Nokea
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.
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For steady, incompressible flow through a pipe, the mass flow rate (á¹) is related to the fluid density (Ï), cross-sectional area (A), and average velocity (v) via the continuity equation:
- A. á¹ cannot be determined without additional information
- B. á¹ = ÏvA
- C. Bernoulli's principle is solely applicable here
- D. The equation of state for the specific fluid is required
Correct Answer: B
Rationale: The continuity equation for steady, incompressible flow states that the mass flow rate is the product of the fluid's density, velocity, and cross-sectional area. Hence, á¹ = ÏvA. Choice A is incorrect because the mass flow rate can be determined using the given formula. Choice C is incorrect as Bernoulli's principle does not directly relate to the mass flow rate calculation. Choice D is incorrect as the equation of state is not needed to calculate the mass flow rate in this scenario.
According to the Clausius inequality, for a cyclic process involving heat transfer between a system and its surroundings at a single constant temperature (T), the following inequality must hold true:
- A. There is no relationship between heat transfer and temperature in a cyclic process.
- B. ∫ dQ/T ≥ 0
- C. ∫ Q/T = constant
- D. ∫ dQ/T ≤ 0
Correct Answer: D
Rationale: The Clausius inequality states that for a cyclic process involving heat transfer at a single constant temperature, the integral of heat transfer divided by temperature (∫ dQ/T) must be less than or equal to zero. This inequality reflects the irreversibility of natural processes. Choice A is incorrect as there is a direct relationship between heat transfer and temperature in the Clausius inequality. Choice B is incorrect because the integral of dQ/T must be less than or equal to zero, not greater than or equal to zero. Choice C is incorrect because the integral of Q/T is not a constant in a cyclic process involving heat transfer at a single constant temperature.
In a static fluid, pressure (P) at a depth (h) is governed by the hydrostatic equation:
- A. P = Ïgh
- B. P = γh
- C. P = μgh
- D. P = bh
Correct Answer: A
Rationale: The correct formula for the pressure at a certain depth in a fluid according to the hydrostatic equation is P = Ïgh. Here, Ï represents the fluid's density, g is the gravitational acceleration, and h is the depth. This formula shows that pressure increases linearly with the density of the fluid, the acceleration due to gravity, and the depth. Choices B, C, and D are incorrect because they do not accurately represent the relationship between pressure, density, gravitational acceleration, and depth in a static fluid.
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.
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.