# Stability 1 – Chapter 6 Centre of Gravity

**In a vessel of 8800 tonnes displacement and KG 6.2m, 200 tonnes of cargo was loaded in the lower hold 1.7m above the keel. Find the final KG.**

**Solution:**

**Solution:**

**Given:-**

**Weight = 8800t,****Original KG =6.2m,****Cargo loaded = 200t,****KG = 1.7m**

Ship’s weight | KG | VM |

8800 t | 6.2m | 54560tm |

(+) 200 load | 1.7m | Final VM 54900 tm |

**Final W – 9000 t Final VM 54900 tm**

**So, we can calculate**

**Final KG = (Final VM/ Final W)****Final KG = (54900 / 9000)****= 6.1m**

**Here ‘VM’ stands for vertical moments.**

**600 tonnes of cargo were discharged from a vessel from the upper 11m above the keel. In the original KG displacement were 6m and 12600 tonnes, calculate the KG.**

**Solution:-**

**Solution:-**

**Given:-****Weight =12600 t****Original KG =6m****Cargo discharged = 600 t,**

**Cargo discharge 11 m above the keel**

Ship’s weight | KG | VM |

12,600t | 6m | 75,600tm |

( -) 600t ( discharge) | 11m | (-) 6600tm |

**Final Weight =12000 t Final VM =69000tm**

**We know that :**

**Final KG = (Final VM / Final Weight)**

**Final KG = ( 69,000 / 12000)**

**= 5.75m**

**In a vessel of 9900 tonnes displacement and KG 4m, a heavy lift of 100 tonnes is loaded on the UD (KG 15m ). Find the final KG.**

**Solution:**

**Solution:**

Ship’s weight | KG | VM |

12,600t | 4m | 39,600tm |

(+)100 t load | 15m | ( +)1500tm |

**Final W 10000t Final VM =41000tm**

**We know that:**

**Final KG = (Final VM / Final Weight)****Final KG = ( 41000 / 10000 )****= 4.11m.**

**500 tonnes of cargo of discharge from the lower the lower hold (KG 3m ) of a vessel whose displacement and KG before discharging were 11500 tonnes and 6.3m . Find the final KG.**

**Solution:**

**Solution:**

**Given:-**

**Weight = 11500t****Initial KG = 6.3m****Cargo discharged = 500t, KG =3m**

Ship’s weight | KG | VM |

11500t | 4m | 39,600tm |

(+)100 t load | 15m | ( +)1500tm |

**Final W =11000t Final VM =70950tm**

**We know that:**

**Final KG = (Final VM / Final Weight)****Final KG = (70,950/11000)****=6.45m**

**500 tonnes of cargo was shifted 15 meters vertically downwards in a vessel of 10000 tonnes displacement. Find the effect it has on the KG of the vessel and whether KG increases or decreases.**

**Solution:**

**Solution:**

**Given:-**

**Weight =10000t,****Cargo shifted downward =500t,**

**We know that:-**

**GG1() = (w x d)/( total weight)****= (500 x 15)/ 10000****=0.75m**

**Since, The weight is shifted vertically downward, the KG of ship will also go down parallel to the KG of the weight**

**Hence, KG of the ship decrease by 0.75m**

**In a vessel of 9000 tonnes displacement , KG 10.5m, 300 tonnes of cargo was shifted from the LH (KG 2.5m)to the UDC (KG 11.5m). Find the resultant KG of teh vessel.**

*Solution :*

*Solution :*

**Weight =9000 t****Original KG = 10.5m ,****Cargo shifted = 300 t**

**Vertical Distance of cargo shifted****= (height of UD – height of LH)****= (11.5 -2.5)****= 9m upwards.**

Ship’s weight | KG | VM |

9000t | 10.5m | 94500tm |

(+)300t | 9m | (+)2700tm |

**Final W = 9000 Final VM =200t**

**We know that :**

**Final KG = (Final VM / Final Weight)****Final KG = (97200 / 9,000)****= 10.8m.**

**In a vessel of 9009 tones displacement, KG 8.7m, how many tonnes of cargo can be loaded on the upper deck (KG 15m ) so that the final KG would be comes 9m.**

**Solution:-**

**Solution:-**

**Given:-****Weight = 9009 t,****Original KG =8.7m,**

**Let cargo loaded be X tonnes****Final KG =9m**

Ship’s weight | KG | VM |

9009 t | 8.7m | 94500tm |

(+) X t (load) | 15m | (+) (15 X) tm |

**Final W = (9009 + X) t Final VM =(78378.3 + 15X) tm**

**We know that:**

**Final KG = (Final VM / Final Weight)****Final KG = (78378.3 +15X ) /(9009 + X)****9.0 = (78378.3 + 15X)/ (9009+X)****9 x (9009+X) = (78378.3 + 15X)****(81081 + 9X) = (15X + 78378.3)****Hence, 6X = 78378 .3 – 81081****6X = 2702.7t****X = 450.45 t**