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 = Vosin(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.

19. A solenoid of 10cm in diameter and 2.0m in length carries 25 Amperes current. It produces an internal magnetic feld of 100 mT. How many turns of wire does this solenoid have?(A) 3183；(B) 32； (C)6366； (D) 64； (E) 12732. 

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)

複選題21. Two balls of masses my = 1 kg and mo = 100 kg, with initial speed 1 m/s and 10 m/s, respectively, collide inelastically in space. They stick together after the collision. Which of the following is true in the Center of Mass Frame? (A) The total momentum does not change； (B) The total kinetic energy does not change； (C)The magnitude of velocity change of me is less than that of mi； (D) The magnitude of momentum change of me is less than that of my； (E) The magnitude of kinetic energy change of me is less than that of my.

複選題22. Consider a damped harmonic oscillator, which of the following is true?(A) If it is underdamped, the resonant frequency increases with larger damping； (B) If it is underdamped, the amplitude decays faster with larger damping； (C)If it is underdamped, and is driven by an external sinusoidal force, the amplitude of the oscillation is maximum if the frequency of the force is the same as the resonance frequency； (D) In order to damp the kinetic energy and the elastic energy as fast as possible, one should design the oscillator to be at critical damping condition； (E) If it is overdamped, the system does not oscillate and returns to the equilibrium position slowly. 

複選題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.

複選題24. A magnetic dipole made of a conductive ring carrying a current I. Observ- ing from far away； which of the following statements are FALSE?(A) If the magnetic dipole is placed in a uniform magnetic feld, it experiences no net magnetic force. (B) The magnetic dipole experiences a net torque if its dipole moment is parallel to the uniform magnetic feld. (C)The magnetic dipole may experience a net force induced by another magnetic dipole. (D) The magnetic field induced by the magnetic dipole is approximately proportional to the area of the ring. (E) The magnetic field induced by the dipole is approximately inversely proportional to the square of the distance from it.

複選題25. Which of the following is a statement or a consequence of 2nd law of thermal dynamics?(A) The efficiency of any heat engine operates between two heat reservoir is less or equal to the Carnot engine. (B) Heat can never pass from a colder to a warmer body without some other changes occurring at the same time. (C)Entropy of an object always increases when it is in contact with a heat reservoir. (D) Isolated perpetual motion machine is not possible.(E) The entropy of a thermal system going through a cyclic process always increases or stays the same after a full cycle.

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