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A body floating in a liquid is said to be in neutral equilibrium, if its metacentre
  • a)
    coincides with its centre of gravity
  • b)
    lies above its centre of gravity
  • c)
    lies below its centre of gravity
  • d)
    lies between the centre of buoyancy and centre of gravity
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A body floating in a liquid is said to be in neutral equilibrium, if i...
Neutral equilibrium is a state in which a body is in equilibrium but can be easily displaced without any external force. In the case of a body floating in a liquid, neutral equilibrium occurs when the metacentre coincides with the centre of gravity.

Understanding the Metacentre and Centre of Gravity:
1. The centre of gravity (CG) of a body is the point at which the entire weight of the body can be considered to act vertically downwards.
2. The metacentre (M) is a point in the body where the line of action of the buoyant force intersects with the vertical line passing through the CG.

Conditions for Neutral Equilibrium:
In order for a body to be in neutral equilibrium, the following conditions must be met:

1. The metacentre must coincide with the centre of gravity:
When the metacentre and centre of gravity align, any slight tilt or displacement of the body will cause the buoyant force to pass through the CG, resulting in a purely vertical force. As a result, the body will not have any tendency to rotate and will remain in a state of neutral equilibrium.

Explanation of Other Options:
a) If the metacentre lies above the centre of gravity, the body will be in stable equilibrium. This means that when the body is slightly tilted, a restoring moment is created that brings the body back to its original position.
b) If the metacentre lies below the centre of gravity, the body will be in unstable equilibrium. In this case, any slight tilt of the body will result in a destabilizing moment, causing the body to further tilt.
d) If the metacentre lies between the centre of buoyancy and centre of gravity, the body will be in a state of unstable equilibrium. Similar to option b, any tilt of the body will result in an unstable situation.

Conclusion:
In conclusion, a body floating in a liquid is said to be in neutral equilibrium when its metacentre coincides with its centre of gravity. This alignment ensures that the body remains in a state of equilibrium but can be easily displaced without any external force.
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A body floating in a liquid is said to be in neutral equilibrium, if its metacentrea)coincides with its centre of gravityb)lies above its centre of gravityc)lies below its centre of gravityd)lies between the centre of buoyancy and centre of gravityCorrect answer is option 'A'. Can you explain this answer?
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