ideal gas constant, R, is 0.082 Liter-atm/K/mole.)(A) 24.1 liter； (B) 22.1 liter； (C)18.4 liter； (D) 16.9 liter； (E) 12.3 liter.

12. Same initial condition as in problem 10, but this time we insulate the system from the environment such that the expansion process is quasi-static and adiabatic. Starting with 20℃ and 10 liter, what is the volume of the chamber when the pressure reaches 1 atm? Assuming the specific heat are and (A) 24 liter； (B) 22.1 liter； (C)18.4 liter； (D) 16.9 liter； (E) 12.3 liter.

15. A string of length L and linear density λ is stretched to a tension T. What is the expression of its resonance frequencies of standing waves?(A) (B)(C)(D)(E),where n is any positive integer. (Hint: Wave equation of small displacement y is )

16. Two parallel infinite wires 2cm apart carry currents of 1A and 8A, separately. What is the force per meter between them?(A) (B) N/m； (C)(D) (E)

17. A 1.2 mF capacitor is connected across a generator whose output is V = V_osin(2πft), with Vo = 20 V, f = 60 Hz, and t in seconds. Find the peak current and absolute value of the current at t = 5ms.(A) 9.05A, 2.80A； (B) 9.05A, 1.80A； (C)1.44A, 0.45A； (D) 1.44A, 0.25A； (E) 9.05A, 8.61A.

18. The deBroglie wavelength of a non-relativistic particle with mass m and speed u is:(A)(B)(C) (D) (E) . Here h is the Planck constant and c is the speed of light.

20. The following fgure shows a conductive sphere with a spherical cavity in the center. The total charge on the conductor is zero, but a point charge Q is placed at the center of the cavity. How does the electric potential (V) as a function of the distance from the center (r) looks like?(A)(B) (C)(D)(E)

23. A square conductive loop of side L and resistance R is pulled with constant speed u out of a uniform magnetic field B. The magnetic feld is perpendicular to and pointing into the plane of the loop, as shown in the figure. Which of the following is correct?
(A) The induced EMF is BLu； (B) The induced current is BLU/R； (C)The force required to pull the loop is B²L²u/R； (D) The power required to pull the loop is B²L²U²/R²； (E) The direction of the electric current is clockwise.