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For an immersed neutrally buoyant body to be in stable equilibrium, the center of gravity of the body is directly

  • A.above the metacenter.
  • B.below the metacenter.
  • C.above the center of buoyancy.
  • D.below the center of buoyancy.

Answer: D

The centre of gravity must be below the center of buoyancy.

For a fully immersed body the centre of buoyancy, the centroid of the displaced volume, stays fixed relative to the body as it tilts, so the metacentre coincides with it. A small tilt then creates a restoring couple only if the weight acts below the buoyant force, that is if G lies directly below B.

With G above B the couple overturns the body. The metacentre conditions (G below or above M) apply to floating bodies, whose waterplane area lets B shift as they heel.

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