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A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.
- a)L/D<9/16
- b)L/D<3/4
- c)L/D<2/3
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is req...
By principle of buoyancy,
Weight of cylinder = Weight of water displaced
h=2L/3
AG=L/2
AB=L/3
BG=AG-AB=L/6
GM= Metacentric height=I/∀ – BG=3D2/32L-L/6
For stable equilibrium, GM should be positive
GM>0
i.e L/D<3/4.
Most Upvoted Answer
A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is req...
= 2.25
To float with its longitudinal axis vertical, the weight of the cylinder should be equal to the weight of the displaced oil. Let the diameter of the cylinder be D and its height be L. Then, the volume of the cylinder is πD^2L/4 and its weight is (πD^2L/4) × 0.6g, where g is the acceleration due to gravity.
The weight of the displaced oil is (πD^2L/4) × (0.9-1)g = -(πD^2L/4) × 0.1g, as the weight of the displaced oil is equal to the weight of the cylinder.
Equating the two weights, we get:
(πD^2L/4) × 0.6g = -(πD^2L/4) × 0.1g
Simplifying, we get:
D^2/L = 2.25
Therefore, the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil is 2.25.
To float with its longitudinal axis vertical, the weight of the cylinder should be equal to the weight of the displaced oil. Let the diameter of the cylinder be D and its height be L. Then, the volume of the cylinder is πD^2L/4 and its weight is (πD^2L/4) × 0.6g, where g is the acceleration due to gravity.
The weight of the displaced oil is (πD^2L/4) × (0.9-1)g = -(πD^2L/4) × 0.1g, as the weight of the displaced oil is equal to the weight of the cylinder.
Equating the two weights, we get:
(πD^2L/4) × 0.6g = -(πD^2L/4) × 0.1g
Simplifying, we get:
D^2/L = 2.25
Therefore, the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil is 2.25.
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A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.a)L/D<9/16b)L/D<3/4c)L/D<2/3d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?
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A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.a)L/D<9/16b)L/D<3/4c)L/D<2/3d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.a)L/D<9/16b)L/D<3/4c)L/D<2/3d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.a)L/D<9/16b)L/D<3/4c)L/D<2/3d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?.
A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.a)L/D<9/16b)L/D<3/4c)L/D<2/3d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.a)L/D<9/16b)L/D<3/4c)L/D<2/3d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.a)L/D<9/16b)L/D<3/4c)L/D<2/3d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?.
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