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Q2) A ship of 5000 tonne displacement floats at a mean draught of 7 m when 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) = 3.706 m

Height of transverse metacentre above the keel (KM)= 5.926 m

tonne per centimetre immersion (TPC) = 10.0

To achieve a satisfactory stable condition with a metacentric height of 400 mm, a load of 500 tonne is added to the ship on the centreline at a Kg of 2.5 m.

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

(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+1/2 BM tan² θ)