Question

Three blocks $\text{A, B,}$ and $\text{C}$ each of $1\text{kg}$ mass and having relative densities $2.5,5,$and$0.5$ respectively, are completely immersed in a tank of water individually. Find the block that displaces the maximum volume of water. Also, find the volume of water displaced and the buoyant force acting on it.

• A. $\text{A}$ displaces $400\text{cc}$, ${\text{F}}_B\approx 40\text{N}$
• B. $\text{B}$ displaces $400\text{cc}$, ${\text{F}}_B\approx 20\text{N}$
• C. $\text{C}$ displaces $2000\text{cc}$, ${\text{F}}_B\approx 20\text{N}$
• D. $\text{A}$ displaces $2000\text{cc}$, ${\text{F}}_B\approx 2\text{N}$

Answer 1

The correct option is C $\text{C}$ displaces $2000\text{cc}$, ${\text{F}}_B\approx 20\text{N}$

Since it is given that all the blocks are completely immersed in the water tank, the block with the largest volume will displace the most amount of water.

Since density of water is 1 g/cc, the densities of the objects are the same as their relative densities.

${\text{V}}_{\text{A}}=\frac{{\text{m}}_{\text{A}}}{{\text{d}}_{\text{A}}}=\frac{1000}{2.5}=400\text{cc}$

${\text{V}}_{\text{B}}=\frac{{\text{m}}_{\text{B}}}{{\text{d}}_{\text{B}}}=\frac{1000}{5}=200\text{cc}$

${\text{V}}_{\text{C}}=\frac{{\text{m}}_{\text{C}}}{{\text{d}}_{\text{C}}}=\frac{1000}{0.5}=2000\text{cc}$

Therefore, $\text{C}$ displaces the maximum volume of water.
${\text{V}}_{\text{disp, max}}=2000\text{cc}$

Force of buoyancy acting on $\text{C}$,
${\text{F}}_{\text{B}}={\text{V}}_{\text{liq,disp}}\times {\text{d}}_{\text{liq}}=2000\times 1$
$=2000\text{g}\approx 20\text{N}$
$\Rightarrow {\text{F}}_B\approx 20\text{N}$