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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.
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Which of these substances is most compressible?
- A. Gold
- B. Water
- C. Mercury
- D. Methane
Correct Answer: D
Rationale: Methane, a gas at room temperature and pressure, is the most compressible substance among the options provided. Gases are generally more compressible compared to liquids and solids because their particles have more space between them, allowing for greater compression when pressure is applied. Gold, water, and mercury, being solid and liquid substances, respectively, have particles arranged closely together, making them less compressible. Therefore, the correct answer is Methane.
What is the diameter of a loop if its radius is 6 meters?
- A. 6 m
- B. 12 m
- C. 18 m
- D. 36 m
Correct Answer: B
Rationale: The diameter of a loop is calculated by multiplying the radius by 2. Since the radius is 6 meters, the diameter is 6 2 = 12 meters. Therefore, the correct answer is 12 meters. Choice A (6 m) is the radius, not the diameter. Choices C (18 m) and D (36 m) are incorrect as they do not reflect the correct calculation for determining the diameter of a loop.
A 120-volt heat lamp draws 25 amps of current. What is the lamp's resistance?
- A. 96 ohms
- B. 104 ohms
- C. 150 ohms
- D. 4.8 ohms
Correct Answer: D
Rationale: To find the resistance of the lamp, we use Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I), expressed as: R = V / I. Given that the voltage (V) is 120 volts and the current (I) is 25 amps, we substitute these values into the formula: R = 120 V / 25 A = 4.8 ohms. Therefore, the resistance of the lamp is 4.8 ohms. Choice A, 96 ohms, is incorrect as it is not the result of the correct calculation. Choice B, 104 ohms, is incorrect as it does not match the calculated resistance. Choice C, 150 ohms, is incorrect as it is not the correct resistance value obtained through the calculation.
When a small object floats on the surface of a liquid, the surface tension creates a:
- A. Buoyant force acting upwards
- B. Pressure difference causing sinking
- C. Drag force opposing motion
- D. Restoring force towards equilibrium
Correct Answer: D
Rationale: Surface tension creates a restoring force that holds the object on the surface. The liquid's surface behaves like a stretched membrane, and when disturbed, it tends to return the object to its original position, creating a restoring force. The other choices are incorrect: A buoyant force acts on objects submerged in a fluid, not floating on the surface; pressure differences usually affect sinking objects, not floating ones; drag force is a resistance force that opposes motion, not related to surface tension.
Entropy (S) is a thermodynamic property related to the system's disorder. According to the second law of thermodynamics, in a spontaneous process:
- A. The total entropy of the system and surroundings increases.
- B. The total entropy of the system and surroundings decreases.
- C. The total entropy of the system remains constant.
- D. The total entropy of the surroundings increases, while the system's entropy decreases.
Correct Answer: A
Rationale: The second law of thermodynamics asserts that the entropy of an isolated system (or the combined system and surroundings) will always increase in a spontaneous process, reflecting an increase in disorder. Therefore, the correct answer is that the total entropy of the system and surroundings increases. Choice B is incorrect because entropy always tends to increase in a spontaneous process, as dictated by the second law of thermodynamics. Choice C is incorrect as entropy typically increases in natural processes. Choice D is incorrect because the second law of thermodynamics states that the total entropy of the system and surroundings always increases in a spontaneous process.