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 ?
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(a) The volume of the boat immersed in water will be that volume of water which weight =50 kg. Since the density of water =1000 kg/m³, this volume will be =50/1000 m³ =1/20 m³.
Hence the fraction of the volume of the boat immersed in water =(1/20 m³)/(1 m³) =1/20.
(b) In the leak condition, when the outer water level comes to the top of the side of the boat, the total volume of water displaced is equal to the internal volume of the boat = 1m³. The force of buoyancy = weight of this water = 1000 kg.
This force balances the weight of the boat plus the weight of the water inside. If the weight of the water inside be X kg, then X+50 = 1000
→X =950 kg
Hence the volume of inside water =950/1000 m³ =0.950 m³
The inside water volume fraction =(0.950 m³)/(1 m³)
=19/20.
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