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Q2. A vessel of 10000 tonne displacement floats at a draught of 7.2 m in sea water of density 1025 kg/m³.

Further hydrostatic data for the above condition are:

centre of buoyancy above the keel (KB) = 3.844 m

transverse metacentre above the keel (KM) = 7.186 m

tonne per centimetre immersion (TPC) = 18

The vessel in the above condition is unstable and heels to an angle of 80. To restore positive stability, ballast Of 540 tonne is now loaded at a Kg of 0.5 m.

Calculate EACH Of the following for the final condition:

(a) the transverse metacentric height; (13)

(b) the righting moment when the vessel is heeled to an angle of 150.  (3)

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

GZ = sin θ (GM + ½ BM tan² θ)