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Q3. The following particulars apply to a ship of 125 m length when floating in water of density 1025 kg/m³ at an even keel draught of 6.425 m.

Displacement = 10850 tonne

Centre of gravity above the keel (KG) = 6.69 m

Centre of buoyancy above the keel (KB) = 3.57 m

Water plane area = 1756 m²

Centre of floatation from midship (LCF) = 2.5 m aft

Second moment of area of the waterplane about a transverse axis through midships = 1.526  10 6 m⁴

(a) Calculate the moment to change trim by 1 cm (MCT 1 cm) (4)

(b) The ship in the above condition now undergoes the following changes of loading.

50 tonne added with its LCG 27.5 m forward of midships.

230 tonne removed with its LCG 2 m aft of midships

120 tonne moved 46 m aft.

Calculate EACH of the following for the new condition:

(i) The new end draughts of the ship; (9)

(ii) The longitudinal position at which a mass of 188 tonne should be added to restore the ship to an even keel draught. (3)