Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > A solid cylinder of diameter 4.5 has a height...
Start Learning for Free
A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.
- a)1.9 m
- b)3.8 m
- c)5.7 m
- d).95 m
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the ...
Explanation:BG= Centre of pontoon – Centre of immersed portion=1.25-0.45*2.5=0.125
Metacentric height=I/∀ -BG
I=π*r⁴
∀= π*r*r*h
Metacentric height=1.9 m.
Metacentric height=I/∀ -BG
I=π*r⁴
∀= π*r*r*h
Metacentric height=1.9 m.
Most Upvoted Answer
A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the ...
Given data:
Diameter of cylinder = 4.5 m
Height of cylinder = 2.5 m
Specific gravity of cylinder = 0.45
To find: Metacentric height of cylinder when it is floating in water with its axis vertical
Solution:
Metacentric height: It is the distance between the center of gravity of the floating body and the metacentre.
Metacentre: It is the point through which the line of action of the buoyant force passes when the body is slightly tilted.
Steps to find the metacentric height of the cylinder:
1. Determine the weight of the cylinder:
Weight of the cylinder = Volume of the cylinder x Density of the cylinder x g
Density of the cylinder = Specific gravity of the cylinder x Density of water = 0.45 x 1000 kg/m³ = 450 kg/m³
Volume of the cylinder = πr²h = π(4.5/2)² x 2.5 = 39.48 m³
Weight of the cylinder = 39.48 x 450 x 9.81 = 173,260 N
2. Determine the weight of the water displaced by the cylinder:
Volume of water displaced = Volume of the cylinder = 39.48 m³
Weight of the water displaced = Volume of water displaced x Density of water x g = 39.48 x 1000 x 9.81 = 387,653 N
3. Determine the position of the center of gravity of the cylinder:
For a solid cylinder, the center of gravity is at the center of the cylinder.
4. Determine the position of the metacentre:
For a cylinder floating with its axis vertical, the metacentre is at the center of the cylinder.
5. Determine the metacentric height:
Metacentric height = Distance between the center of gravity and the metacentre
The center of the cylinder is at its midpoint.
Therefore, the metacentric height = (Height of the cylinder/2) - (Radius of the cylinder/2) = (2.5/2) - (4.5/2)/2 = 1.9 m
Therefore, the metacentric height of the cylinder when it is floating in water with its axis vertical is 1.9 m.
Hence, the correct option is (a) 1.9 m.
Diameter of cylinder = 4.5 m
Height of cylinder = 2.5 m
Specific gravity of cylinder = 0.45
To find: Metacentric height of cylinder when it is floating in water with its axis vertical
Solution:
Metacentric height: It is the distance between the center of gravity of the floating body and the metacentre.
Metacentre: It is the point through which the line of action of the buoyant force passes when the body is slightly tilted.
Steps to find the metacentric height of the cylinder:
1. Determine the weight of the cylinder:
Weight of the cylinder = Volume of the cylinder x Density of the cylinder x g
Density of the cylinder = Specific gravity of the cylinder x Density of water = 0.45 x 1000 kg/m³ = 450 kg/m³
Volume of the cylinder = πr²h = π(4.5/2)² x 2.5 = 39.48 m³
Weight of the cylinder = 39.48 x 450 x 9.81 = 173,260 N
2. Determine the weight of the water displaced by the cylinder:
Volume of water displaced = Volume of the cylinder = 39.48 m³
Weight of the water displaced = Volume of water displaced x Density of water x g = 39.48 x 1000 x 9.81 = 387,653 N
3. Determine the position of the center of gravity of the cylinder:
For a solid cylinder, the center of gravity is at the center of the cylinder.
4. Determine the position of the metacentre:
For a cylinder floating with its axis vertical, the metacentre is at the center of the cylinder.
5. Determine the metacentric height:
Metacentric height = Distance between the center of gravity and the metacentre
The center of the cylinder is at its midpoint.
Therefore, the metacentric height = (Height of the cylinder/2) - (Radius of the cylinder/2) = (2.5/2) - (4.5/2)/2 = 1.9 m
Therefore, the metacentric height of the cylinder when it is floating in water with its axis vertical is 1.9 m.
Hence, the correct option is (a) 1.9 m.
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. Can you explain this answer?
Question Description
A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. 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 solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. 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 solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. Can you explain this answer?.
A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. 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 solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. 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 solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.a)1.9 mb)3.8 mc)5.7 md).95 mCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup