The strength of a magnetic field is measured in units of:
- A. Amperes
- B. Tesla
- C. Volts
- D. Coulombs
Correct Answer: B
Rationale: The Tesla (T) is the unit of measurement for the strength of a magnetic field. One Tesla is defined as one weber per square meter. Amperes (choice A) measure electric current, Volts (choice C) measure electric potential, and Coulombs (choice D) measure electric charge, making them incorrect choices for measuring the strength of a magnetic field.
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A concave mirror with a focal length of 2 cm forms a real image of an object at an image distance of 6 cm. What is the object's distance from the mirror?
- A. 3 cm
- B. 6 cm
- C. 12 cm
- D. 30 cm
Correct Answer: B
Rationale: The mirror formula, 1/f = 1/do + 1/di, can be used to solve for the object distance. Given that the focal length (f) is 2 cm and the image distance (di) is 6 cm, we can substitute these values into the formula to find the object distance. Plugging in f = 2 cm and di = 6 cm into the formula gives us 1/2 = 1/do + 1/6. Solving for do, we get do = 6 cm. Therefore, the object's distance from the mirror is 6 cm. Choice A (3 cm), Choice C (12 cm), and Choice D (30 cm) are incorrect distances as the correct object distance is determined to be 6 cm.
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.
If a wave has a frequency of 60 hertz, which of the following is true?
- A. It completes one cycle per minute.
- B. It measures 60 m from crest to crest.
- C. It completes 60 cycles per second.
- D. It measures 60 m from crest to trough.
Correct Answer: C
Rationale: The frequency of a wave is the number of cycles it completes in one second. A wave with a frequency of 60 hertz completes 60 cycles per second. Therefore, choice C is correct. Choice A is incorrect because a frequency of 60 hertz means 60 cycles per second, not per minute. Choice B is incorrect as the frequency of the wave does not determine the distance from crest to crest. Choice D is also incorrect as the frequency does not relate to the distance from crest to trough.
A spring has a spring constant of 20 N/m. How much force is needed to compress the spring from 40 cm to 30 cm?
- A. 200 N
- B. 80 N
- C. 5 N
- D. 2 N
Correct Answer: D
Rationale: The change in length of the spring is 40 cm - 30 cm = 10 cm = 0.10 m. The force required to compress or stretch a spring is given by Hooke's Law: F = k x, where F is the force, k is the spring constant (20 N/m in this case), and x is the change in length (0.10 m). Substituting the values into the formula: F = 20 N/m 0.10 m = 2 N. Therefore, the correct answer is 2 N. Choice A (200 N) is incorrect because it miscalculates the force. Choice B (80 N) is incorrect as it does not apply Hooke's Law correctly. Choice C (5 N) is incorrect as it underestimates the force required.
When two long, parallel wires carry currents in the same direction, the wires will experience a force of:
- A. An unpredictable force depending on wire material
- B. Repulsion
- C. No force
- D. Attraction
Correct Answer: D
Rationale: When two wires carry current in the same direction, they create magnetic fields that interact with each other. This interaction results in an attractive force between the wires due to the alignment of their magnetic fields. Choice A is incorrect because the force can be predicted based on the direction of the currents and the magnetic fields produced. Choice B is incorrect because when currents flow in the same direction, they do not repel each other. Choice C is incorrect because there is indeed a force present due to the interaction of magnetic fields, resulting in attraction between the wires.