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Q2. A ship of 4000 tonne displacement floats at a mean draught of 6 m in sea water of density 1025 kg/m³ but is unstable and has an angle of loll.

Hydrostatic particulars for the ship in the upright condition at the above displacement are as follows:

Centre of buoyancy above the keel (KB) = 3.225 m

Height of transverse metacentre above the keel (KM) = 5.865 m

Tonne per centimetre immersion (TPC) = 8.0

To achieve a satisfactory stable condition with a metacentric height of 350 mm, a load of 480 tonne at a Kg of 2.5 m is added to the ship on the centreline.

Calculate, for the original unstable condition, EACH of the following:

(a) the height of the original centre of gravity above the keel (KG); (12)

(b) the angle of loll. (4)

Note: The vessel may be considered ‘wall-sided’ between the limits of draught,

hence: GZ = sin θ (GM + ½ BM tan² θ)