Question

A boat floating in fresh water (density $1000kg/m^3$) displaces water weighing $35.2kN$. The change in volume of the displaced water if it were floating in sea water of density $1.1\times {10}^{3}kg/m^3$ will be (take $g=10m/s^2$):

• A. $32m^3$
• B. $35.2m^3$
• C. $3.2m^3$
• D. $0.32m^3$

Answer 1

Answer: (D)

$0.32m^3$

Let mass of boat = $M$

When boat is floating in fresh water -

$Mg$ = Weight of displaced water = $35.2\times {10}^3$

Mass of water displaced $m=\frac{35.2\times {10}^3}{g}$ $=\frac{35.2\times {10}^3}{10}=$ $3520kg$

So volume displaced of fresh water $V_w=\frac{m}{{\rho }_w}=\frac{3520}{1000}=3.52m^3$

Now when the boat is floating in sea water-

$35200={\rho }_s{V}_{s}g$ , where ${\rho }_s$ and $V_s$ are density and volume of displaced water of sea respectively

Volume displaced of sea water $V_s=\frac{35200}{1100\times g}=3.2m^3$

So change in volume = $3.52-3.20=0.32m^3$