let's know about equilibrium of the ship, stable or tender ship, unstable ship or stiff ship

Equilibrium :
In the upright position, the weight of the ship acts vertically down through the centre of gravity G, while the upthrust acts through the centre of buoyancy B. Since the weight is equal to the upthrust, and the centre of gravity and the centre of buoyancy are in the same vertical line, the ship is in equilibrium.

Stable ship : 
When the ship is inclined by an external force to an angle theta, the centre of gravity remains in the same position but the centre of buoyancy moves from B to B1. The buoyancy, therefore, acts up through B1 while the weight still acts down through G, creating a moment of g x GZ which tends to return the ship to the upright. g x GZ is known as the righting moment and GZ the righting lever.
Since this moment tends to right the ship the vessel is said to be stable or tender ship.

Tender ship :
Small metacentric height GM, will have small Righting lever GZ, at any angle and will roll easily.
GM is said to be POSITIVE when G is lies below M
and vessel is stable.

Unstable ship :
If the centre of gravity lies above the transverse
metacenter the moment acts in the opposite direction, increasing the angle of heel. The vessel is then unstable and will not return to the upright, the metacentric height being regarded as negative.
Stiff ship :
Larger metacentric height GM , wil have large righting lever GZ, at any angle resistance to rolling.

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