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The conditions for the stable equilibrium of a floating body are:
- a)The meta-centre should lie above the centre of gravity
- b)The centre of buoyancy and the centre of gravity must lie on the same vertical line
- c)A restoring couple should be formed
- d)All the above are correct
Correct answer is option 'D'. Can you explain this answer?
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The conditions for the stable equilibrium of a floating body are:a)Th...
Condition of stable equilibrium for a floating body in terms of metacentric height (GM) as follows: 
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- Stable equilibrium : GM > 0 (M is above G)
- Neutral equilibrium : GM = 0 (M coinciding with G)
- Unstable equilibrium : GM < 0="" (m="" is="" below="" g)="" />
(a) Equilibrium Position (b)Tilted Position
Condition of stable equilibrium for a floating body in terms of centre of buoyancy and the centre of gravity:
- Stable equilibrium: If its centre of gravity is directly below the centre of buoyancy
- Neutral equilibrium: If its centre of gravity is coincident with the centre of buoyancy
- Unstable equilibrium: If its centre of gravity is directly above the centre of buoyancy
A submerged body is in equilibrium when the centre of gravity is located below the centre of buoyancy. If the body is tilted slightly in any direction, the buoyant force and the weight always produce a restoring couple trying to return the body to its original position.
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The conditions for the stable equilibrium of a floating body are:a)Th...
Conditions for the stable equilibrium of a floating body:
a) The meta-centre should lie above the centre of gravity:
The meta-centre is the point through which the vertical line passing through the centre of buoyancy always passes, regardless of the body's orientation. The centre of gravity is the point where the entire weight of the body acts vertically downwards. For a floating body to be in stable equilibrium, the meta-centre should be located above the centre of gravity. This ensures that any small disturbance or tilting of the body will create a restoring couple, which tends to bring the body back to its original position.
b) The centre of buoyancy and the centre of gravity must lie on the same vertical line:
The centre of buoyancy is the point through which the buoyant force, acting upwards, can be considered to act. It is the point of application of the resultant buoyant force. The centre of gravity, as mentioned earlier, is the point where the weight of the body acts vertically downwards. In order for a floating body to be in stable equilibrium, these two points must lie on the same vertical line. This ensures that the buoyant force and the weight of the body act in the same vertical line, maintaining the stability of the body.
c) A restoring couple should be formed:
A restoring couple is a couple (pair of equal and opposite forces) that tends to bring the body back to its original position when it is tilted or disturbed. In the case of a floating body, the difference in the positions of the meta-centre and the centre of gravity creates a restoring couple. This couple is formed due to the shift in the centre of buoyancy when the body tilts. The restoring couple ensures that any disturbance or tilting of the body is counteracted, bringing the body back to its stable equilibrium position.
Summary:
In summary, all the above conditions are correct for the stable equilibrium of a floating body. The meta-centre should be located above the centre of gravity, the centre of buoyancy and the centre of gravity must lie on the same vertical line, and a restoring couple should be formed. These conditions ensure that the body remains stable and returns to its original position when disturbed, maintaining its equilibrium.
a) The meta-centre should lie above the centre of gravity:
The meta-centre is the point through which the vertical line passing through the centre of buoyancy always passes, regardless of the body's orientation. The centre of gravity is the point where the entire weight of the body acts vertically downwards. For a floating body to be in stable equilibrium, the meta-centre should be located above the centre of gravity. This ensures that any small disturbance or tilting of the body will create a restoring couple, which tends to bring the body back to its original position.
b) The centre of buoyancy and the centre of gravity must lie on the same vertical line:
The centre of buoyancy is the point through which the buoyant force, acting upwards, can be considered to act. It is the point of application of the resultant buoyant force. The centre of gravity, as mentioned earlier, is the point where the weight of the body acts vertically downwards. In order for a floating body to be in stable equilibrium, these two points must lie on the same vertical line. This ensures that the buoyant force and the weight of the body act in the same vertical line, maintaining the stability of the body.
c) A restoring couple should be formed:
A restoring couple is a couple (pair of equal and opposite forces) that tends to bring the body back to its original position when it is tilted or disturbed. In the case of a floating body, the difference in the positions of the meta-centre and the centre of gravity creates a restoring couple. This couple is formed due to the shift in the centre of buoyancy when the body tilts. The restoring couple ensures that any disturbance or tilting of the body is counteracted, bringing the body back to its stable equilibrium position.
Summary:
In summary, all the above conditions are correct for the stable equilibrium of a floating body. The meta-centre should be located above the centre of gravity, the centre of buoyancy and the centre of gravity must lie on the same vertical line, and a restoring couple should be formed. These conditions ensure that the body remains stable and returns to its original position when disturbed, maintaining its equilibrium.
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The conditions for the stable equilibrium of a floating body are:a)The meta-centre should lie above the centre of gravityb)The centre of buoyancy and the centre of gravity must lie on the same vertical linec)A restoring couple should be formedd)All the above are correctCorrect answer is option 'D'. Can you explain this answer?
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The conditions for the stable equilibrium of a floating body are:a)The meta-centre should lie above the centre of gravityb)The centre of buoyancy and the centre of gravity must lie on the same vertical linec)A restoring couple should be formedd)All the above are correctCorrect answer is option 'D'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about The conditions for the stable equilibrium of a floating body are:a)The meta-centre should lie above the centre of gravityb)The centre of buoyancy and the centre of gravity must lie on the same vertical linec)A restoring couple should be formedd)All the above are correctCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The conditions for the stable equilibrium of a floating body are:a)The meta-centre should lie above the centre of gravityb)The centre of buoyancy and the centre of gravity must lie on the same vertical linec)A restoring couple should be formedd)All the above are correctCorrect answer is option 'D'. Can you explain this answer?.
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The conditions for the stable equilibrium of a floating body are:a)The meta-centre should lie above the centre of gravityb)The centre of buoyancy and the centre of gravity must lie on the same vertical linec)A restoring couple should be formedd)All the above are correctCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The conditions for the stable equilibrium of a floating body are:a)The meta-centre should lie above the centre of gravityb)The centre of buoyancy and the centre of gravity must lie on the same vertical linec)A restoring couple should be formedd)All the above are correctCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The conditions for the stable equilibrium of a floating body are:a)The meta-centre should lie above the centre of gravityb)The centre of buoyancy and the centre of gravity must lie on the same vertical linec)A restoring couple should be formedd)All the above are correctCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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