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A rock has a volume of 6 cm3 and a mass of 24 g. What is its density?
- A. 4 g/cm3
- B. 4 cm3/g
- C. 144 g/cm3
- D. 144 cm3/g
Correct Answer: A
Rationale: Density is calculated by dividing the mass of an object by its volume. In this case, the mass of the rock is 24 g and its volume is 6 cm3. By dividing 24 g by 6 cm3, we find that the density of the rock is 4 g/cm3. Choice A is the correct answer because density is expressed in units of mass per unit volume (g/cm3). Choice B is incorrect as it represents the reciprocal of density. Choices C and D are significantly higher values and do not match the calculated density of the rock.
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According to the Law of Universal Gravitation, the gravitational force between two objects is directly proportional to what factor?
- A. the gravitational constant
- B. the distance between them
- C. the product of their masses
- D. the square of the distance between them
Correct Answer: C
Rationale: According to the Law of Universal Gravitation, the gravitational force between two objects is directly proportional to the product of their masses. The equation is: F = G (mâ‚ mâ‚‚) / r², where F is the gravitational force, G is the gravitational constant, mâ‚ and mâ‚‚ are the masses of the two objects, and r is the distance between them. Choice A is incorrect because the gravitational constant is a constant value. Choice B is incorrect because the distance between the objects affects the strength of the gravitational force inversely proportional to the square of the distance, not directly proportional. Choice D is incorrect as it represents the inverse square law, where the gravitational force decreases with the square of the distance between the objects.
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.
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 780-watt refrigerator is powered by a 120-volt power source. What is the current being drawn?
- A. 660 amperes
- B. 150 amperes
- C. 6.5 amperes
- D. 0.15 amperes
Correct Answer: C
Rationale: To calculate the current being drawn by the refrigerator, you can use the formula: Current (I) = Power (P) / Voltage (V). Given that the power of the refrigerator is 780 watts and the voltage is 120 volts, you can plug these values into the formula to find the current: I = 780 watts / 120 volts = 6.5 amperes. Therefore, the current being drawn by the 780-watt refrigerator is 6.5 amperes. Choice A, 660 amperes, is incorrect as it is significantly higher than the correct answer. Choice B, 150 amperes, is also incorrect and too high. Choice D, 0.15 amperes, is incorrect as it is too low. The correct answer is 6.5 amperes.
Which mathematical quantity is scalar?
- A. Distance
- B. Velocity
- C. Acceleration
- D. Displacement
Correct Answer: A
Rationale: Distance is a scalar quantity because it has only magnitude and no direction. It is simply the total length of the path travelled by an object. Scalars are quantities that are fully described by their magnitude alone, without any reference to direction. Velocity and acceleration are vector quantities as they have both magnitude and direction. Displacement is also a vector quantity as it is the change in position of an object and includes both magnitude and direction.