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Why are boats more buoyant in salt water than in fresh water?
- A. Salt decreases the mass of the boats.
- B. Salt increases the volume of the water.
- C. Salt affects the density of the boats.
- D. Salt increases the density of the water.
Correct Answer: D
Rationale: Salt increases the density of water, making saltwater more buoyant than freshwater. The higher density of saltwater provides more lift to a boat, enabling it to float more easily compared to in freshwater. Choice A is incorrect because salt does not affect the mass of the boats. Choice B is incorrect as salt does not increase the volume of water. Choice C is incorrect since salt affects the density of water, not the boats themselves. Therefore, the correct answer is that salt increases the density of the water, resulting in boats being more buoyant in salt water than in fresh water.
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A bicycle and a car are both traveling at a rate of 5 m/s. Which statement is true?
- A. The bicycle has more kinetic energy than the car.
- B. The bicycle has less kinetic energy than the car.
- C. Both vehicles have the same amount of kinetic energy.
- D. Only the car has kinetic energy.
Correct Answer: B
Rationale: Kinetic energy is determined by both the mass and the velocity of an object. While both the bicycle and the car are moving at the same velocity (5 m/s), the car has significantly more mass than the bicycle. As a result, the car has more kinetic energy than the bicycle, even though their speeds are identical. Therefore, choice B is correct. Choices A, C, and D are incorrect because they do not consider the influence of mass on kinetic energy. Choice A is incorrect as the car has more kinetic energy due to its greater mass. Choice C is incorrect because the vehicles have different masses. Choice D is incorrect as both the bicycle and the car possess kinetic energy.
Which of the following describes a vector quantity?
- A. 5 miles per hour due southwest
- B. 5 miles per hour
- C. 5 miles
- D. None of the above
Correct Answer: A
Rationale: A vector quantity is characterized by both magnitude and direction. In the provided options, choice A, '5 miles per hour due southwest,' fits this definition as it includes both the magnitude (5 miles per hour) and the direction (southwest), making it a vector quantity. Choices B and C only provide the magnitude without indicating any direction, hence they do not represent vector quantities.
A 110-volt hair dryer delivers 1,525 watts of power. How many amperes does it draw?
- A. 167.75 amperes
- B. 1.635 amperes
- C. 1.415 amperes
- D. 13.9 amperes
Correct Answer: D
Rationale: To determine the amperes drawn by the hair dryer, we use the formula: Amperes = Watts / Volts. The hair dryer operates at 1,525 watts with 110 volts. Dividing 1,525 watts by 110 volts yields 13.9 amperes. Therefore, the correct answer is 13.9 amperes. Choices A, B, and C are incorrect because they do not result from the correct calculation using the formula.
The buoyant force, F_b, experienced by an object submerged in a fluid is given by:
- A. F_b = W, the object's weight
- B. F_b = W_d, the weight of the fluid displaced by the object
- C. F_b = Ï, the density of the fluid
- D. F_b = V, the object's volume
Correct Answer: B
Rationale: The correct formula for the buoyant force experienced by an object submerged in a fluid is given by Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. This is represented by the formula F_b = W_d, where W_d is the weight of the fluid displaced by the object. This force acts in the opposite direction to gravity and is responsible for objects floating or sinking in fluids. Choice A is incorrect because the buoyant force is not equal to the object's weight. Choice C is incorrect because the density of the fluid is not directly related to the buoyant force. Choice D is incorrect because the object's volume is not the determining factor for the buoyant force.
A 5-cm candle is placed 20 cm away from a concave mirror with a focal length of 10 cm. What is the image distance of the candle?
- A. 20 cm
- B. 40 cm
- C. 60 cm
- D. 75 cm
Correct Answer: C
Rationale: To find the image distance of the candle, we use the mirror formula: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. In this case, the focal length f = 10 cm and the object distance do = 20 cm. Substituting these values into the formula gives us 1/10 = 1/20 + 1/di. Solving for di, we get di = 60 cm. Therefore, the image distance of the candle is 60 cm. Choice A (20 cm) is incorrect because it represents the object distance, not the image distance. Choice B (40 cm) is incorrect as it does not consider the mirror formula calculation. Choice D (75 cm) is incorrect as it does not match the correct calculation based on the mirror formula.