4.Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. (G = 6.67 x 10^-11 Nㆍm²/kg²) The mass of Ekapluto is closest to
(A)1.0 x 10²³ kg,
(B) 3.0 x 10²³ kg,
(C) 1.0 x 10²⁴ kg,
(D) 1.0 x 10²² kg,
(E) 3.0 x 10²² kg.

1. What is the value ofπ(8.104)2, written with the correct number of significant figures? (A)206.324,(B)206.323,(C)206.3,(D) 206,(E) 200.

2. Block A (0.40 kg) and block B (0.30 kg) are on a frictionless table (see figure). Spring 1 connects block A to a frictionless peg at O and spring 2 connects block A and block B. When the blocks are in uniform circular motion about O, the springs have lengths of 0.60 m and 0.40 m, as shown. The springs are ideal and massless, and the linear speed of block B is 2.0 m/s. If the spring constant of spring 1 is equal to 30 N/m, the unstretched length of spring 1 is closest to (A) 0.51 m, (B)0.53 m, (C) 0.55 m, (D) 0.54 m, (E) 0.52 m. 00000000003 0.60 m heQ00- -0.40 m-

3. Two optically flat glass plates, 16.0 cm long, are in contact at one end and separated by 0.0200 mm at the other end. The space between the plates is occupied by oil with index of refraction 1.45. The index of refraction of the glass plates is 1.55. The plates are illuminated at normal incidence with monochromatic light, and fringes are observed. If the dark fringes are spaced 2.00 mm apart, what is the wavelength of the monochromatic light? (A) 475 nm, (B) 425 nm, (C) 525 nm, (D) 675 nm, (E) 725 nm.

5. A nonuniform electric field is directed along the x-axis at all points in space. This magnitude of the field varies with x, but not with respect to y or z. The axis of a cylindrical surface, 0.80 m long and 0.20 m in diameter, is aligned parallel to the x-axis, as shown in the figure. The electric fields E1 and E2, at the ends of the cylindrical surface, have magnitudes of 9000 N/C and 5000 N/C respectively, and are directed as shown. (ε = 8.85 x 10-12 C2/N ㆍm2) The charge enclosed by the cylindrical surface is closes(A) -2.4 nC.(B) -4.8 nC.(C)-1.1 nC.(D)4.8 nC.(E) 1.1 nc.

6. In the figure, two masses, M = 16 kg and m = 12.80 kg, are connected to a very light rigid bar and are attached to an ideal massless spring of spring constant 100 N/m. The system is set into oscillation with an amplitude of 78 cm. At the instant when the acceleration is at its maximum, the 16-kg mass separates from the 12.80-kg mass, which then remains attached to the spring and continues to oscillate. What will be the amplitude of oscillation of the 12.80-kg mass? (A) 35 cm, (B) 62 cm, (C) 98 cm, (D) 78 cm, (E) 180 cm.

7. A rectangular block twice as high as it is wide is resting on a board. The coefficient of static friction between board and incline is 0.46. If the board's incline angle is gradually increased,(A) the block will first tip over than slide. (B) the block will first slide than tip over. (C) will the block first tip over or begin sliding depends on its moment of inertia. (D) will the block first tip over or first begin sliding depends on the coefficient of kinetic friction between board and incline. (E) None of the above.

8. A paint sprayer pumps air through a constriction in a 2.50-cm diameter pipe, as shown in the figure. The flow causes the pressure in the constricted area to drop and paint rises up the feed tube and enters the air stream. The speed of the air stream in the 2.50-cm diameter sections is 5.00 m/s. The density of the air is 1.29 kg/m3, and the density of the paint is 1200 kg/m3 . We can treat the air and paint as incompressible ideal fluids. What is the maximum diameter of the constriction that will allow the sprayer to operate?(A)12.2mm，(B)9.65 mm, (C) 14.3 mm, (D) 4.05 mm, (E) 8.07 mm. 

9. A hot piece of iron is thrown into the ocean and its temperature eventually stabilizes. Which of the following statements concerning this process is correct? (A) The ocean gains less entropy than the iron loses. (B) The change in the entropy of the iron-ocean system is zero. (C) The entropy lost by the iron is equal to the entropy gained by the ocean. (D) The entropy gained by the iron is equal to the entropy lost by the ocean. (E) The ocean gains more entropy than the iron loses.

10. A spaceship approaches the earth with a speed 0.50c. A passenger in the spaceship measures his heartbeat as 70 beats per minute. What is his heartbeat rate (beats per minute) according to an observer that is at rest relative to the earth? (A) 69,(B) 73,(C)80,(D) 65,(E) 61.

11. A heat engine performs the reversible cycle abca with 9.0 moles of an ideal gas, as shown in the figure. Path ca is an adiabatic process. The temperatures at points a and b are 300 K and 500 K, respectively. The volume at point c is 0.20 m3. The adiabatic constant of the gas is 1.60. The thermal efficiency of this engine is closest to (A)0.13, (B) 0.10, (C) 0.16, (D) 0.07, (E) 0.19.

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