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Two objects attract each other with a gravitational force of 12 units. If the distance between them is halved, what is the new force of attraction between the two objects?
- A. 3 units
- B. 6 units
- C. 24 units
- D. 48 units
Correct Answer: C
Rationale: The gravitational force between two objects is inversely proportional to the square of the distance between them. When the distance is halved, the new force of attraction will be 12 units x (1/(0.5)^2) = 12 units x 4 = 24 units. Therefore, the correct answer is C. Choice A and B are incorrect as they do not consider the inverse square law of gravitational force. Choice D is incorrect as reducing the distance between the objects does not lead to a squared increase in force.
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A hummingbird's wings beat at 25 beats per second. What is the period of the wing beating in seconds?
- A. 0.04 s
- B. 0.25 s
- C. 0.4 s
- D. 4 s
Correct Answer: A
Rationale: The period represents the time for one complete cycle of the wing beating. To calculate the period, you take the reciprocal of the frequency. In this case, with the wings beating at 25 beats per second, the period is 1/25, which equals 0.04 seconds. Therefore, choice A, 0.04 seconds, is correct. Choices B, C, and D are incorrect because they do not reflect the correct calculation of the period based on the given frequency of 25 beats per second.
What is the phenomenon by which light bends as it passes through a prism known as?
- A. Reflection
- B. Electrical conduction
- C. Diffraction
- D. Refraction
Correct Answer: D
Rationale: Refraction is the phenomenon by which light bends as it passes through a prism or any other medium boundary. When light transitions from one medium to another, such as air to glass in the case of a prism, it changes speed and direction due to the change in the medium's refractive index. This change in speed causes the light to bend. Reflection, on the other hand, is the bouncing back of light when it hits a surface. Diffraction refers to the bending of light around obstacles or through narrow openings. Electrical conduction involves the movement of electrically charged particles through a conductor, which is unrelated to the bending of light.
A 25-cm spring stretches to 28 cm when a force of 12 N is applied. What would its length be if that force were doubled?
- A. 31 cm
- B. 40 cm
- C. 50 cm
- D. 56 cm
Correct Answer: A
Rationale: When the 12 N force stretches the spring from 25 cm to 28 cm, it causes a length increase of 28 cm - 25 cm = 3 cm. Therefore, each newton of applied force causes an extension of 3 cm / 12 N = 0.25 cm/N. If the force is doubled to 24 N, the spring would extend by 24 N 0.25 cm/N = 6 cm more than its original length of 25 cm. Thus, the new length of the spring would be 25 cm + 6 cm = 31 cm. Choice A, 31 cm, is the correct answer as calculated. Choices B, C, and D are incorrect as they do not consider the relationship between force and extension in the spring, leading to incorrect calculations of the new length.
If a 5-kg ball is moving at 5 m/s, what is its momentum?
- A. 10 kgâ‹…m/s
- B. 16.2 km/h
- C. 24.75 kgâ‹…m/s
- D. 25 kgâ‹…m/s
Correct Answer: D
Rationale: The momentum of an object is calculated by multiplying its mass by its velocity. In this case, the mass of the ball is 5 kg and its velocity is 5 m/s. Therefore, the momentum of the ball is 5 kg 5 m/s = 25 kgâ‹…m/s. Choice A (10 kgâ‹…m/s) is incorrect as it does not account for both mass and velocity. Choice B (16.2 km/h) is incorrect as it provides a speed in a different unit without considering mass. Choice C (24.75 kgâ‹…m/s) is incorrect as it does not correctly calculate the momentum based on the given mass and velocity.
Which conclusion can be drawn from Ohm's law?
- A. Voltage and current are inversely proportional when resistance is constant.
- B. The ratio of the potential difference between the ends of a conductor to current is a constant, R.
- C. Voltage is the amount of charge that passes through a point per second.
- D. Power (P) can be calculated by multiplying current (I) by voltage (V).
Correct Answer: B
Rationale: Ohm's law states that the ratio of the potential difference (voltage) between the ends of a conductor to the current flowing through it is a constant. Mathematically, this is represented as V = I x R, where V is voltage, I is current, and R is the constant resistance. Therefore, the correct conclusion that can be drawn from Ohm's law is that the ratio of the potential difference between the ends of a conductor to current is a constant, denoted as R. This relationship is fundamental to understanding the behavior of electrical circuits and the effect of resistance on voltage and current. Choice A is incorrect because Ohm's law actually states that voltage and current are directly proportional when resistance is constant. Choice C is incorrect because voltage is not the amount of charge that passes through a point per second; rather, it is the electric potential energy per unit charge. Choice D is incorrect because although power (P) can be calculated by multiplying current (I) by voltage (V), this is not a conclusion directly drawn from Ohm's law.