WBCS Preliminary Examination 2023 — General Studies · Question 135 of 200

Answer: (B) Above the centre of gravity

The centre of buoyancy is the centre of gravity of the displaced liquid, the point through which the upthrust acts. PSC's answer is that it should be above the centre of gravity, so that a tilt produces a restoring couple; this is exactly true for a fully submerged body such as a submarine or a balloon. For a body floating partly immersed, such as a ship, the precise condition is that the metacentre must lie above the centre of gravity; if the two coincide the equilibrium is neutral, and if the metacentre is below, the body capsizes. Related laws: Archimedes' principle and the law of flotation (a floating body displaces its own weight of liquid). OFFICIAL ANSWER IS A SIMPLIFICATION. PSC's keys give (B) 'Above the centre of gravity', retained as correct_answer. Strictly this holds for fully submerged bodies; for a partly immersed floating body the stability condition is that the metacentre (not the centre of buoyancy) lies above the centre of gravity. Ships are stable with the centre of buoyancy below the centre of gravity.