50. For a car traveling with speed v around a curve of radius r, determine a formula fbr the angle θ, at which a road should be banked so that no friction is required.
(A)
(B)
(C)
(D)
(E)0

46. In human, blood flows from the heart into the aorta, from which it passes into the major arteries. These branch into the small arteries (arterioles), which in turn branch into myriads of tiny capillaries. The radius of the aorta is about 1.2 cm, and the blood passing through it has a speed of about 40 cm/s. A typical capillary has a radius of about 4✖10-4 cm, and blood flows through it at a speed of about 5x10-4 m/s. Estimate the number of capillaries that are in the body. (A) 1✖109 (B) 3✖109 (C) 5✖l09 (D) 7✖109 (E)9✖109

47. An electron travels at 2✖107 m/s in a plane perpendicular to a uniform 0.01 T magnetic field. What is the radius of the travel path? (electron mass = 9.1✖10-31 kg, charge on electron = 1.6✖10-19 Coul) (A) 5.2 cm (B) 3.8 cm (C) 2.1 cm (D) 1.1 cm (E) 0.5 cm

48. A soap bubble appears green (wavelength:540 nm) at the point on its front surface nearest the viewer. What is the smallest thickness the soap bubble film could have? Assume that the index of refraction of the soap film is n=1.35. (A) 100 nm (B) 150 nm (C) 200 nm (D) 250 nm (E) 300 nm

49. An engine's heat input per second is 8.0 kJ at 500 K reservoir and output per second is 4.0kJ at 300 K reservoir. What is the Carnot efficiency of this engine? (A) 20% (B) 40% (C) 50% (D) 80% (E) none of the above

51. Calcualte the moment of inertia of a hollow cylinder when the rotational axis is through the center. The inner radius is R1 and outer radius is R2?The total mass of the hollow cylinder is M. (A) (B) (C)(D)(E)

52. Consider a parallel-plate capacitor. Each plate has area A. One plate carries a uniform surface charge density σ and the other carries a uniform surface charge density -σ. Each plate of a parallel-plate capacitor exerts a force Fon the other. Calculate the force. (A)(B) (C)(D)(E)

53. An observer is moving with speed u toward a stationary source which emits sound waves of frequency f. What is the frequency f' heard by the observer? Assume the speed of sound to be v. (A)f'=f (B) (C)(D)(E)

54. To charges (+q) are located on the x axis as the figure shows. What is die resulting electric field at points on the y axis?(A) (B)(C)(D)(E)0

55. An ice skater with rotational inertia I and angular speed ω pulls his arms in and increases his angular speed to 3ω. Calculate the change in kinetic ener^. (A) (B) (C)(D)Iω2 (E)

56. A cylindrical container with a radius of 2R and a height of 2R contains liquid with a density of ρ, filling 17/18 of its volume. When a plastic ball of radius R is placed m 1he liquid, the liquid perfectly fills tiie container witiiout any liquid spilled out. What is the density of the plastic ball in terms of ρ? (A)ρ/4 (B)ρ/3 (C)ρ/2 (D)3ρ/4 (E)2ρ/3