4. Two planets have masses M and m, and the ratio M/m = 25. The distance between the planets is R. The point P is between the planets as shown in the right, and the distance between M and P is x. At P, the gravitational force on an object due to M and m are equal in magnitude. The value of x is

(A) 5R/6
(B) 25R/36
(C) R/25
(D) 6R/5
(E) none of these.

1. A particle moving along the x-axis has a position function given by x(t) = (4.00 m/s³) t³ − (5.00 m/s) t + (6.00 m). What is the average acceleration of the particle between t = 1.00 s and t = 2.00 s. (A) 24 m/s² (B) 12 m/s² (C) 36 m/s² (D) 18 m/s² (E) 30 m/s²

2. A dog's hair has been cut and is now getting longer by 1.04 mm each day. With winter coming on, this rate of hair growth is steadily increasing, by 0.132 mm/day every week. By how much will the dog's hair grow during 5 weeks? (A) 12.0 mm (B) 24.0 mm (C) 36.0 mm (D) 48.0 mm (E) 60.0 mm

3. A cube of side 2a and mass M is sliding on a frictionless surface with uniform velocity v₀, as shown in the right Fig. a. It hits a small obstacle at the end of the table, which causes the cube to tilt as in Fig. b. Find the minimum value of v₀ such that the cube will fall off the table (g is the gravitational acceleration constant on earth). (A)(B)(C) (D)(E)

5. A mass m₂ = 1.5 kg rests on a horizontal table. The static and kinetic coefficients of friction between m₂ and the table are μₛ = 0.3 and μₖ = 0.25, respectively. The mass m₂ is attached by strings to masses m₁ = 2.5 kg and m₃ = 4.5 kg as shown in the right. Masses m₁ and m₃ hang freely. The system is initially held at rest. After it is released, the acceleration of m₂ is approximately (A) 1.9 m/s² (B) 2.4 m/s² (C) 3.0 m/s² (D) zero (E) 13 m/s²

6. If the coefficient of static friction between your coffee cup and the horizontal dashboard of your car is μₛ = 0.800, how fast can you drive on a horizontal roadway around a right turn of radius 30.0 m before the cup starts to slide? (A) 25.2 m/s (B) 20.8 m/s (C) 10 m/s (D) 15.3 m/s (E) 12.6 m/s

7. A 2.00-kg object is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 20.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest with an initial position of xᵢ = 0.200 m, and it subsequently undergoes simple harmonic oscillations. The total energy of the oscillating system is (A) 0.50 J. (B) 1.25 J. (C) 1.50 J. (D) 1.75 J. (E) 2.00 J.

8. The "Principle of Equipartition of Energy" states that the energy of a gas is shared equally: (A) among the molecules (B) between kinetic and potential energy (C) between translational and vibrational kinetic energy (D) among the relevant degrees of freedom (E) between heat and work.

9. A source at rest emits light of wavelength 500 nm. When it is moving at 0.90 C (C is light speed) away from an observer, the observer detects light of wavelength: (A) 26 nm (B) 115 nm (C) 500 nm (D) 2200 nm (E) 9500 nm

10. The specific heat of a substance is: (A) the amount of heat energy to change the state of one gram of the substance. (B) the amount of heat energy per unit mass emitted by oxidizing the substance. (C) the amount of heat energy per unit mass to raise the substance from its freezing to its boiling point. (D) the amount of heat energy per unit mass to raise the temperature of the substance by 1°C. (E) the temperature of the object divided by its mass.

11. A Carnot refrigerator extracts 35 kJ as heat during each cycle, operating with a coefficient of performance of 4.60. What is the energy per cycle transferred as heat to the room? (A) 15.0 kJ (B) 21.0 kJ (C) 25.9 kJ (D) 30.4 kJ (E) 42.6 kJ

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