Q. 12

A ferry boat has internal volume 1 m3 and weight 50 kg. (a) Neglecting the thickness of the wood, find the fraction of the volume of the boat immersed in water. (b) If a leak develops in the bottom and water starts coming in, what fraction of the boat’s volume will be filled with water before water starts coming in from the sides?

Answer :

(a)The volume of boat immersed is equal to the weight of the boat. Here, the mass of the boat, . Let the volume of the boat be V and the density of water be .

Therefore, the buoyant force should be equal to the weight of the boat.





(b) If the water comes up from the sides, this would mean that the boat is completely immersed in water. The volume of the boat, , and


Therefore, buoyant force would be


This buoyant force is equal to the weight of the boat and the weight of water. Let the mass of water be “”.


Therefore,



The volume of water would be,


Fraction of water filled in the boat = (ANS)


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