Buoyancy & Floatation in points :
1 The upward force exerted by a liquid on a body when the body is immersed in the liquid is known as buoyancy or force of buoyancy.
2 The point through which force of buoyancy is supposed to act is called center of buoyancy.
3 The point about which a body starts oscillating when the body is tilted is known as metacenter.
4 The distance between the metacenter and center of gravity is known as metacentric height.
5 The metacentric height GM is given by :
\[GM = \frac{I}{V}  BG\]
where :
I : moment of inertia of the floating body (in plan) at water surface about the axis YY
V : volume of the body submerged in water
BG : distance between center of gravity and center of buoyancy
6 Conditions of equilibrium of a floating body are :

 Stable equilibrium occurs for a floating body when M is above G

 Unstable equilibrium occurs for a floating body when M is below G
 Neutral equilibrium occurs for a floating body when M and G coincide
7 Conditions of equilibrium of a submerged body :

 Stable equilibrium occurs for a submerged body when B is above G

 Unstable equilibrium occurs for a submerged body when B is below G
 Neutral equilibrium occurs for a submerged body when B and G coincide
8 The value of metacentric height GM experimentally is given by :
\[GM = \frac{{{w_1} \times x}}{{W \times \tan \theta }}\]
where :
w_{1} : movable weight
x : distance through which w_{1} is moved
W : weight of the ship or floating body including w_{1}
θ : angle through the ship or floating body is tilted due to the movement of w_{1}
9 The time period of oscillation or rolling of a floating body is given by :
\[T = 2\pi \sqrt {\frac{{{K^2}}}{{GM \times g}}} \]
where :
K : radius of gyration
GM : metacentric height
T : time of one complete oscillation
You can also check other Fluid Mechanics Highlights on the following links :
Fluid Mechanics  Fluid Properties Highlights
Fluid Mechanics  Fluid Statics Highlights
Fluid Mechanics  Hydrostatic Forces on Surfaces Highlights
Fluid Mechanics  Fluid Kinematics Highlights
Fluid Mechanics  Dynamics of Fluid Flow Highlights
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