A boat of length 5 m and breadth 2 m is floating on a lake. A man weighing 110 kg gets on it. How much does the boat sink in the water if the density of water is 1000 kg/m³?

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Solution

Length of the boat = 5 m
Breadth of the boat = 2 m
Let the height by which the boat sinks in water be x m.
Density of water = 1000 kg/m³
Weight of man = 110 kg
From Archemedes principle, the weight of the person is balanced by buoyancy force. This buoyancy force is the weight of the water displaced.
Weight of man = buoyancy force
mg = Vρg
or, m = Vρ
∴ 110 kg = (5×2×x) m³ ×1000 kg/m³
⇒ x =110/(5×2×1000)=0.011
So, the boat sinks in water by 0.011 m = 1.1 cm

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