32. The plates of a parallel-plate capacitor have area』and separation d. Two different dielectrics each All half the space between the plates of a parallel-plate capacitor (as shown in figure). Determine ti)e correct unit and the capacitance in terms of K₁, K₂, tiie area A of the plates, and die separation d, where K₁and K₂ are the dielectric constants of two dielectrics . is the vacuum permittivity.
(A)
(B)
(C)
(D)
(E)

28. The pKb of die base cyclohexamine, C6H11NH2, is 3.36. What is the pKa of the conjugate acid, C6H11NH3+? (Kw=1.0X10-14 at25°C) (A) 3.36 (B) 14.00 (C) 10.64 (D)7.64 (E)-10.64

29. Ellipsometry is commonly used to measure the thickness of films. Which of the following signal is detected in ellipsometry? (A) resonance angle (B) reflected laser spot (C) second-harmonic generation (D) polarized light (E) none of the above

30. Which of the following is not a feature of carrier g^s used in gases chromatogr/)hy? (A) The carrier gas should be chemically inert. (B) The carrier gas should be inexpensive. (C) The purity of carrier gas should not be very high. (D) The carrier gas should be suitable for tiie detector employed. (E) None of the above.

31. Determine tiie correct unit and magnitude of the electric field at distance x from the midpoint of a very long line of unifonnly distributed positive charge. Assume x is much smaller then the length of the wire, and let λ be the charge par unit length.(A)(B)(C)(D)(E)

33. A system comprises three particles with masses of 2.0 kg, 3.0 kg, and 5.0 kg, respectively. A force F = 3.0i + 4.0j (N) acts on the 2,0-kg particle, where i and/ are unit vectors that point along x and y coordinate axes, respectively. What is the acceleration of the center of mass ac caused by the force? (A) ac = 0.30i+ 0.40j (m/s2) (B) ac = 0.60i + 0.80j (m/s2) (C) ac = 3.0i +1.0j  (m/s2) (D) ac = 3.0i + 4.0j (m/s2) (E) ac = 15i + 20j (m/s2)

34. Assume that a satellite of mass jl/oibits Earth in a perfect circle of radius R. If the satellite is replaced with another one with mass 2Mbut with the same circling radius, what is the ratio of the period of the first satellite to the period of the second one (i.e., T1/T2)? (A) 1/2 (B)l (C)l (D)(E)2

35. A 5.0-kg block moves with velocity v = 3.0i + 5.0j(m/s) on a horizontal surface of coefficient of kinetic friction μ = 0.30, where i and J are unit vectors that point along tiie x and、coordinate axes, respectively. When the block comes to rest, what is the total thermal ehei^y increased? (A)1.2x 102J (B)63 J (C) 38 J (D)26J (E)85 J

36. A wheel rotates initially at a rate of 10 rad/s and begins to accelerate at a rate of 2 rad/s2. After 3 seconds the rate of the rotation will be (A) 6 rad/s (B) 9 rad/s (C) 10 rad/s (D) 16 rad/s (E) 19 rad/s

37. A force-tune curve for a ball struck by a bat is shown in the figure. What is the impulse on the ball?(A) 12000 (N●s) (B) 6000 (N●s) (C) 3000 (N●s) (D)6(N●s) (E) 3 (N●s)

38. A force of 20 N acts on a wagon at an angle of 30° to the ground. Calculate the work done by the force Wien the wagon is dragged 100 m along the ground.(A) 600 J (B) 800 J (C)100J (D) 1300 J (E) 1700 J