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For a floating body to remain in stable equilibrium, where should its centre of buoyancy be located relative to its centre of gravity?

1. vertically below its centre of gravity
2. horizontally in line with its centre of gravity
3. vertically above its centre of gravity
4. it can be located anywhere

Correct answer: vertically above its centre of gravity

Solution

When a floating body is tilted, the centre of buoyancy shifts. For stable equilibrium the resulting couple must restore the body. This happens when the centre of buoyancy lies above the centre of gravity, so the buoyant force and weight form a restoring couple (equivalently, the metacentre lies above the centre of gravity).

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