A body floating in a liquid is said to be in neutral equilibrium, if its metacentre
- Acoincides with the centre of gravity.Correct
- Blies above the centre of gravity.
- Clies below the centre of gravity.
- Dlies between the centre of buoyancy and centre of gravity.
Solution
Concept
When a floating body tilts slightly, its stability depends on the position of the metacentre relative to the centre of gravity. For neutral equilibrium, the metacentre coincides with the centre of gravity.
Step-by-step solution
1. Understand the types of equilibrium for a floating body: stable, unstable, and neutral equilibrium. 2. In a stable equilibrium, the metacentre lies above the centre of gravity, so it creates a restoring couple. 3. In an unstable equilibrium, the metacentre lies below the centre of gravity, so it creates an overturning couple. 4. In a neutral equilibrium, the metacentre coincides with the centre of gravity, meaning the body stays in any new position without any restoring or overturning couple. Answer: (A) coincides with the centre of gravity.
Explanation
A floating body is in neutral equilibrium when any small tilt does not create a restoring or overturning moment. This happens when the metacentre (the point about which the body oscillates) exactly coincides with the centre of gravity of the body.
Why the other options are wrong
B: This represents stable equilibrium. C: This represents unstable equilibrium. D: This position does not define neutral equilibrium.
Shortcut
Stable = M above G; Unstable = M below G; Neutral = M coincides with G.
Common mistake
Confusing neutral equilibrium with unstable equilibrium where M lies below G.
Correct answer: A) coincides with the centre of gravity.