Q59 / 270 · NDA 2026 (Phase 1) · General Ability
A floating body is in stable state. Which one of the following is correct?
- AThe centre of gravity of the body is above its centre of buoyancy.
- BThe centre of gravity of the body is below its centre of buoyancy.
- CThe centre of gravity of the body coincides with its centre of buoyancy.
- Correct answerDThe centre of gravity of the body is below the metacentre.
Solution
For a floating body, the condition for equilibrium and stability depends on the relative positions of its centre of gravity and its metacentre.
When a floating body is given a small angular displacement, its centre of buoyancy shifts. The point where the vertical line passing through the new centre of buoyancy intersects the original vertical axis is known as the metacentre.
For the body to be in a stable state, a restoring couple must act on it to bring it back to its original vertical position. This restoring couple is only produced if the metacentre lies above the centre of gravity.
Thus, for stable equilibrium of a floating body, its centre of gravity must be below the metacentre.
When a floating body is given a small angular displacement, its centre of buoyancy shifts. The point where the vertical line passing through the new centre of buoyancy intersects the original vertical axis is known as the metacentre.
For the body to be in a stable state, a restoring couple must act on it to bring it back to its original vertical position. This restoring couple is only produced if the metacentre lies above the centre of gravity.
Thus, for stable equilibrium of a floating body, its centre of gravity must be below the metacentre.
Hence, the correct answer is option: 'D'.