Question

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 develops in the bottom and water starts coming in, what fraction of the boat’s volume will be filled with water before starts coming in from the sides?

Answer 1

a)  as the boat is floating on water surface,
      weight of water displaced = weight of boat
      1000 kg/m³ * volume of boat immersed in water = 50 kg
       volume of boat immersed in water = 0.05 m³
     percentage or fraction of boat immersed in water = 0.05 m³/ 1 m³ = 0.05 or 5%
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b)  there is a hole developed in the bottom of the boat.  So, water enters the boat.  Then the boat starts getting heavier. So the boat starts sinking in to water.  So the sides of the boat go down and touch the surface water level.

  At the time water starts entering from the sides, the volume of the boat that is immersed inside the water  = 1 m³ = total volume of boat.
  we neglected the thickness of wood. so internal volume = external volume.
         weight of 1 m³ of water = 1000 kg
   So weight of boat + water inside the boat = 1000 kg
       weight of water inside the ferry boat = 1000 kg - 50 kg = 950 kg
       volume of 950 kg of water = 0.95 m³

  So 95% or 0.95 of the volume of boat will be filled with water before water starts coming in from the sides.