# Stability 1 – Chapter 7 Final KG

**A ship of displacement 2000t and KG 4.2m, loads 300t 0f cargo (KG 2.0m ), 200t of cargo (KG 3.2m) and 500t of bunkers ( KG 0m ). Find her final KG.**

**Solution:**

**Solution:**

Ship’s weight | KG | VM |

2000t (load) | 4.2m | 3400 tm |

300t (load) | 2.0m | (+) 600 tm |

200t (load) | 3.2m | (+) 640 tm |

500t (load ) | 1.0 m | (+)500 tm |

**Final W = 300t ****Final VM = 10140 tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = 10140 / 3000****= 3.38m**

**A ship of displacement 3000t and KG 3.9m, loads cargo and follows :- 200t in N0.1 LH ( KG 3.0m )300t on the deck ( KG 6.4m ), 150t and NO.3 TD (KG 5.2m ) and 350t in NO.4 LH (KG 4.0m ). Find the final KG .**

**Solution:**

**Solution:**

Ship’s weight | KG | VM |

3000 t | 3.9m | 11700tm |

200t (load) | 3.0m | (+) 600tm |

300t | 6.4m | (+) 1920tm |

150t | 5.2m | (+) 780tm |

350t | 4m | (+)1400tm |

**Final W = 4000 t ****Final VM = 16400 tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = (16400/4000)****= 4.1m**

**A ship of load displacement 10,000 t, KG 6.0m, discharge cargo of 250t ( KG 3.0m ) and 150t ( KG 4.0m). Find her final KG.**

**Solution :**

**Solution :**

Ship’s weight | KG | VM |

10000t | 6.0m | 60000 tm |

(-) 250t (discharge) | 3.0m | (-) 750 tm |

(-) 150t (discharge) | 4.0m | (-) 600 tm |

**Final W = 9600t ****Final VM = 58650 tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = (58650 / 9600)****= 6.109m.**

**Ship of 2000t displacement of KG 3.66m , loads 1500t( KG5.5m ) 3500t (KG 4.60m ), and takes 1520t of bunkers (KG 0.60m ). She discharge 2000t cargo ( KG 2.44m ). and consume 900t of bunkers ( KG 0.40m ). Find the KG at the and of the voyage.**

**Solution :**

**Solution :**

Ship’s weight | KG | VM |

2000t | 3.66m | 7320tm |

1500t(load) | 5.5m | (+)8250tm |

3500t (load) | 4.60m | (+)16100tm |

1520t ( load) | 0.60m | (+)912tm |

2000t ( discharge) | 2.44m | (-) 4880tm |

900t (discharge) | 0.40m | (-)360tm |

**Final W = 5620t ****Final VM = 27342tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = (27342) / (5620)****= 4.865m**

**A ship of 3200t displacement KG 6.2m , loads 5200t of cargo (KG 4.8 ). Find the amount of deck cargo (KG 10.2m ) that can be loaded so that the KG shall be 6.0m when loading is completed .**

**Solution:**

**Solution:**

Ship’s weight | KG | VM |

3200t | 6.2m | 19840tm |

(+) 5200t (load) | 4.8m | (+)24960 tm |

(+) X t | 10m | (+) 10X tm |

**Final W = (8400 + X )t ****Final VM =(44800 +10X);**

**We know that:-**

**Final KG = (Final VM) / (Final W)****6 = (44800 + 10X )/( 8400 + X)****6 (8400 + X ) = ( 44800 +10X)****(50400 + 6X ) = (10X + 44800)****( 10X – 6X) = (50400 – 44800)****4X = 5600****X = 1400t**

**Hence , amount of deck cargo to be loaded to get required KG is 1400 t**

**A ship 0f 2600t displacement , KG 4.88m, loads of 4600 t of homogeneous cargo (KG 5.0m ). Find how much deck cargo (KG 10m ) may be loaded to obtain a final KG of 5.11m.**

**Solution:**

**Solution:**

Ship’s weight | KG | VM |

2600t | 4.88m | 12688 tm |

4600t (load) | 5.0m | 23000 tm |

X t (load) | 10m | 10X tm |

**Final W = (7200 + X) t ****Final VM =(35688 + 10X) tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****5.11 = (35688 + 10X )/( 7200 + X )****5.11( 7200 + X) = (35688 + 10X)****(36792 + 5.11X ) = (35688 +10X)****(36792 – 35688) = (10X – 5.11X )****X = 1104 / 4.89****X =225.766t.**

**Hence amount of deck cargo added to get desired KG is 225.76 t.**

**A heavy-lift derrick is used to discharge a 100t package from a ship of displacement 8000t kg 8.2m . If the KG of the weight while on board is 3m and if the derrick head is 25m above the keel , find the kg of the ship (a) while discharging and( b ) after discharging**

**Solution :**

CASE 1

Ship’s weight | KG | VM |

8000t | 8.2m | 65600tm |

100t ( while disch) | (25 -3m) | (+)2200tm |

**Final W = 8000t ****Final VM = 67800t**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = ( 67800/8000)****= 8.475m**

Case – 2

Ship’s weight | KG | VM |

8000t | 8.2m | 65600tm |

(-)100t | 3m | (-)300tm |

**Final W = 7900t ****Final VM = 65300tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = (65300/7900)****= 8.266m**

**On a ship of 15000t displacement kg 7.9m , a weight of 200t is loaded on the UD (KG 12m ) above the Find the KG of the ship (a) while loading , and (b) After loading .**

**Solution :**

**Solution :**

Case – 1

Ship’s weight | KG | VM |

15000t | 7.9m | 118500tm |

(+) 200t (while loading) | 30m | (+) 6000tm |

**Final W = 15200T ****Final VM = 124500tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = (124500/15200)****= 8.190m**

Case – 2

Ship’s weight | KG | VM |

15000t | 7.9m | 118500tm |

(+ )200t (loaded) | 12m | +2400tm |

**Final W = 15200 ****Final VM = 120900 tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = (120900/15200)****=7.954m.**

**On a ship of 11000 t displacement KG7.2m a shore crane is used to shift a heavy-lift from the UD (KG 12m to the LH (KG 3m ) . Find the kg of the ship (a) during shifting is (b) after shifting .**

**Solution :**

**Solution :**

Case -1

Ship’s weight | KG | VM |

11000t | 7.2m | 79200tm |

(-)180t (while shifting) | 12m | (-)2160tm |

**Final W = 10820t ****Final VM = 77040 tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = 77040 / 10820****= 7.120m**

Case – 2

Ship’s weight | KG | VM |

11000t | 7.2m | 79200tm |

180t (After shift) | (12-3)m | (-)1620tm |

**Final W = 11000 ****Final VM = 77580tm**

**We know that:-**

**Final KG = (Final VM) / (Final W)****Final KG = (77580/11000)****= 7.053m.**