Question

A ferry boat has internal volume 1 $m^3$ 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

m = 50 kg

V = 1 $m^3$

= internal volume

=external volume of the boat

(a) Let $V_1\to$ volume of boat inside water
= volume of water displaced in $m^3$.
Since, weight of the boat is balanced by the buyoyant force,

$\Rightarrow mg=V_1\times {\rho }_w\times g$

$\Rightarrow 50=V_1\times {10}^3$

$\Rightarrow v_1=\frac{5}{100}=0.05m^3$

(b) Let $v_1\to$ volume of boat filled with water before water starts coming in from the side.

$\therefore mg+v^1{\rho }_w\times g=V\times {\rho }_w\times g$

[Boat must have displaced v amount of water]

$\Rightarrow 50+v^1\times {10}^3=1\times {10}^3$

$\Rightarrow v^1=\frac{{10}^3-50}{{10}^3}$

= $\frac{950}{1000}=0.95m^3$

$\Rightarrow$ Fraction of volume = $\frac{19}{20}$