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?  

Answer 1

Given: 

Mass of the ferryboat, m = 50 kg
Internal volume, V = 1 m³ = External volume of the ferry boat
Density of water, \[\rho_w\]  = 10³ kg/m^​3

(a) Let V₁ be the volume of the boat inside the water. It is equal to the volume of the water displaced in 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\[ = \frac{19}{20}\]