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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 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?
Solution
Internal volume, V = 1 m3 = External volume of the ferry boat
Density of water, \[\rho_w\] = 103 kg/m3
As the weight of the boat is balanced by the buoyant force, we have:
\[\text{mg} = V_1 \times \rho_w \times g\]
\[ \Rightarrow 50 = V_1 \times {10}^3 \]
\[ \Rightarrow V_1 = \frac{5}{100} = 0 . 05 \text{ m}^3\]
(b) Let V2 be the volume of the boat filled with water before water starts coming in from the side.
\[\therefore \text {mg + V}_2 \rho_\text{w} \times \text{g = V} \times \rho_\text{w} \times g [\text{ V is the volume of the water displaced by the boat }. ]\]
\[ \Rightarrow 50 + V_2 \times {10}^3 = 1 \times {10}^3 \]
\[ \Rightarrow V_2 = \frac{{10}^3 - 50}{{10}^3}\]
\[ = \frac{950}{1000} = 0 . 95 \text{ m}^3 \]
Fraction of the boat's volume filled with water\[ = \frac{19}{20}\]
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