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Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?
- a)The resistive force of liquid on the plate is inversely proportional to h
- b)The resistive force of liquid on the plate is independent of the area of the plate
- c)The tangential (shear) stress on the floor of the tank increases with u0
- d)The tangential (shear) stress on the plate varies linearly with the viscosity η of the liquid.
Correct answer is option 'A,C,D'. Can you explain this answer?
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Understanding the Resistive Force on a Floating Plate
When analyzing the resistive force experienced by a thin square plate floating on a viscous liquid, we consider several key principles of fluid dynamics.
Statement A: The resistive force is inversely proportional to h
- This statement is true. The resistive force (drag force) acting on the plate is influenced by the height of the liquid column (h). A greater height results in a higher pressure gradient, which can lead to increased flow velocity and reduced resistive force. Therefore, the force is inversely related to h.
Statement B: The resistive force is independent of the area of the plate
- This statement is false. The resistive force is directly proportional to the area of the plate in contact with the liquid. A larger area increases the interaction between the plate and the liquid, resulting in a greater drag force.
Statement C: The tangential (shear) stress on the floor of the tank increases with u0
- This statement is true. As the plate is pulled with a velocity u0, the fluid underneath experiences shear, causing an increase in shear stress on the tank floor. The faster the plate moves, the greater the shear stress due to increased fluid motion.
Statement D: The tangential (shear) stress on the plate varies linearly with the viscosity η of the liquid
- This statement is true. Shear stress is defined as the product of viscosity and the velocity gradient. Hence, if the viscosity of the liquid increases, the shear stress at the plate's surface will also increase linearly.
Conclusion
- The correct statements are A, C, and D, while B is incorrect. Understanding these principles is crucial for problems involving fluid dynamics and drag forces in the JEE context.
When analyzing the resistive force experienced by a thin square plate floating on a viscous liquid, we consider several key principles of fluid dynamics.
Statement A: The resistive force is inversely proportional to h
- This statement is true. The resistive force (drag force) acting on the plate is influenced by the height of the liquid column (h). A greater height results in a higher pressure gradient, which can lead to increased flow velocity and reduced resistive force. Therefore, the force is inversely related to h.
Statement B: The resistive force is independent of the area of the plate
- This statement is false. The resistive force is directly proportional to the area of the plate in contact with the liquid. A larger area increases the interaction between the plate and the liquid, resulting in a greater drag force.
Statement C: The tangential (shear) stress on the floor of the tank increases with u0
- This statement is true. As the plate is pulled with a velocity u0, the fluid underneath experiences shear, causing an increase in shear stress on the tank floor. The faster the plate moves, the greater the shear stress due to increased fluid motion.
Statement D: The tangential (shear) stress on the plate varies linearly with the viscosity η of the liquid
- This statement is true. Shear stress is defined as the product of viscosity and the velocity gradient. Hence, if the viscosity of the liquid increases, the shear stress at the plate's surface will also increase linearly.
Conclusion
- The correct statements are A, C, and D, while B is incorrect. Understanding these principles is crucial for problems involving fluid dynamics and drag forces in the JEE context.
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Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer?
Question Description
Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer?.
Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer?.
Solutions for Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer?, a detailed solution for Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer? has been provided alongside types of Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?a)The resistive force of liquid on the plate is inversely proportional to hb)The resistive force of liquid on the plate is independent of the area of the platec)The tangential (shear) stress on the floor of the tank increases with u0d)The tangential (shear) stress on the plate varies linearly with the viscosity ηof the liquid.Correct answer is option 'A,C,D'. Can you explain this answer? tests, examples and also practice JEE tests.
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