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8. Two stars a and 3, with masses satisfying ma/m3 = 10, are in circular orbits around each other. In the rest frame of this system, find the ratio of the speeds va/vg. (A) (B) 6 19 (D) 9 (E) 10

8. Two stars a and 3, with masses satisfying ma/m3 = 10, are in circular orbits around each other. In the rest frame of this system, find the ratio of the speeds va/vg. (A) (B) 6 19 (D) 9 (E) 10

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8. Two stars a and 3, with masses satisfying ma/m3 = 10, are in circular orbits around each other. In the rest frame of this system, find the ratio of the speeds va/vs. (A) (c) / 9. A helium balloon is released from the floor in a room at rest, then slowly rises and comes to rest touching the ceiling. During this process, the gravitational potential energy of the balloon has increased. Since energy is conserved, the energy of something else must have decreased during this process. Which of the following is the main contribution to this decrease? (A) The kinetic energy of the balloon decreased. (B) The elastic potential energy of the balloon decreased. (C) The thermal energy of the air in the balloon decreased. (D) The thermal energy of the air in the room decreased. (E) The gravitational potential energy of the air in the room decreased. (A) (B) 10. An archer takes aim at a target that is 100 m away. Assuming she holds the bow at the same height as the center of the target and shoots an arrow with velocity v = 100 m/s, at what angle above the horizontal should she aim the bow so that the arrow hits the center of the target? arccos (1/5) 2 (A) 17h 16 (B) arcsin (1/5) 2 (B) (D) 9 (C) 13h 12 arccos (1/10) 2 11. A projectile is thrown from a horizontal surface, and reaches a maximum height h and also lands a distance h from the launch point. Neglecting air resistance, what is the maximum height for a projectile thrown directly upward with the same initial speed? (D) m (E) 10 arcsin (1/10) 2 12. A block of mass m is initially held in place by two massless strings, as shown. arctan(2/5) 2 (E) 2h The tension in the diagonal string is T₁. Next, the horizontal string is cut, and immediately afterward the tension in the diagonal string is T2. Which of the following is true? (A) T₁ <mg <T₂ (B) T₂ <mg <T₁ (C) T₁ <T₂ <mg (D) mg <T₂ <T₁ (E) T₁=T₂ <mg
Transcribed Image Text:8. Two stars a and 3, with masses satisfying ma/m3 = 10, are in circular orbits around each other. In the rest frame of this system, find the ratio of the speeds va/vs. (A) (c) / 9. A helium balloon is released from the floor in a room at rest, then slowly rises and comes to rest touching the ceiling. During this process, the gravitational potential energy of the balloon has increased. Since energy is conserved, the energy of something else must have decreased during this process. Which of the following is the main contribution to this decrease? (A) The kinetic energy of the balloon decreased. (B) The elastic potential energy of the balloon decreased. (C) The thermal energy of the air in the balloon decreased. (D) The thermal energy of the air in the room decreased. (E) The gravitational potential energy of the air in the room decreased. (A) (B) 10. An archer takes aim at a target that is 100 m away. Assuming she holds the bow at the same height as the center of the target and shoots an arrow with velocity v = 100 m/s, at what angle above the horizontal should she aim the bow so that the arrow hits the center of the target? arccos (1/5) 2 (A) 17h 16 (B) arcsin (1/5) 2 (B) (D) 9 (C) 13h 12 arccos (1/10) 2 11. A projectile is thrown from a horizontal surface, and reaches a maximum height h and also lands a distance h from the launch point. Neglecting air resistance, what is the maximum height for a projectile thrown directly upward with the same initial speed? (D) m (E) 10 arcsin (1/10) 2 12. A block of mass m is initially held in place by two massless strings, as shown. arctan(2/5) 2 (E) 2h The tension in the diagonal string is T₁. Next, the horizontal string is cut, and immediately afterward the tension in the diagonal string is T2. Which of the following is true? (A) T₁ <mg <T₂ (B) T₂ <mg <T₁ (C) T₁ <T₂ <mg (D) mg <T₂ <T₁ (E) T₁=T₂ <mg
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