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For floating bodies, how is the metacentric radius defined?
- a)The distance between centre of gravity and the metacentre.
- b)Second moment of area of plane of flotation about centroidal axisperpendicular to plane of rotation/immersed volume.
- c)The distance between centre of gravity and the centre of buoyancy.
- d)Moment of inertia of the body about its axis of rotation/immersedvolume.
Correct answer is option 'A'. Can you explain this answer?
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For floating bodies, how is the metacentric radius defined?a)The dista...
Ans. (a) Metacentric Radius or Metacentric Height is the distance between Centre of Gravity and the Metacentre.
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For floating bodies, how is the metacentric radius defined?a)The dista...
Metacentre is a point about which a floating body oscillate and metacentric height is the distance b/w centre of gravity and metacentric point.
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For floating bodies, how is the metacentric radius defined?a)The dista...
Definition of Metacentric Radius
The metacentric radius is a parameter used to evaluate the stability of a floating body. It is defined as the distance between the center of gravity (G) of the body and the metacentre (M). The metacentre is the intersection point of the vertical line passing through the center of buoyancy (B) and the line of action of the buoyant force when the body is inclined.
Explanation of Option A
Option A states that the metacentric radius is the distance between the center of gravity and the metacentre. This statement is correct and accurately defines the metacentric radius. Let's understand why.
When a body is floating in a fluid, it experiences two opposing forces: the weight of the body acting downward and the buoyant force acting upward. The buoyant force is equal to the weight of the fluid displaced by the body and acts through the center of buoyancy.
When the body is in equilibrium, these two forces should be aligned in the same vertical line. However, if the body is tilted or inclined, the buoyant force will no longer act through the center of gravity. Instead, it will create a moment about the center of gravity, causing the body to rotate. This rotation can be clockwise or counterclockwise depending on the direction of the inclination.
To analyze the stability of the floating body, we need to consider the position of the metacentre. The metacentre is located above the center of gravity, and its height determines the stability of the body. If the metacentre is higher, the body will have greater stability, and if it is lower, the body will be less stable.
Role of Metacentric Radius
The metacentric radius is a measure of the distance between the center of gravity and the metacentre. It quantifies the stability of the body. A greater metacentric radius indicates a higher stability, while a smaller metacentric radius indicates a lower stability.
The metacentric radius can be calculated using various methods, including experimental measurements or theoretical calculations based on the geometry and mass distribution of the body. It is an important parameter in naval architecture and ship design, as it helps engineers ensure the stability and safety of ships and other floating structures.
In conclusion, option A correctly defines the metacentric radius as the distance between the center of gravity and the metacentre of a floating body. This parameter plays a crucial role in determining the stability of the body and is widely used in the field of naval architecture.
The metacentric radius is a parameter used to evaluate the stability of a floating body. It is defined as the distance between the center of gravity (G) of the body and the metacentre (M). The metacentre is the intersection point of the vertical line passing through the center of buoyancy (B) and the line of action of the buoyant force when the body is inclined.
Explanation of Option A
Option A states that the metacentric radius is the distance between the center of gravity and the metacentre. This statement is correct and accurately defines the metacentric radius. Let's understand why.
When a body is floating in a fluid, it experiences two opposing forces: the weight of the body acting downward and the buoyant force acting upward. The buoyant force is equal to the weight of the fluid displaced by the body and acts through the center of buoyancy.
When the body is in equilibrium, these two forces should be aligned in the same vertical line. However, if the body is tilted or inclined, the buoyant force will no longer act through the center of gravity. Instead, it will create a moment about the center of gravity, causing the body to rotate. This rotation can be clockwise or counterclockwise depending on the direction of the inclination.
To analyze the stability of the floating body, we need to consider the position of the metacentre. The metacentre is located above the center of gravity, and its height determines the stability of the body. If the metacentre is higher, the body will have greater stability, and if it is lower, the body will be less stable.
Role of Metacentric Radius
The metacentric radius is a measure of the distance between the center of gravity and the metacentre. It quantifies the stability of the body. A greater metacentric radius indicates a higher stability, while a smaller metacentric radius indicates a lower stability.
The metacentric radius can be calculated using various methods, including experimental measurements or theoretical calculations based on the geometry and mass distribution of the body. It is an important parameter in naval architecture and ship design, as it helps engineers ensure the stability and safety of ships and other floating structures.
In conclusion, option A correctly defines the metacentric radius as the distance between the center of gravity and the metacentre of a floating body. This parameter plays a crucial role in determining the stability of the body and is widely used in the field of naval architecture.
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For floating bodies, how is the metacentric radius defined?a)The distance between centre of gravity and the metacentre.b)Second moment of area of plane of flotation about centroidal axisperpendicular to plane of rotation/immersed volume.c)The distance between centre of gravity and the centre of buoyancy.d)Moment of inertia of the body about its axis of rotation/immersedvolume.Correct answer is option 'A'. Can you explain this answer?
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For floating bodies, how is the metacentric radius defined?a)The distance between centre of gravity and the metacentre.b)Second moment of area of plane of flotation about centroidal axisperpendicular to plane of rotation/immersed volume.c)The distance between centre of gravity and the centre of buoyancy.d)Moment of inertia of the body about its axis of rotation/immersedvolume.Correct answer is option 'A'. 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 For floating bodies, how is the metacentric radius defined?a)The distance between centre of gravity and the metacentre.b)Second moment of area of plane of flotation about centroidal axisperpendicular to plane of rotation/immersed volume.c)The distance between centre of gravity and the centre of buoyancy.d)Moment of inertia of the body about its axis of rotation/immersedvolume.Correct answer is option 'A'. 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 For floating bodies, how is the metacentric radius defined?a)The distance between centre of gravity and the metacentre.b)Second moment of area of plane of flotation about centroidal axisperpendicular to plane of rotation/immersed volume.c)The distance between centre of gravity and the centre of buoyancy.d)Moment of inertia of the body about its axis of rotation/immersedvolume.Correct answer is option 'A'. Can you explain this answer?.
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