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The metacentric heights of two floating bodies A and B are 1 m and 1.5 m respectively. Select the correct statement.
- a)The bodies A and B have equal stability
- b)The body A is more stable than body B
- c)The body B is more stable than body A
- d)The bodies A and B are unstable
Correct answer is option 'C'. Can you explain this answer?
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The metacentric heights of two floating bodies A and B are 1 m and 1.5...
Answer: Option C
The metacentric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the center of gravity of a ship and its metacenter. A larger metacentric height implies greater initial stability against overturning. The metacentric height also influences the natural period of rolling of a hull, with very large metacentric heights being associated with shorter periods of a roll which are uncomfortable for passengers. Hence, a sufficiently, but not excessively, high metacentric height is considered ideal for passenger ships.
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The metacentric heights of two floating bodies A and B are 1 m and 1.5...
Metacentric height is a parameter that determines the stability of a floating body. It is the distance between the center of gravity (G) of the body and the metacenter (M), which is the intersection point of the vertical line passing through the center of buoyancy (B) and the centerline of the body when it is in equilibrium.
The metacentric height (GM) is calculated using the formula GM = BM - BG, where BM is the distance between the center of buoyancy and the metacenter, and BG is the distance between the center of buoyancy and the center of gravity.
In this case, the metacentric height of body A is 1 m and the metacentric height of body B is 1.5 m. Based on these values, we can conclude that:
1. Body A has a metacentric height of 1 m.
2. Body B has a metacentric height of 1.5 m.
Based on the definition of metacentric height, we can make the following observations:
1. A higher metacentric height indicates greater stability because it implies that the metacenter is located above the center of gravity. This means that the body will tend to return to its original position after being disturbed.
2. Conversely, a lower metacentric height indicates lesser stability because it implies that the metacenter is located below the center of gravity. This means that the body will tend to capsize or overturn when disturbed.
Considering these observations, we can conclude that:
- The body B is more stable than body A because it has a higher metacentric height. This means that body B will have a greater tendency to return to its original position when disturbed compared to body A.
- Therefore, the correct statement is option 'C': The body B is more stable than body A.
It is important to note that stability is a crucial factor in the design and operation of floating bodies, such as ships and offshore structures. A higher metacentric height is generally desirable to ensure safe and stable operations in various environmental conditions.
The metacentric height (GM) is calculated using the formula GM = BM - BG, where BM is the distance between the center of buoyancy and the metacenter, and BG is the distance between the center of buoyancy and the center of gravity.
In this case, the metacentric height of body A is 1 m and the metacentric height of body B is 1.5 m. Based on these values, we can conclude that:
1. Body A has a metacentric height of 1 m.
2. Body B has a metacentric height of 1.5 m.
Based on the definition of metacentric height, we can make the following observations:
1. A higher metacentric height indicates greater stability because it implies that the metacenter is located above the center of gravity. This means that the body will tend to return to its original position after being disturbed.
2. Conversely, a lower metacentric height indicates lesser stability because it implies that the metacenter is located below the center of gravity. This means that the body will tend to capsize or overturn when disturbed.
Considering these observations, we can conclude that:
- The body B is more stable than body A because it has a higher metacentric height. This means that body B will have a greater tendency to return to its original position when disturbed compared to body A.
- Therefore, the correct statement is option 'C': The body B is more stable than body A.
It is important to note that stability is a crucial factor in the design and operation of floating bodies, such as ships and offshore structures. A higher metacentric height is generally desirable to ensure safe and stable operations in various environmental conditions.
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The metacentric heights of two floating bodies A and B are 1 m and 1.5 m respectively. Select the correct statement.a)The bodies A and B have equal stabilityb)The body A is more stable than body Bc)The body B is more stable than body Ad)The bodies A and B are unstableCorrect answer is option 'C'. Can you explain this answer?
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The metacentric heights of two floating bodies A and B are 1 m and 1.5 m respectively. Select the correct statement.a)The bodies A and B have equal stabilityb)The body A is more stable than body Bc)The body B is more stable than body Ad)The bodies A and B are unstableCorrect answer is option 'C'. 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 The metacentric heights of two floating bodies A and B are 1 m and 1.5 m respectively. Select the correct statement.a)The bodies A and B have equal stabilityb)The body A is more stable than body Bc)The body B is more stable than body Ad)The bodies A and B are unstableCorrect answer is option 'C'. 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 The metacentric heights of two floating bodies A and B are 1 m and 1.5 m respectively. Select the correct statement.a)The bodies A and B have equal stabilityb)The body A is more stable than body Bc)The body B is more stable than body Ad)The bodies A and B are unstableCorrect answer is option 'C'. Can you explain this answer?.
The metacentric heights of two floating bodies A and B are 1 m and 1.5 m respectively. Select the correct statement.a)The bodies A and B have equal stabilityb)The body A is more stable than body Bc)The body B is more stable than body Ad)The bodies A and B are unstableCorrect answer is option 'C'. 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 The metacentric heights of two floating bodies A and B are 1 m and 1.5 m respectively. Select the correct statement.a)The bodies A and B have equal stabilityb)The body A is more stable than body Bc)The body B is more stable than body Ad)The bodies A and B are unstableCorrect answer is option 'C'. 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 The metacentric heights of two floating bodies A and B are 1 m and 1.5 m respectively. Select the correct statement.a)The bodies A and B have equal stabilityb)The body A is more stable than body Bc)The body B is more stable than body Ad)The bodies A and B are unstableCorrect answer is option 'C'. Can you explain this answer?.
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