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If a floating body is given a small angular displacement and after the removal of that Force or moment, body comes back to its original position. It is called as Stable Equilibrium.

For stable equilibrium of a floating body, the metacentre M must be above the centre of gravity G.

In order to sustain stability, the Metacentric ht of any floating body must be positive.Greater the positivity of the metacentric height of a body, the greater stability it is able to attain. Also the center of gravity should be as minimum as possible.

The conditions for stable equilibrium differs in case of submerged and floating bodies.It becomes more complicated when floating bodies are considered. Now as the body rotates responding to any disturbance the center of buoyancy can shift. This could render the body stable even though the center of gravity is above the center of buoyancy.

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Umama's first paragraph is exactly correct, and indeed, this defines the general idea of stability for all systems.

All readers will be familiar with the idea that the weight, the force of gravity, acts through the center of mass of the vessel.

There is a point called the center of bouyancy that is the effective location of all the bouyant forces acting on the hull (bouyant forces are pressure forces). The net bouyant force acts upward at the center of bouyancy. The center of bouyancy is located below the waterline.

Thus we have two vertical forces acting on the hull: (1) the weight force acting downward at the CG, and (2) the bouyant force acting upward at the center of bouyancy. The question becomes "Does this force pair tend to restore the hull to an upright position, or does it tend to tip it further toward capsize?"

The metacentre, that Umama mentioned, is the intersection of the (vertical) bouyant force with the inclined center plane of the hull. As Umama mentioned, the condition for stability is that the metacentre must be above the CG for stability. If the metacentre is above the CG, the two forces combine to give a righting moment (a moment tending to restore the hull to normal floating position). If the metacentre is below the CG, the two forces develop and overturning moment and stability is lost.

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Umama's first paragraph is exactly correct, and indeed, this defines the general idea of stability for all systems.

All readers will be familiar with the idea that the weight, the force of gravity, acts through the center of mass of the vessel.

There is a point called the center of bouyancy that is the effective location of all the bouyant forces acting on the hull (bouyant forces are pressure forces). The net bouyant force acts upward at the center of bouyancy. The center of bouyancy is located below the waterline.

Thus we have two vertical forces acting on the hull: (1) the weight force acting downward at the CG, and (2) the bouyant force acting upward at the center of bouyancy. The question becomes "Does this force pair tend to restore the hull to an upright position, or does it tend to tip it further toward capsize?"

The metacentre, that Umama mentioned, is the intersection of the (vertical) bouyant force with the inclined center plane of the hull. As Umama mentioned, the condition for stability is that the metacentre must be above the CG for stability. If the metacentre is above the CG, the two forces combine to give a righting moment (a moment tending to restore the hull to normal floating position). If the metacentre is below the CG, the two forces develop and overturning moment and stability is lost.

what will be the condition of a ping pong ball floating on water when given a smaller angular displacement and why

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On 2015/1/26 at 7:14 PM, Goutam Kumar Das said:

what will be the condition of a ping pong ball floating on water when given a smaller angular displacement and why

I think it is called neutral equilibrium, as the CG and CB are not shifting when the ball is rolling or trimming. Therefore the ball will stop rolling due to the fluid friction but not the righting moment.

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