12. The inventor of engine claims that it has a work output W = 180 J per cycle and operates between the boiling and freezing points of water with an efficiency of e = 60%. If engine
actually exists, what would be the entropy change for the system (reservoirs and engine) per cycle?
(A) -0.51 J/K
(B) -0.36 J/K
(C) 0 J/K
(D) 0.36 J/K
(E) 0.51 J/K.

1. Two masses placed on a flat surface (friction coefficient μ = 0.1) are connected by a spring. Initially, the spring has an extension of 1 m and both masses are at rest. Given m₁ = m₂ = 1 kg, and k = 9.8 N/m; what is the maximum compression of the spring? (A) 1 m (B) 0.8 m (C) 0.6 m (D) 0.4 m (E) None of the above

2. A puck m₁ is sliding without friction on ice at 5 m/s along +x direction. It collides with another puck m₂ initially at rest. After collision, m₁ no longer moves along +x and its speed reduces to 4 m/s. Given m₂ = 3m₁, find θ₁ + θ₂ = (A) 75° (B) 90° (C) 115.66° (D) 121.33° (E) 135°

3.A block of mass 1 kg rests on a horizontal table for which the coefficient of static friction is 0.75.One can apply a force to pull the block. Let's say the force makes an angle of to the horizontal table. What is the minimum value of the force needed to start the block moving? (A) 4.56 N(B) 5.88 N (C) 6.92 N (D) 7.35 N (E) 9.02 N.

4. Four uniform solid balls of radius R are made by lead, copper, iron, and aluminum. Released from rest at the same height on an incline, rolling without slipping. Which has the largest translational speed at the bottom? (A) Lead (B) Copper (C) Iron (D) Aluminum (E) All the same

5. A pendulum consists of a massless rod and a uniform circular disk (mass 2 kg, radius 20 cm). Distance from pivot to center of disk is 60 cm. Released at 30° from vertical. What is the speed of the center of mass when the rod is vertical? (I = 1/2 MR²) (A) 1.18 m/s (B) 1.22 m/s (C) 1.26 m/s (D) 1.30 m/s (E) 1.34 m/s

6. A block of mass m = 0.6 kg is attached to a vertical spring (k = 0.1 N/m) via a string over a pulley (I = 1/2 MR², M = 2 kg, R = 0.1 m). The string does not slip. What is the angular frequency of small oscillations? (A) 0.10 rad/s (B) 0.20 rad/s (C) 0.25 rad/s (D) 0.32 rad/s (E) 0.50 rad/s

7. A wire stretches 4 cm when force F is applied. The same force is applied to a wire of the same material but with twice the diameter and twice the length. The second wire stretches (A) 1 cm (B) 2 cm (C) 4 cm (D) 8 cm (E) None of the above

8.To transmit a transverse waves with an average power Pav, speed v, amplitude A and angular frequency w, along a stretched string with a tension F and a linear density μ. If the tension increased fourfold, the wave velocity becomes v'. With the wavelength unchanged, the new frequency is w'. If the same amount of average power (P'av =Pav) is transmitted as before, but with this new w', then the ratio of the new amplitude to the original amplitude must be (A) 0.25(B) 0.35 (C) 0.5 (D) 0.7 (E) 1.

9. An open organ pipe of length 0.6 m resonates in its fundamental mode, while a closed pipe organ of length 0.31 m also resonates in its fundamental mode. What is beat frequency heard byan audience nearby? Take the speed of sound to be 340 m/s. (A) 2.28 Hz (B) 4.57 Hz (C) 6.85 Hz (D) 9.14Hz (E) 11.43 Hz.

10.Two slits separated by 0.5 mm are illuminated with light of wavelength 480 nm. Assume the screen is far away from the slits. What is the path difference between waves that results in the first-order bright fringe? (A) 120 nm (B) 240 nm (C) 480 nm (D) 960 nm (E) None of the above.

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