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As a car is traveling on the highway, its speed drops from 60 mph to 30 mph. What happens to its kinetic energy?
- A. Its energy is halved.
- B. Its energy is doubled.
- C. Its energy is quadrupled.
- D. Its energy is divided by four.
Correct Answer: A
Rationale: The correct answer is A. Kinetic energy is proportional to the square of the velocity. When the speed drops from 60 mph to 30 mph, the kinetic energy is halved. Choice B is incorrect because halving the speed results in halving the kinetic energy, not doubling it. Choice C is incorrect because quadrupling the kinetic energy would require increasing the speed fourfold, not halving it. Choice D is incorrect because dividing the energy by four would imply a different relationship between speed and kinetic energy, which is not the case.
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As the frequency of a sound wave increases, what else is true?
- A. Its wavelength decreases.
- B. Its wavelength increases.
- C. Its amplitude decreases.
- D. Its amplitude increases.
Correct Answer: A
Rationale: The correct answer is A: 'Its wavelength decreases.' The frequency and wavelength of a sound wave are inversely proportional. As the frequency of a sound wave increases (more oscillations per second), its wavelength decreases. This relationship is described by the formula: Speed of Sound = Frequency x Wavelength. Therefore, to maintain the speed of sound constant, when the frequency increases, the wavelength must decrease. Choices B, C, and D are incorrect because an increase in frequency does not lead to an increase in wavelength or changes in amplitude.
Power (P) represents the rate of work done. Which formula accurately depicts power?
- A. P = W / F
- B. P = d / t
- C. P = W x t
- D. P = F / t
Correct Answer: D
Rationale: Power (P) is defined as the rate of work done over time. The correct formula for power is P = W/t, where W is the work done, and t is the time taken. Therefore, option D, P = F / t, correctly represents power as work divided by time. Option A, P = W / F, is incorrect as it represents work divided by force, not power. Option B, P = d / t, is incorrect as it represents distance divided by time, not power. Option C, P = W x t, is incorrect as it represents work multiplied by time, not power. It's important to understand the distinction between work, power, force, time, and other related concepts to solve physics problems accurately.
An object with a charge of 4 μC is placed 50 cm from another object with a charge twice as great. What is the magnitude of the resulting repulsive force?
- A. 0.1152 N
- B. 1.152 N
- C. 10^−3 N
- D. 2.5 10^−3 N
Correct Answer: D
Rationale: The force between two charges is calculated using Coulomb's Law, which states that the force is proportional to the product of the two charges and inversely proportional to the square of the distance between them. Given that one charge is twice as great as the other and the distance between them is 50 cm, we can calculate the repulsive force. The magnitude of the resulting repulsive force is 2.5 10^−3 N. Choice A is incorrect as it does not match the calculated value. Choice B is incorrect as it is significantly higher than the correct answer. Choice C is incorrect as it represents 10^−3 N, which is lower than the calculated value.
According to the zeroth law of thermodynamics, two systems are in thermal equilibrium if:
- A. They have the same pressure.
- B. They have the same volume.
- C. They have the same temperature.
- D. They are made of the same material.
Correct Answer: C
Rationale: The correct answer is C: "They have the same temperature." The zeroth law of thermodynamics states that if two systems are each in thermal equilibrium with a third system, they are also in thermal equilibrium with each other. This implies that they have the same temperature.
Choice A is incorrect because pressure is not the determining factor for thermal equilibrium. Choice B is incorrect because volume alone does not dictate thermal equilibrium. Choice D is incorrect as the materials the systems are made of do not determine thermal equilibrium according to the zeroth law of thermodynamics.
In the mechanical power equation P = E / t, power is measured in ___________.
- A. ohms
- B. Joules
- C. volts
- D. watts
Correct Answer: D
Rationale: In the mechanical power equation P = E / t, power is measured in watts. Watts are the standard unit of power in the International System of Units (SI), named after the Scottish engineer James Watt. Watts are defined as joules per second, reflecting the rate at which energy is transferred or converted. Ohms (choice A) are the unit of electrical resistance, Joules (choice B) are the unit of energy, and volts (choice C) are the unit of electric potential difference. Therefore, the correct answer is watts as it directly relates to power in the given equation.