32. A particle collides with an identical particle at rest relative to an inertial frame S. These two (noninteracting) particles has speed 0.6c moving toward each other along the x direction in their center-of-momentum frame (namely, in the inertial frame in which the total momentum of the system vanishes), denoted by S'. What is the speed of frame S'relative to frame S?
(A) 1.2c
(B)
(C)
(D) 0.6c
(E) (2 - √3)c 

28. At a certain temperature, cis-1,2-dimethylcyclopropane (M) and trans-1,2- dimethylcyclopropane (N) undergo the following transformation. The rate laws for the reactions can be expressed as , with ky and k, being constants at a given temperature, called the forward and reverse rate constants, respectively, and the equilibrium constant of the reaction, K = 3. Which of the following statements is correct? (A) At this temperature, the conversion of M is 66.7%. (B) As the temperature increases, both , increase. (C) At room temperature, N is a gas under 1 atm. (D) M is more stable than N. (E) Heating this reaction increases the equilibrium constant K.

29. When the following monosaccharide form furanose, a new bond is formed between which two atoms (use underlined numbers)? (A) (B)(C)(D)(E)

30. Consider the complex ions . The wavelengths of absorbed electromagnetic radiation for these ions in solution are (in no specific order) 293 nm, 442 nm, and 768 nm. Which of the following statements is correct? (A) absorbs 293-nm electromagnetic radiation. (B) absorbs 442-nm electromagnetic radiation. (C) absorbs 768-nm electromagnetic radiation. (D) The solution of is blue. (E) The solution of is red.

31. The capacitor in the figure (right) is initially uncharged. w The emf of the battery is 8 = 10 volts. The values of the resistors are: R1 = R2 = R3 = 1 Ω. The capacitor C is 10 μF. Τ The switch is initially open and is closed at t = 0. What is R R R switch C the final charge on the capacitor if one waits long enough? (A)10 μC (B) 50 μC (C) 100 μC (D) 200 μC (E) 0

33. The wave function of a transverse wave propagating on a rope is y(x, t) = 5sin(πχ 4πt), where x and y are measured in meters and t is in seconds. What is the velocity (m/s) of a particle on the rope at x = 2 m and t = 0.5s? (A) 0 (B) -4 (C) 5π (D) 10π (E) 20π

34. A conductor of radius r, length 1, and resistivity p has resistance R. Assume that the volume of this conductor is conserved. What is the new resistance if it is stretched to double its original length? 1 (A) (B)(C) R (D) 2R (E) 4R

35. The molar specific heat at constant volume is , and the molar specific heat at constant pressure is . For an ideal gas at a fixed temperature, which of the following statements is true? (A) is always greater than , because part of the absorbed heat is used to do work to the environment. (B) is always greater than , because the environment absorbs additional heat. (C) is always less than , because part of the absorbed heat is used to do work to the environment. (D) is always less than , because the environment absorbs additional heat. (E) There is no certain relation between and .

36. Which of the following statements about the specific heat of an ideal gas is correct? (A) The specific heat at constant pressure is greater than the specific heat at constant volume because work is done by the gas at constant volume. (B) The specific heat at constant pressure is greater than the specific heat at constant volume because work must be done by the gas at constant pressure. (C) The specific heat is greater for a more massive gas. (D) The specific heat is greater at lower temperature. (E) The specific heat is proportional to the absolute temperature.

37. A neutron has a mass of 1.67 × kg. The de Broglie wavelength is 1.4 × m. What is the velocity of the neutron? (Plank's constant h = 6.63 × J.s) (A) 1.55 × 102 m/s (B) 7.01 × 102 m/s  (C) 2.99 × 106 m/s(D) 2.83 × 103 m/s(E) 3.53 × 103 m/s

38. For designing an anti-reflective coating for a glass surface in an optical device at a free-space wavelength of 552 nm. The refractive index of the glass is 1.50. Determine the minimum thickness (nm) of the optical coating with a refractive index of 1.38. (A) 276 (B) 184 (C) 138 (D) 100 (Ε) 92.0