If two bodies are moving in opposite directions with non-zero velocities, which of the following statements is true?a)Relative velocity andgt; Absolute velocityb)Relative velocity andlt; Absolute velocityc)Relative velocity = Absolute velocityd)Relative velocity andlt;= Absolute velocityCorrect answer is option 'A'. Can you explain this answer?

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If two bodies are moving in opposite directions with non-zero velocities, which of the following statements is true?

a)
Relative velocity > Absolute velocity
b)
Relative velocity < Absolute velocity
c)
Relative velocity = Absolute velocity
d)
Relative velocity <= Absolute velocity

Correct answer is option 'A'. Can you explain this answer?

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If two bodies are moving in opposite directions with non-zero velociti...

The formula for relative velocity is, Vector V_R = Vector V_A – Vector V_B. When both the velocities are opposite in direction, the equation becomes V_R = V_A – (-V_B). Hence the magnitudes add up making the relative velocity greater than the absolute velocity of any of the two bodies.

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If two bodies are moving in opposite directions with non-zero velociti...

Understanding Relative Velocity
When two bodies are moving in opposite directions, the concept of relative velocity becomes important. Relative velocity refers to the velocity of one body as observed from another body.

Key Definitions
- **Absolute Velocity**: The velocity of an object measured with respect to a stationary observer.
- **Relative Velocity**: The velocity of one object in relation to another object.

Calculating Relative Velocity
When two bodies, A and B, are moving in opposite directions with velocities \( v_A \) and \( v_B \) respectively, the relative velocity \( v_{AB} \) can be calculated as:
\[ v_{AB} = v_A + v_B \]
This equation shows that the relative velocity is the sum of their absolute velocities since they are moving in opposite directions.

Comparing Relative and Absolute Velocity
- **Absolute Velocities**: Each body has its own absolute velocity, \( v_A \) and \( v_B \).
- **Relative Velocity**: The result of their relative motion adds the magnitudes of their absolute velocities.

Conclusion
Given that both velocities are non-zero and moving in opposite directions:
- The relative velocity \( v_{AB} \) is greater than either of the absolute velocities \( v_A \) or \( v_B \).
Thus, the correct statement is:

Relative velocity > Absolute velocity
This illustrates that the combined effect of two bodies moving in opposite directions results in a relative velocity that exceeds the individual absolute velocities of the bodies.

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Directions:Read the passages and choose the best answer to each question.PassageNear the end of the 19th century, British engineer Osborne Reynolds ran a set of experiments to observe and predict the transition between laminar (steady) and turbulent ﬂow of a liquid through a pipe. In Reynolds’ experiments, dye was forced through a liquid to show visually when the ﬂow changed from laminar to turbulent. Laminar ﬂow is common only in cases in which the ﬂow channel is relatively small, the ﬂuid is moving slowly, and its viscosity (the degree to which a ﬂuid resists ﬂow under an applied forc e) is relatively high. In turbulent ﬂow, the speed of the ﬂuid at any given point is continuously undergoing changes in both magnitude and direction. Reynolds demonstrated that the transition from laminar to turbulent ﬂow in a pipe depends upon the value of a mathematical quantity equal to the velocity of ﬂow (V ) times the diameter of the tube (D) times the mass density (ρ) of the ﬂuid divided by its absolute viscosity (µ). The “Reynolds number,” as it is called, is determined by the following equation:Several students designed similar experiments to observe ﬂow rates of different liquids. To conduct the experiments, the students were given the following apparatus: Liquid supply tank with clear test section tube and ‘bell mouth’ entrance 1 Rotameter to measure the velocity of ﬂow (ﬂow rate) Tap water • Motor oil 4, 10-ft long smooth pipes of various diameters: 0.25-inch, 0.50-inch, 0.75-inch, 1.0-inchFigure 1 illustrates an approximation of the set-up of each experiment.Figure 2 shows approximate viscosities of the water and motor oils used in the experiments.Experiment 1In Experiment 1, students began with a pipe of diameter 0.25 inches. The pipe was set first at a 15° angle and tap water was released steadily from the tank into the pipe. The velocity of flow (V) was measured. The pipe was then set at a 30° angle, a 45° angle, and a 60° angle, water was released steadily from the tank into the pipe, and the velocity of flow was measured. The process was then repeated for each diameter of pipe using the same amount of water each time. All data were recorded in Table 1. Temperature of the water was held constant at 20°C.Experiment 2In the second experiment, the tap water was replaced by Motor Oil A and the processes were repeated. The results are given in Table 2.Experiment 3In a third experiment, the tap water was replaced by Motor Oil B and the processes were repeated.Q.Which of the following conclusions is best supported by information in the passage? As viscosity increases

