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An object with a charge of 4 μC is placed 1 meter from another object with a charge of 2 μC. What is the magnitude of the resulting force between the objects?
- A. 0.04 N
- B. 0.072 N
- C. 80 N
- D. 8 10−6 N
Correct Answer: A
Rationale: To find the magnitude of the resulting force between two charges, we can use Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula for Coulomb's law is:
F = k (|q1 q2| / r²),
where F is the force, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges. Substituting the given values into the formula:
F = (9 10â¹ N·m²/C²) ((4 10â»â¶ C) (2 10â»â¶ C) / (1 m)²) = 0.04 N.
Therefore, the magnitude of the resulting force between the objects is 0.04 N.
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How might the energy use of an appliance be expressed?
- A. Power = energy time
- B. Time + energy = power
- C. Energy = power time
- D. Energy/power = time
Correct Answer: C
Rationale: The energy use of an appliance can be expressed using the formula Energy = Power Time. In this formula, Energy represents the amount of electricity consumed by the appliance, Power indicates the rate at which the appliance uses electricity (measured in watts), and Time represents the duration for which the appliance is being used (measured in hours). By multiplying the power rating of the appliance by the time it is in use, one can calculate the total energy consumed. Option C is the correct choice because it accurately represents the relationship between power, time, and energy. Choices A, B, and D present incorrect representations of the relationship between energy, power, and time, making them wrong answers.
When a hot cup of coffee is placed on a cold table, heat transfer primarily occurs through which process?
- A. Radiation
- B. Conduction
- C. Convection within the coffee
- D. A combination of conduction and convection
Correct Answer: B
Rationale: When a hot cup of coffee is placed on a cold table, heat transfer primarily occurs through conduction. Conduction is the process of heat transfer through direct contact between objects at different temperatures. In this scenario, the heat from the hot coffee cup is transferred to the cold table through direct contact, making conduction the primary mode of heat transfer. Choice A (Radiation) is incorrect because radiation is the transfer of heat through electromagnetic waves, which is not the primary mode of heat transfer in this scenario. Choice C (Convection within the coffee) is incorrect because convection is the transfer of heat through the movement of fluids, which is not the primary mode of heat transfer in this scenario. Choice D (A combination of conduction and convection) is incorrect because while convection may play a minor role due to air currents around the cup, the primary mode of heat transfer in this scenario is conduction.
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.
Two objects attract each other with a gravitational force of 12 units. If you double the mass of both objects, what is the new force of attraction between them?
- A. 3 units
- B. 6 units
- C. 24 units
- D. 48 units
Correct Answer: C
Rationale: The gravitational force between two objects is directly proportional to the product of their masses. When you double the masses of both objects, the force of attraction between them increases by a factor of 2 x 2 = 4. Therefore, the new force of attraction between the two objects will be 12 units x 4 = 24 units. Choices A, B, and D are incorrect because doubling the mass results in a quadruple increase in force, not a linear one.
When two identical charged spheres, both positively charged, are brought close together, the electrostatic force between them will be:
- A. Slightly attractive
- B. Zero
- C. Strongly attractive
- D. Strongly repulsive
Correct Answer: D
Rationale: When two positively charged spheres are brought close together, they will experience a repulsive force due to their like charges. The electrostatic force causes the spheres to repel each other, making the correct answer D: Strongly repulsive. The force is not dependent on the material of the spheres, and the force is definitely not zero, as like charges repel. Choice A is incorrect as like charges do not attract each other. Choice C is incorrect as like charges repel, not attract.