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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.
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Fluid dynamics is a subfield of fluid mechanics concerned with:
- A. Equilibrium properties of fluids at rest (Fluid Statics)
- B. The motion and behavior of fluids under various conditions
- C. Phase transitions of fluids between liquid, gas, and solid states
- D. Engineering applications of fluids (related but broader than fluid dynamics)
Correct Answer: B
Rationale: Fluid dynamics is the study of fluids in motion and their behavior under different conditions, including how they flow, mix, and interact with their surroundings. It focuses on the dynamic aspects of fluids rather than their static properties when at rest, which is the realm of fluid statics. Phase transitions of fluids between liquid, gas, and solid states are more related to thermodynamics than fluid dynamics. While engineering applications involve fluid dynamics, the field itself is more specialized in studying the movement and behavior of fluids.
When a crane hoists a massive object at a constant velocity compared to lifting the same object gradually, the work done by the crane is:
- A. Less
- B. More
- C. Identical
- D. Dependent on the object's mass
Correct Answer: C
Rationale: The work done by the crane is identical in both scenarios. Work is defined as the force applied over a distance. Since the force needed to lift the object is equal to its weight and the displacement is the same, the work done is identical, whether the object is lifted gradually or at a constant velocity. Choice A is incorrect because the work done is the same in both cases. Choice B is incorrect as well since the work done does not increase. Choice D is incorrect as the mass of the object does not affect the work done by the crane in this scenario.
Enthalpy (H) is a thermodynamic property defined as the sum of a system's internal energy (U) and the product of its pressure (P) and volume (V). The relationship between these is:
- A. H = U + PV
- B. H = U - PV
- C. H = U / PV
- D. H = PV / U
Correct Answer: A
Rationale: Enthalpy (H) is defined as H = U + PV, where U represents internal energy, P is pressure, and V is volume. Enthalpy includes both the internal energy of a system and the energy required to create space for the system against an external pressure. Therefore, the correct relationship between enthalpy, internal energy, pressure, and volume is H = U + PV. Choice B is incorrect as subtracting PV would not account for the work done against pressure. Choice C is incorrect as dividing U by PV doesn't represent the definition of enthalpy. Choice D is incorrect as dividing PV by U is not the correct relationship based on the definition of enthalpy.
Ocean waves build during a storm until there is a vertical distance from the high point to the low point of 6 meters and a horizontal distance of 9 meters between adjacent crests. The waves hit the shore every 5 seconds. What is the speed of the waves?
- A. 1.2 m/s
- B. 1.8 m/s
- C. 2.0 m/s
- D. 2.4 m/s
Correct Answer: B
Rationale: To find the speed of the waves, we use the formula: speed = wavelength / period. The wavelength is the horizontal distance between adjacent crests, which is 9 meters in this case. The period is the time it takes for one wave to pass a fixed point, given as 5 seconds. Therefore, speed = 9 meters / 5 seconds = 1.8 m/s. Choice A (1.2 m/s) is incorrect because it miscalculates the speed. Choice C (2.0 m/s) and Choice D (2.4 m/s) are incorrect as they do not correctly calculate the speed using the provided data.
Faraday's law of electromagnetic induction states that a changing magnetic field in a conductor induces a/an:
- A. Increase in resistance
- B. Electromotive force
- C. Static electric charge
- D. Decrease in capacitance
Correct Answer: B
Rationale: Faraday's law of electromagnetic induction states that a changing magnetic field induces an electromotive force in a conductor. This electromotive force is responsible for generating electricity in power plants and various electrical devices. The induced current is a result of the changing magnetic field, not an increase in resistance (choice A), static electric charge (choice C), or a decrease in capacitance (choice D). Hence, the correct answer is B.