36. A uniform and thin stick of mass (m) and length (l) is held vertically by two strings of negligible mass. fmmediately after one string is cut, what is the magnitude of linear acceleration of the middle of the stick? (The moment of inertia of the thin stick is ml²/3 for an axis through one end.)

(A) g/4
(B) g/2
(C) 3g/4
(D) g
(E) 3g/2

32. fn designing buildings to be erected in an area prone to earthquakes, what relationship should the designer try to achieve between the natural frequency of the building and the typical earthquake frequencies?(A) The natural frequency of the building should be exactly the same as typical earthquakefrequencies.(B) The natural frequency of the building should be very different from typical earthquakefrequencies.(C) The natural frequency of the building should be almost the same as typical earthquakefrequencies but slightly higher.(D) The natural frequency of the building should be almost the same as typical earthquakefrequencies but slightly lower.(E) No need to consider.

33. A 2 kg object is attached to an ideal massless horizontal spring of spring constant 100.0 N/m andis at rest on a frictionless horizontal table. The spring is aligned along the x-axis and is fixed to apeg in the table. Suddenly this mass is struck by another 2 kg object traveling along the x-axis at 3 m/s, and the two masses stick together. What are the amplitude and period of the oscillationsthat result from this collision?(A) 0.30 m, 1.26 s (B) 0.30 m, 0.88 s (C) 0.42 m, 0.88 s(D) 0.42 m, 1.26 s (E) 0.42 m, 5.00 s

34. Two blocks connected by a cord (of negligible mass) that passes over a frictionlesspulley (also of negligible mass). The arrangement is known as Atwood’s machine.One block has mass m1=1.3 kg; the other has mass m2=2.8 kg. What is the magnitudeof the tension of the cord?(A) 11.0 N (B) 12.8 N (C) 15.7 N (D) 17.7 N (E) 20.0 N

35. A stuntman drives a car (without negative lift) over the top of a hill, and thecross section of which can be approximated by a circle of radius R =250 m. What is the greatest speed at which he can drive without the carleaving the road at the top of the hill? (Gravitational acceleration g = 10 m/s2)(A) 130 Km/h (B) 140 Km/h (C) 150 Km/h (D) 180 Km/h (E) 200 Km/h

37. A uniformly charged ring with a radius of α is placed on the xy planewith its central axis aligned with the z-axis. ff the total charge on the ring isQ, what is the electric field at z = z0? (k = 1/4πε0, = )(A) (B) (C)(D) (E)

38. A technician wearing a brass bracelet enclosing area 0.005 m2 places her hand in a solenoid whose magnetic B-field is 7.0 T directed perpendicular to the plane of the bracelet. The resistance R around the bracelet’s circumference is 0.02 Ω. An unexpected power failure causes the field to drop to 1.5 T in a time interval of 20 ms. Estimate the power delivered to the bracelet.(A) 23.6 W (B) 31.5 W (C) 47.3 W (D) 63.1 W (E) 94.6 W

39. The howler monkey is the loudest land animal and, under some circumstances, can be heard up to a distance of 8.9 km. Assume the acoustic output of a howler to be uniform in all directions and that the threshold of hearing is W/m2. A juvenile howler monkey has an acoustic output of 63 μW. What is the ratio of the acoustic intensity produced by the juvenile howler to the reference intensity I0, at a distance of 200 m?(A) 63 (B) 125 (C) 175 (D) 250 (E) 375

40. A parallel-plate capacitor without dielectrics is charged with +Q0 and -Q0 on their two metalplates, and the charging battery is disconnected. When a dielectric layer with a dielectric constant k (k ≥ 1) is inserted to fill the gap between the two metal plates, what is the bound charge on the surface of the dielectric layer in contact with the metal plate?(A) Q0(k − 1)/k (B) (k − 1)Q0 (C) (2 − k)Q0(D) kQ0/(k − 1) (E) Q0/(k + 1)

41. The human ear canal is, on average, 2.5 cm long. ft is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range)of the standing waves in the ear canal. Recall that, at 20C, the speed of sound in air is about 343 m/s.(A) 1715 Hz (B) 3430 Hz (C) 6860 Hz (D) 13720 Hz (E) 20580 Hz

42. The charge Q is -3.0 nC. How much charge q1 is needed to bringcharge q2 into static equilibrium?(A) -6 nC (B) 6 nC (C) 3 nC (D) 12 nC (E) -12 nC