Equilibrium Stability of Floating Bodies : Buoyant Force

Equilibrium Stability of Floating Bodies

Buoyant Force:

It is the upward force or thrust exerted by a liquid on the body when the body is immersed in the liquid.The tendency of a liquid to uplift an immersed body is known as buoyancy.

Archimedes’s Principle

When a body immersed wholly or partially in a liquid, it is lifted up by a force equal to the weight of liquid displaced by the body.

The point through which the buoyant force is supposed to act, is known as the centre of buoyancy.If the force of buoyancy is more than the weight of liquid displaced, then the body will float. If the force of buoyancy is less than the weight of liquid displaced then the body will sink.

The equilibrium of bodies is of the following types:

i)                    Stable Equilibrium

ii)                   Unstable Equilibrium

iii)                 Neutral Equilibrium

Meta Centre

The point about which a floating body starts oscillating, when a small angular displacement is given is called meta-centre and it is denoted by M.

The distance between meta-centre (M) and centre of gravity (G) of floating body is known as meta-centre height. That is denoted by GM ;

And mathematically

GM = I/V -BG

 

Where, I = MOI of the sectional area of floating body at the water surface

              V = Volume of submerged body

              BG = Distance between the centre of buoyancy (B) and the centre of gravity (G)

 

Conditions of Equilibrium

The meta-centric height (GM) is experimentally given by:

 

GM = 

 

Where, w= Movable weight

X= distance through which w is moved

W= Weight of floating body including w

q= Angle through which floating body is tilted

The time period of oscillation (T) of a floating body is given by;

T= 2p

 

Where, k= Radius of gyration of floating body about its centre of gravity.

GM= Meta-Centric height