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Directions:Read the passages and choose the best answer to each question.PassageNear the end of the 19th century, British engineer Osborne Reynolds ran a set of experiments to observe and predict the transition between laminar (steady) and turbulent ﬂow of a liquid through a pipe. In Reynolds’ experiments, dye was forced through a liquid to show visually when the ﬂow changed from laminar to turbulent. Laminar ﬂow is common only in cases in which the ﬂow channel is relatively small, the ﬂuid is moving slowly, and its viscosity (the degree to which a ﬂuid resists ﬂow under an applied forc e) is relatively high. In turbulent ﬂow, the speed of the ﬂuid at any given point is continuously undergoing changes in both magnitude and direction. Reynolds demonstrated that the transition from laminar to turbulent ﬂow in a pipe depends upon the value of a mathematical quantity equal to the velocity of ﬂow (V ) times the diameter of the tube (D) times the mass density (ρ) of the ﬂuid divided by its absolute viscosity (µ). The “Reynolds number,” as it is called, is determined by the following equation:Several students designed similar experiments to observe ﬂow rates of different liquids. To conduct the experiments, the students were given the following apparatus: Liquid supply tank with clear test section tube and ‘bell mouth’ entrance 1 Rotameter to measure the velocity of ﬂow (ﬂow rate) Tap water • Motor oil 4, 10-ft long smooth pipes of various diameters: 0.25-inch, 0.50-inch, 0.75-inch, 1.0-inchFigure 1 illustrates an approximation of the set-up of each experiment.Figure 2 shows approximate viscosities of the water and motor oils used in the experiments.Experiment 1In Experiment 1, students began with a pipe of diameter 0.25 inches. The pipe was set first at a 15° angle and tap water was released steadily from the tank into the pipe. The velocity of flow (V) was measured. The pipe was then set at a 30° angle, a 45° angle, and a 60° angle, water was released steadily from the tank into the pipe, and the velocity of flow was measured. The process was then repeated for each diameter of pipe using the same amount of water each time. All data were recorded in Table 1. Temperature of the water was held constant at 20°C.Experiment 2In the second experiment, the tap water was replaced by Motor Oil A and the processes were repeated. The results are given in Table 2.Experiment 3In a third experiment, the tap water was replaced by Motor Oil B and the processes were repeated.Q.Based on Experiment 1, the relationship between the angle of the pipe and the velocity of ﬂow

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Directions:Read the passages and choose the best answer to each question.PassageNear the end of the 19th century, British engineer Osborne Reynolds ran a set of experiments to observe and predict the transition between laminar (steady) and turbulent ﬂow of a liquid through a pipe. In Reynolds’ experiments, dye was forced through a liquid to show visually when the ﬂow changed from laminar to turbulent. Laminar ﬂow is common only in cases in which the ﬂow channel is relatively small, the ﬂuid is moving slowly, and its viscosity (the degree to which a ﬂuid resists ﬂow under an applied forc e) is relatively high. In turbulent ﬂow, the speed of the ﬂuid at any given point is continuously undergoing changes in both magnitude and direction. Reynolds demonstrated that the transition from laminar to turbulent ﬂow in a pipe depends upon the value of a mathematical quantity equal to the velocity of ﬂow (V ) times the diameter of the tube (D) times the mass density (ρ) of the ﬂuid divided by its absolute viscosity (µ). The “Reynolds number,” as it is called, is determined by the following equation:Several students designed similar experiments to observe ﬂow rates of different liquids. To conduct the experiments, the students were given the following apparatus: Liquid supply tank with clear test section tube and ‘bell mouth’ entrance 1 Rotameter to measure the velocity of ﬂow (ﬂow rate) Tap water • Motor oil 4, 10-ft long smooth pipes of various diameters: 0.25-inch, 0.50-inch, 0.75-inch, 1.0-inchFigure 1 illustrates an approximation of the set-up of each experiment.Figure 2 shows approximate viscosities of the water and motor oils used in the experiments.Experiment 1In Experiment 1, students began with a pipe of diameter 0.25 inches. The pipe was set first at a 15° angle and tap water was released steadily from the tank into the pipe. The velocity of flow (V) was measured. The pipe was then set at a 30° angle, a 45° angle, and a 60° angle, water was released steadily from the tank into the pipe, and the velocity of flow was measured. The process was then repeated for each diameter of pipe using the same amount of water each time. All data were recorded in Table 1. Temperature of the water was held constant at 20°C.Experiment 2In the second experiment, the tap water was replaced by Motor Oil A and the processes were repeated. The results are given in Table 2.Experiment 3In a third experiment, the tap water was replaced by Motor Oil B and the processes were repeated.Q.According to the passage, laminar ﬂow was most likely to be observed under which of the following conditions?

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If two bodies are moving in opposite directions with non-zero velocities, which of the following statements is true?a)Relative velocity > Absolute velocityb)Relative velocity < Absolute velocityc)Relative velocity = Absolute velocityd)Relative velocity <= Absolute velocityCorrect answer is option 'A'. Can you explain this answer?

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