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I know the basic law of flotation for a body in a fluid , but when it is subjected to a constant force at any point of the body along which point the moment will be created ?

I have a confusion between C.O.G. , C.O.B. and meta center.

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Let's look over some of the important "centres":

  • An object can geometrically be "averaged" down to it's centre of mass (COM), if we need to work with it as a point-particle.
  • Gravity "averages" down to the centre of gravity (COG) of the object

At the surface of the Earth within a height and depth of a few tens of kilometres, and elsewhere where $g$ can be considered constant, the COG equals the COM.

  • The buoyancy force "averages" down to the centre of gravity of the displaced fluid. We call that the centre of buoyancy (COB).

So, to work with buoyancy, find the COM of the volume that is displaced as if it was still made up of the fluid. This is the COB. See this explanation for more.

  • The metacentre is the point on a floating ship's symmetry axis (or just on the vertical axis through the object when it is in equilibrium) that is right above the COB.

This metacentre point indicates the stability of the ship. If the metacenter is below the COG, the ship will want to capsize (both torques cause same tilting); if above, the ship will want to tilt back towards equilibrium (torques cause opposite tilts). See this explanation for more.

Note that a metacentre naturally only makes sense for a floating object, and not a submerged one.

Also note that you don't really need the metacentre to know the stability. How far horizontally the COB is from the COG tells the same thing. But a metacentre may be a more convenient measure, which is based on the object itself.

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  • $\begingroup$ Yes I understand the concepts of these centres. So what is the answer of my 1st question about the point along which the moment will act ? Is it the meta centre? $\endgroup$ Commented Jul 7, 2018 at 13:30

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