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Consider the following statements:
The metacentric height of a floating body depends
1. Directly on the shape of its water-line area.
2. On the volume of liquid displaced by the body.
3. On the distance between the metacentre and the centre ofgravity.
4. On the second moment of water-line area.
Of these statements correct are:
The metacentric height of a floating body depends
1. Directly on the shape of its water-line area.
2. On the volume of liquid displaced by the body.
3. On the distance between the metacentre and the centre ofgravity.
4. On the second moment of water-line area.
Of these statements correct are:
- a)1 and 2
- b)2 and 3
- c)3 and 4
- d)1 and 4
Correct answer is option 'B'. Can you explain this answer?
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Consider the following statements:The metacentric height of a floating...
Ans. (b) The metacentric height of a floating body depends on (2) and (3), i.e. volume of liquid displaced by the body and on the distance between the metacentre and the centre of gravity.
Most Upvoted Answer
Consider the following statements:The metacentric height of a floating...
Metacentric Height of a Floating Body
The metacentric height of a floating body is an important parameter that determines the stability of the body. It is the distance between the metacentre and the centre of gravity of the body. The metacentre is the point of intersection of the vertical line passing through the centre of buoyancy of the body and the vertical line passing through the new centre of buoyancy when the body is tilted. The metacentric height can be calculated using the following formula:
GM = I / V
Where,
GM = Metacentric height
I = Second moment of water-line area
V = Volume of liquid displaced by the body
Factors affecting the Metacentric Height
1. Shape of Water-Line Area
The shape of the water-line area of the floating body directly affects the metacentric height. If the water-line area is large, the metacentric height will be greater, and vice versa.
2. Volume of Liquid Displaced
The volume of liquid displaced by the floating body also affects the metacentric height. If the volume of liquid displaced is large, the metacentric height will be greater, and vice versa.
3. Distance between Metacentre and Centre of Gravity
The distance between the metacentre and the centre of gravity of the floating body affects the metacentric height. If the distance is greater, the metacentric height will be greater, and vice versa.
4. Second Moment of Water-Line Area
The second moment of water-line area is a measure of the distribution of the area around the waterline. It directly affects the metacentric height. If the second moment of water-line area is large, the metacentric height will be greater, and vice versa.
Conclusion
From the above discussion, it can be concluded that the correct statements regarding the factors affecting the metacentric height of a floating body are option B, i.e., 2 and 3. The metacentric height depends on the volume of liquid displaced by the body and the distance between the metacentre and the centre of gravity.
The metacentric height of a floating body is an important parameter that determines the stability of the body. It is the distance between the metacentre and the centre of gravity of the body. The metacentre is the point of intersection of the vertical line passing through the centre of buoyancy of the body and the vertical line passing through the new centre of buoyancy when the body is tilted. The metacentric height can be calculated using the following formula:
GM = I / V
Where,
GM = Metacentric height
I = Second moment of water-line area
V = Volume of liquid displaced by the body
Factors affecting the Metacentric Height
1. Shape of Water-Line Area
The shape of the water-line area of the floating body directly affects the metacentric height. If the water-line area is large, the metacentric height will be greater, and vice versa.
2. Volume of Liquid Displaced
The volume of liquid displaced by the floating body also affects the metacentric height. If the volume of liquid displaced is large, the metacentric height will be greater, and vice versa.
3. Distance between Metacentre and Centre of Gravity
The distance between the metacentre and the centre of gravity of the floating body affects the metacentric height. If the distance is greater, the metacentric height will be greater, and vice versa.
4. Second Moment of Water-Line Area
The second moment of water-line area is a measure of the distribution of the area around the waterline. It directly affects the metacentric height. If the second moment of water-line area is large, the metacentric height will be greater, and vice versa.
Conclusion
From the above discussion, it can be concluded that the correct statements regarding the factors affecting the metacentric height of a floating body are option B, i.e., 2 and 3. The metacentric height depends on the volume of liquid displaced by the body and the distance between the metacentre and the centre of gravity.
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Consider the following statements:The metacentric height of a floating body depends1. Directly on the shape of its water-line area.2. On the volume of liquid displaced by the body.3. On the distance between the metacentre and the centre ofgravity.4. On the second moment of water-line area.Of these statements correct are:a)1 and 2b)2 and 3c)3 and 4d)1 and 4Correct answer is option 'B'. Can you explain this answer?
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Consider the following statements:The metacentric height of a floating body depends1. Directly on the shape of its water-line area.2. On the volume of liquid displaced by the body.3. On the distance between the metacentre and the centre ofgravity.4. On the second moment of water-line area.Of these statements correct are:a)1 and 2b)2 and 3c)3 and 4d)1 and 4Correct answer is option 'B'. 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 Consider the following statements:The metacentric height of a floating body depends1. Directly on the shape of its water-line area.2. On the volume of liquid displaced by the body.3. On the distance between the metacentre and the centre ofgravity.4. On the second moment of water-line area.Of these statements correct are:a)1 and 2b)2 and 3c)3 and 4d)1 and 4Correct answer is option 'B'. 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 Consider the following statements:The metacentric height of a floating body depends1. Directly on the shape of its water-line area.2. On the volume of liquid displaced by the body.3. On the distance between the metacentre and the centre ofgravity.4. On the second moment of water-line area.Of these statements correct are:a)1 and 2b)2 and 3c)3 and 4d)1 and 4Correct answer is option 'B'. Can you explain this answer?.
Consider the following statements:The metacentric height of a floating body depends1. Directly on the shape of its water-line area.2. On the volume of liquid displaced by the body.3. On the distance between the metacentre and the centre ofgravity.4. On the second moment of water-line area.Of these statements correct are:a)1 and 2b)2 and 3c)3 and 4d)1 and 4Correct answer is option 'B'. 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 Consider the following statements:The metacentric height of a floating body depends1. Directly on the shape of its water-line area.2. On the volume of liquid displaced by the body.3. On the distance between the metacentre and the centre ofgravity.4. On the second moment of water-line area.Of these statements correct are:a)1 and 2b)2 and 3c)3 and 4d)1 and 4Correct answer is option 'B'. 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 Consider the following statements:The metacentric height of a floating body depends1. Directly on the shape of its water-line area.2. On the volume of liquid displaced by the body.3. On the distance between the metacentre and the centre ofgravity.4. On the second moment of water-line area.Of these statements correct are:a)1 and 2b)2 and 3c)3 and 4d)1 and 4Correct answer is option 'B'. Can you explain this answer?.
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ample number of questions to practice Consider the following statements:The metacentric height of a floating body depends1. Directly on the shape of its water-line area.2. On the volume of liquid displaced by the body.3. On the distance between the metacentre and the centre ofgravity.4. On the second moment of water-line area.Of these statements correct are:a)1 and 2b)2 and 3c)3 and 4d)1 and 4Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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