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A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:
- a)0.2
- b)0.4
- c)0.5
- d)0.75
Correct answer is option 'C'. Can you explain this answer?
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A cylindrical vessel having its height equal to its diameter isfilled ...
Ans. (c)
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A cylindrical vessel having its height equal to its diameter isfilled ...
Given information:
- A cylindrical vessel has its height equal to its diameter.
- The vessel is filled with liquid.
- The vessel is moved horizontally with an acceleration equal to the acceleration due to gravity.
To find:
The ratio of the liquid left in the vessel to the liquid at static equilibrium condition.
Solution:
1. Analysis of the situation:
- When the vessel is at static equilibrium, the liquid inside is at rest and experiences a downward force due to gravity.
- When the vessel is moved horizontally with an acceleration equal to the acceleration due to gravity, the liquid inside experiences a pseudo force in the opposite direction.
- This pseudo force acts on the liquid and tends to push it towards the side opposite to the direction of acceleration.
2. Effect of acceleration on the liquid:
- Due to the acceleration, the liquid inside the vessel moves towards the side opposite to the direction of acceleration.
- As the liquid moves, it forms a parabolic shape, with the highest point being at the center of the vessel.
- The height of the parabolic shape is determined by the acceleration and the diameter of the vessel.
3. Calculation of the height of the parabolic shape:
- Let the diameter of the vessel be D, and the acceleration be a.
- The height of the parabolic shape can be given by the equation: h = (a/2g) * D^2
- where h is the height of the parabolic shape, a is the acceleration, and g is the acceleration due to gravity.
- Since the height of the vessel is equal to its diameter, the height of the parabolic shape can be written as h = (a/2g) * h^2
4. Calculation of the ratio of the liquid left:
- The volume of the liquid left in the vessel can be calculated by subtracting the volume of the parabolic shape from the total volume of the vessel.
- The volume of the parabolic shape can be calculated using the formula for the volume of a paraboloid: V = (π/2) * h^2 * (3D - h)
- The total volume of the vessel can be calculated using the formula for the volume of a cylinder: V_total = π * (h/2)^2 * h
5. Calculation of the ratio:
- The ratio of the liquid left to the liquid at static equilibrium condition can be given by the formula: ratio = (V_total - V) / V_total
6. Substituting the values:
- Substituting the values of V and V_total in the ratio formula, we get: ratio = [π * (h/2)^2 * h - (π/2) * h^2 * (3D - h)] / [π * (h/2)^2 * h]
7. Simplifying the ratio:
- Simplifying the ratio formula, we get: ratio = (4h - 3D) / (4h)
8. Substituting the value of h:
- Substituting the value of h from the equation h = (a/2g) * D^2, we get: ratio = (2aD^2 - 3D) / (2aD^
- A cylindrical vessel has its height equal to its diameter.
- The vessel is filled with liquid.
- The vessel is moved horizontally with an acceleration equal to the acceleration due to gravity.
To find:
The ratio of the liquid left in the vessel to the liquid at static equilibrium condition.
Solution:
1. Analysis of the situation:
- When the vessel is at static equilibrium, the liquid inside is at rest and experiences a downward force due to gravity.
- When the vessel is moved horizontally with an acceleration equal to the acceleration due to gravity, the liquid inside experiences a pseudo force in the opposite direction.
- This pseudo force acts on the liquid and tends to push it towards the side opposite to the direction of acceleration.
2. Effect of acceleration on the liquid:
- Due to the acceleration, the liquid inside the vessel moves towards the side opposite to the direction of acceleration.
- As the liquid moves, it forms a parabolic shape, with the highest point being at the center of the vessel.
- The height of the parabolic shape is determined by the acceleration and the diameter of the vessel.
3. Calculation of the height of the parabolic shape:
- Let the diameter of the vessel be D, and the acceleration be a.
- The height of the parabolic shape can be given by the equation: h = (a/2g) * D^2
- where h is the height of the parabolic shape, a is the acceleration, and g is the acceleration due to gravity.
- Since the height of the vessel is equal to its diameter, the height of the parabolic shape can be written as h = (a/2g) * h^2
4. Calculation of the ratio of the liquid left:
- The volume of the liquid left in the vessel can be calculated by subtracting the volume of the parabolic shape from the total volume of the vessel.
- The volume of the parabolic shape can be calculated using the formula for the volume of a paraboloid: V = (π/2) * h^2 * (3D - h)
- The total volume of the vessel can be calculated using the formula for the volume of a cylinder: V_total = π * (h/2)^2 * h
5. Calculation of the ratio:
- The ratio of the liquid left to the liquid at static equilibrium condition can be given by the formula: ratio = (V_total - V) / V_total
6. Substituting the values:
- Substituting the values of V and V_total in the ratio formula, we get: ratio = [π * (h/2)^2 * h - (π/2) * h^2 * (3D - h)] / [π * (h/2)^2 * h]
7. Simplifying the ratio:
- Simplifying the ratio formula, we get: ratio = (4h - 3D) / (4h)
8. Substituting the value of h:
- Substituting the value of h from the equation h = (a/2g) * D^2, we get: ratio = (2aD^2 - 3D) / (2aD^
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A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer?
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A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer?.
A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer?.
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A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A cylindrical vessel having its height equal to its diameter isfilled with liquid and moved horizontally at acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is:a)0.2b)0.4c)0.5d)0.75Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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