*1 . A ship of 10000t displacement has a GM of 0.4m. Calculate the moment of statical stability when she is heeled by 5 degree.*

*1 . A ship of 10000t displacement has a GM of 0.4m. Calculate the moment of statical stability when she is heeled by 5 degree.*

*Solution:*

*Solution:*

*GZ =Righting lever, GM = Metacentric height*

*We know that Righting moment = (W x GZ )*

*Where, W = displacement for all of keel, M = Transverse meta centre.*

*Displacement (W) = 10000t, *

* GM = 0.4m, heel = 5degree*

*We know that *

*RM ( righting moment or moment of statical stability)*

*= (W x GM x sinθ) *

*= (10000 x 0.4 x sin 5 ^{0} )*

*= 348.62tm**A ship of 12000t displacement is heeled by 6 degree. If her righting lever is then 0.1m, find the moment of statical stability . If her KM is 8.2m , find her KG .*

*Solution :*

*Solution :*

*Displacement (W) = 12000t,*

* Heel = 6degree*

* GZ = 0.1m & KM = 8.2m*

*We know that :*

*GZ = GM sinθ,*

*0.1 = GM sin 6 ^{0}. *

*GM = (0.1 / sin 6*^{0})

*= 0.956m*

*KG = (KM – GM)*

*= (8.2 – 0.956)*

*= 7.44m**RM (righting moment or moment of statical stability)*

*= (W GM sinθ)*

*= (12000 x 0.956 x sin6 ^{0 })*

*= 1199.15 tm.**When a ship of 14000t displacement is heeled by 8 deegre , her moment of statical stability is 400tm . If KG 7.3m, find KM.*

*Solution :*

*Solution :*

*Displacement (W)= 14000t, *

*Heel = 8degree ,*

* RM = 400tm & KG 7.3m*

*We know that :*

*RM (Righting moment or moment of statical stability)*

* = (W x GM x sinθ) *

* 400 = (14000 x GM x sinθ) *

*GM = 400/ (1400 x sin8 ^{0 )}*

*GM = 2.053m**Now, KM = (KG + GM )*

*= (7.3 + 2.053 )*

*= 9.353m.*

*A ship of 8000t displacement has KB 3.5m, KM 6.5m, and KG 6m . Find her moment of statical stability at 20 degree heel, assuming that her deck edge remains above water (i.e. she is steel wall side at that angle of heel.*

*Solution :*

*Solution :*

*Displacement (W) = 8000t,*

*KB = 3.5m & KM = 6.5m ,*

*KG = 6m, heel= 20degree.*

*We can calculate:*

*GM = (KM – KG)*

*= (6.5 – 6)*

*= 0.5m *

*Since, GZ = Sinθ(GM + 1/2 BM tan ^{2}θ)*

*GZ = sin 20*^{0}(0.5 + 1/2 x 3 x tan^{2}20^{0})

*Again , GZ = 0.239 ,** RM (Righting moment or moment of statical stability)*

* = (W.GZ)*

* = 8000 x 0.239 = 1911.8 tm*

*A ship of 4000t displacement has KG 5.1 m, KB 2.1m, KM 5.5m . Find the moment of statical stability when she heels 24 degree , assuming that she is wall- side.*

*Solution :*

*Solution :*

*Displacement (W) = 4000t, *

*KG = 5.1m ,KB = 2.1m & KM = 5.5m, *

*Heel =24degree*

*Here we can calculate :*

*GM = (KM – KG)*

*= (5.5 – 5.1)*

*= 0.4m *

*Similarly, BM = ( KM – KB)*

*= (5.5 – 2.1)*

*= 3.4m*

*We know that RM can be calculated as :*

*RM (Righting moment or moment of statical stability)*

*= (W.GZ)*

*= W.sinθ ( GM + 1/2 BM tan ^{2}θ) *

*= 4000 x sin24*^{0}(0.4 + 1/2 x 3.4 x tan^{2}24^{0 ) }

*= 1200tm.*
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