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A wave in a rope travels at 12 m/s and has a wavelength of 2 m. What is the frequency?
- A. 38.4 Hz
- B. 6 Hz
- C. 4.6 Hz
- D. 3.75 Hz
Correct Answer: B
Rationale: The frequency of a wave is calculated using the formula: frequency = speed / wavelength. In this case, the speed of the wave is 12 m/s and the wavelength is 2 m. Therefore, the frequency is calculated as 12 m/s / 2 m = 6 Hz. Choice A (38.4 Hz), Choice C (4.6 Hz), and Choice D (3.75 Hz) are incorrect as they do not result from the correct calculation using the given values.
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Which vehicle has the greatest momentum?
- A. A 9,000-kg railroad car traveling at 3 m/s
- B. A 2,000-kg automobile traveling at 24 m/s
- C. A 1,500-kg MINI Coupe traveling at 29 m/s
- D. A 500-kg glider traveling at 89 m/s
Correct Answer: D
Rationale: The momentum of an object is calculated by multiplying its mass by its velocity. The momentum formula is p = m v, where p is momentum, m is mass, and v is velocity. Comparing the momentum of each vehicle: A: 9,000 kg 3 m/s = 27,000 kg·m/s B: 2,000 kg 24 m/s = 48,000 kg·m/s C: 1,500 kg 29 m/s = 43,500 kg·m/s D: 500 kg 89 m/s = 44,500 kg·m/s. Therefore, the glider (500-kg) traveling at 89 m/s has the greatest momentum of 44,500 kg·m/s, making it the correct choice. Options A, B, and C have lower momentum values compared to option D, proving that the 500-kg glider traveling at 89 m/s has the highest momentum among the given vehicles.
Four 5 V batteries are connected in series. What is the total voltage of the circuit?
- A. 5.0 V
- B. 10.0 V
- C. 15.0 V
- D. 20.0 V
Correct Answer: D
Rationale: When batteries are connected in series, their voltages add up. Therefore, the total voltage of the circuit with four 5 V batteries connected in series will be 5 V + 5 V + 5 V + 5 V = 20 V. Choices A, B, and C are incorrect because the voltages of the batteries add up in series, resulting in a total of 20 V.
During adiabatic compression of a gas, what happens to its temperature?
- A. Remains constant
- B. Decreases
- C. Increases
- D. Becomes unpredictable without additional information
Correct Answer: C
Rationale: During adiabatic compression, the gas's temperature increases. This is because no heat is exchanged with the surroundings, and all the work done on the gas results in an increase in internal energy. Choice A is incorrect because the temperature does not remain constant during adiabatic compression. Choice B is incorrect as the temperature does not decrease. Choice D is incorrect as the behavior of the gas's temperature during adiabatic compression is predictable based on the principles of thermodynamics.
When two identical charged spheres, both positively charged, are brought close together, the electrostatic force between them will be:
- A. Slightly attractive
- B. Zero
- C. Strongly attractive
- D. Strongly repulsive
Correct Answer: D
Rationale: When two positively charged spheres are brought close together, they will experience a repulsive force due to their like charges. The electrostatic force causes the spheres to repel each other, making the correct answer D: Strongly repulsive. The force is not dependent on the material of the spheres, and the force is definitely not zero, as like charges repel. Choice A is incorrect as like charges do not attract each other. Choice C is incorrect as like charges repel, not attract.
A box is moved by a 15 N force over a distance of 3 m. What is the amount of work that has been done?
- A. 5 W
- B. 5 Nâ‹…m
- C. 45 W
- D. 45 Nâ‹…m
Correct Answer: D
Rationale: Work done is calculated using the formula: Work = Force x Distance. In this case, the force applied is 15 N and the distance covered is 3 m. Thus, work done = 15 N x 3 m = 45 Nâ‹…m. Therefore, the correct answer is 45 Nâ‹…m. Choice A (5 W) is incorrect because work is measured in joules (J) or newton-meters (Nâ‹…m), not in watts (W). Choice B (5 Nâ‹…m) is incorrect as it miscalculates the work by not multiplying the force by the distance. Choice C (45 W) is incorrect because work is not measured in watts (W) but in newton-meters (Nâ‹…m).