15. A long conductive rod of radius R carries a nonuniform current density J(r) = J₀r/R, where J₀ is a constant and r is the radial distance form the rod axis. What is the expression for the magnetic field strength inside this rod?
(A) μ₀J₀r
(B) μ₀J₀r²/3R
(C) μ₀J₀r²/R
(D) μ₀J₀r²/5R
(E) None of the above.

16. Suppose the magnetic field ( B ) in a plane electromagnetic (EM) wave is given by B = Byĵ, where By = 2×10⁻⁷sin(0.5×10³x + 1.5×10¹¹t) Tesla, ĵ is the unit vector along the y direction, and the SI unit is adopted. What is the expression for the electric field vector E(x,t) (in the SI unit) of this EM wave? (A) 60sin(0.5×10³x + 1.5×10¹¹t) î, where î is the unit vector along the x direction. (B) -60sin(0.5×10³x + 1.5×10¹¹t) î, where î is the unit vector along the x direction. (C) 60sin(0.5×10³x + 1.5×10¹¹t) k̂, where k̂ is the unit vector along the z direction. (D) -60sin(0.5×10³x + 1.5×10¹¹t) k̂, where k̂ is the unit vector along the z direction. (E) None of the above.

17. The reason why viruses can be seen using electron microscope is that the wavelength of electron can be smaller than the size of viruses. Assume an electron microscope has an accelerating voltage of 40 kV. What is the wavelength of the electron? (A) 0.006 nm (B) 0.003 nm (C) 0.06 nm (D) 0.03 nm (E) 0.6 nm.

18. Two rockets A and B are approaching the Earth from opposite directions, each moving at 0.80c relative to the Earth, as shown in the figure. How fast do the spaceships move relative to each other? (A) 0.48c (B) 0.80c (C) 0.98c (D) 1.3c (E) 1.6c.

19. Positronium consists of an election and a positron (a positive electron) orbiting about their common center of mass. According to the Bohr model, what is the expression of the energy level of a positronium? (A) En = -3.4 eV/n² (B) En = -6.8 eV/n (C) En = -6.8 eV/n² (D) En = -13.6 eV/n² (E) En = -13.6 eV/n

20. The fact that light can be polarized indicates which of the following? (A) Polarized light travels faster than non-polarized light. (B) Polarized light is monochromatic. (C) Light travels with a constant speed regardless of the reference frame. (D) Light is longitudinal wave. (E) Light is transverse wave.

1. A particle of mass m =100 g moves straight forward under an acceleration a(t) = 2 + t² (m/s²). If the particle starts at rest, what is the magnitudes of the momentum of the particle at t = 3 sec? (A) 0.2 kg-m/s (B) 0.5 kg-m/s (C) 1.1 kg-m/s (D) 1.5 kg-m/s (E) 2 kg-m/s

2. A circular object of mass m and of radius R rolls smoothly (without sliding) along a frictional incline, as shown in the right figure. In the following, which type of the object will roll with the highest acceleration? (A) A ring (Rotational inertia about the center of mass Icm = mR²) (B) A solid sphere (Icm = 2mR²/5) (C) A spherical shell (Icm = 2mR²/3) (D) A disk (Icm = mR²/2) (E) The same.

3. Peter ties a stone to the end of a thin string (1-meter long), and swings it with a period 2-seconds. The central acceleration of the stone is approximately (m/s²): (A) 10 (B) 20 (C) 30 (D) 40 (E) 50

4. A sinusoidal wave is traveling on a string with velocity 0.4 m/s along the x direction. The displacement of the particles of the string is found to vary with time in the y direction according to the equation y(x,t) = 0.05 sin(kx − 2πt) m where k is the angular wave number of the wave. What is the wave length in meter of this wave? (A) 0.05 (B) 0.4 (C) 1 (D) 2π (E) 5π

5. Following the science fiction, earth is a hollow shell, and there is a cavity in the center of the earth as the inner world. According to gravitation theory, what is the gravity field in that inner world? (A) same as on the surface of the earth (B) linear function as the distance from the center (C) very small (D) proportional to 1/r² (E) proportional to 1/r

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