A floating body is in stable state. Which one of the following is correct?
- A.The centre of gravity of the body is above its centre of buoyancy.
- B.The centre of gravity of the body is below its centre of buoyancy.
- C.The centre of gravity of the body coincides with its centre of buoyancy.
- D.The centre of gravity of the body is below the metacentre.
Correct answer
Explanation
The correct answer is D, The centre of gravity of the body is below the metacentre. A floating body is stable only when its metacentre lies above its centre of gravity.
When a floating body tilts slightly, its centre of buoyancy, the centre of the displaced liquid, shifts to one side. The vertical line through the new centre of buoyancy cuts the central axis of the body at the metacentre. If the metacentre is above the centre of gravity, the weight and the buoyant force form a couple that turns the body back upright. If it is below, the couple tips the body further over. The distance between the two points is the metacentric height, which ship designers always keep positive.
A is wrong: many stable ships have their centre of gravity above the centre of buoyancy, so this alone does not describe stability.
B is wrong: a low centre of gravity helps, but it is not the condition that defines stable floating.
C is wrong: the two points need not coincide, and in a floating body they usually do not.
Exam tip: stable when the metacentre is above G, unstable when below, neutral when they coincide.
Practice Questions
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