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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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Viscosity, μ, is a transport property of a fluid that reflects its:
- A. Inertia
- B. Resistance to flow
- C. Compressibility
- D. Buoyancy generation
Correct Answer: B
Rationale: Viscosity refers to a fluid's resistance to flow. A fluid with high viscosity (like honey) flows slowly, while a fluid with low viscosity (like water) flows more easily. It is a measure of internal friction in the fluid. Choice A, 'Inertia,' is incorrect as inertia is the tendency of an object to resist changes in its state of motion. Choice C, 'Compressibility,' is incorrect as it refers to the ability of a fluid to be compressed. Choice D, 'Buoyancy generation,' is incorrect as it relates to the upward force exerted by a fluid that opposes the weight of an immersed object.
The speed of sound in dry air at 20°C is 343 m/s. If the wavelength of a sound wave is 5 m, what is its frequency?
- A. 171.5 Hz
- B. 79 Hz
- C. 68.6 Hz
- D. 63.6 Hz
Correct Answer: C
Rationale: The speed of sound (v) can be calculated using the formula: v = f λ, where f is the frequency and λ is the wavelength. Given that the speed of sound is 343 m/s and the wavelength is 5 m, we can rearrange the formula to solve for frequency: f = v / λ = 343 / 5 = 68.6 Hz. Therefore, the correct frequency is 68.6 Hz. Choices A, B, and D are incorrect as they do not result from the correct calculation based on the given values.
Which object below has the same density?
- A. A block with a mass of 6.5 grams and a volume of 16.25 cm3
- B. A block with a mass of 80 grams and a volume of 32 cm3
- C. A block with a mass of 48 grams and a volume of 22 cm3
- D. A block with a mass of 100 grams and a volume of 250 cm3
Correct Answer: A
Rationale: Density is calculated by dividing the mass of an object by its volume. The density of object A is 6.5 g / 16.25 cm3 = 0.4 g/cm3. The density of object B is 80 g / 32 cm3 = 2.5 g/cm3. The density of object C is 48 g / 22 cm3 = 2.18 g/cm3. The density of object D is 100 g / 250 cm3 = 0.4 g/cm3. Objects A and D have the same density of 0.4 g/cm3. Therefore, the correct answer is A as it has the same density as object D, making them the only objects with a density of 0.4 g/cm3.
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.
A pitcher throws a 45-g baseball at a velocity of 42 meters per second. What is the ball's momentum?
- A. 0.189 kgâ‹…m/s
- B. 1.89 kgâ‹…m/s
- C. 1.07 kgâ‹…m/s
- D. 0.93 kgâ‹…m/s
Correct Answer: B
Rationale: Momentum is calculated by multiplying mass (in kg) by velocity (in m/s). The mass of the baseball is 0.045 kg (45 grams converted to kg), and the velocity is 42 m/s. Momentum = 0.045 kg 42 m/s = 1.89 kgâ‹…m/s. Therefore, the correct answer is 1.89 kgâ‹…m/s. Choice A is incorrect as it incorrectly converts the mass from grams to kg. Choice C and D are incorrect due to calculation errors.