Stability of floating bodies :

NOTES:

1.      Center of gravity (G): It is the point at which all the weight of the body (Ws) acts towards the center of earth.

Center of buoyancy (B): It is the center of gravity of  the displaced liquid. It acts vertically upwards.

Meta-center (M): It is the point of intersection of the  line of action of the buoyant force (Fb) and the midline of the ship.

Forces acting on the ship:

The weight of the ship (Ws) :   acts downwards through its center of gravity (G) .

2-  Buoyant force (Fb) :     acts upwards through the center of buoyancy (B).

* Stable case of the ship:

When the ship is tilted by a small angle, falls above (G) & the couple { due to the two equal and opposite forces ( Fb & Ws ) } acts in the opposite direction  of ship inclination, so it tends to restore the ship to its original position .

* Unstable case of the ship:

When the ship is tilted by a large angle, the meta-center (M) falls below, the couple acts in the same direction of the ship inclination and the ship becomes unstable.

* Condition for stability:

1.The meta-center (M) must be above the center of gravity.

2.The direction of the couple opposes the direction of the inclination.

3.The arm of the couple must be small to return the ship  steadily.        

N.B

When the center of gravity & meta-centric coincide there is no couple on the ship which will remain inclined.

The ship is then said to be in Natural equilibrium.

Q: Why the meta-center of the ship should lie above the center of gravity to attain stable equilibrium?
A:  Because when the ship is tilted, the couple of the weight & Fb will be small & will return the ship to its original position by easily rolling & comfortable.