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

(a) The fraction of the volume of the boat immersed in water is $0.05 \mathrm{m}^{3}$

(b) At $\frac{19}{20} m^{3}$ of the boat's volume will be filled with water before water starts coming in from the sides

Explanation:

(a) Given,

mass of body =$50 \mathrm{Kg}$

volume of boat= $1 m^{3}$

we know that if body is floating or immersed in a liquid then

weight of the body = buoyant force

weight of body is acting downward and buoyant force is acting in upward direction

$m g=\rho V g$

g cancel out from both sides and by cross multiplication we get

$\mathrm{V}=\frac{m}{\rho}$

$\mathrm{v}=0.05 \mathrm{m}^{3}$

(b) Remaining volume=total boat volume – volume immersed in water

$\mathrm{V}_{\mathrm{m}}^{\prime}=1-\frac{1}{20}$

after this volume water starts coming out.