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    Mechanical Properties of Fluids
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    What will happen if the lower portion of a ship is made light so that centre of buoyancy lies below the centre of gravity of the ship?

    The ship will be in unstable equilibrium if the centre of buoyancy of the ship lies below the centre of gravity. If due to some sea disturbance, ship gets disturbed, the torque produced by weight of the ship and buoyant force will take the ship away from equilibrium position and ship will tumble down.
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    A burning candle is floating in the water. What happens to candle as it burns?
    Water exerts buoyant force to balance the weight of candle. Hence, the candle keep floating in the water. As the candle burns, the weight of the candle decreases and water has to exert less buoyant force. Thus the candle becomes less submerged and it rises. 
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    Wooden plank weighing 8kg floats in water with two-fifth of its volume floating in water. Find the maximum weight that can be placed over the plank so that it may float completely submerged.
    Let V be the volume of the plank.

    Given that two-fifth volume of plank is submerged in water.

    Therefore by law of floatation the weight of wooden plank is equal to the weight of   volume of water.

    That is, 

    Weight of  of water = 8 kg

     Weight of V volume of water=20kg.

    Therefore when wooden plank is fully submerged in water, it displaces 20 kg of water.

    Hence a 20 kg weight can be made to float over the water.

    Thus additional weight that can be put over the plank is (20 – 8)kg = 12 kg.
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    What is meta-center?
    A floating body which is in stable equilibrium, when disturbed from it's position it starts oscillating. The point about which the oscillations take place is called meta-center. Meta centre is the point where lines of action of force of buoyancy intersect. 
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    A cork of density 0.18gm/cc floats in liquid of density 1.44 gm/cc with 20cc of volume inside the liquid. Find the mass and volume of the cork.
    Given, 

    Density of the cork, σ = 0.18 gm/cc

    Density of liquid,ρ = 1.44 gm / cc

    Volume of liquid, V = 20 cc

    Now, according to the law of floatation,

    Weight of cork = Weight of liquid displaced by cork.

    Therefore mass of the cork is given by,

                  mg = Vρg                m =Vρ∴             m=20×1.44                     =28.8gm 

    Volume of the cork, Vc=mσ=28.80.18=160cc
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