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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?
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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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