Discussion
A solid body of uniform specific gravity floats in a deep liquid pool. Take \(B\), \(G\), and \(M\) as the centre of buoyancy, centre of gravity, and metacentre of the body, respectively.
Which one of the following options is correct for the stable floatation of the body in the pool when the body is given a small tilt angle?
Answer: A
\(\overline{MG}\) is the metacentric height and \(G\) should lie below \(M\).
When a floating body tilts slightly, the centre of buoyancy shifts and the buoyant force acts along a line that crosses the body's centre line at the metacentre M. The metacentric height is the distance GM from the centre of gravity to the metacentre.
If M is above G, the weight and buoyancy form a couple that rotates the body back upright: stable equilibrium. If M were below G, the couple would increase the tilt.
MB is the metacentric radius (\(I/V\)), not the metacentric height. Whether B lies above or below M does not decide stability; for most floating bodies B is below G and still stable, because what matters is the position of G relative to M.
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