Floating box

Classical Mechanics Level 2

A box with density $\rho = 800 \text{ kg/m}^3$ is floating face down on a fluid with density $\rho _{f} = 1200 \text{ kg/m}^{3}.$ If the box has a height of $H= 6.0 \text{ cm},$ by what depth $h$ is the box submerged?

The floating box is a rectangular parallelepiped.

4 \text{ cm}

2 \text{ cm}

3 \text{ cm}

5 \text{ cm}

1 solution

Sowmitra Das
Jul 20, 2014

Let, Cross-Sectional Area of the Box be $A$ .
$\therefore$ Volume of liquid displaced by box $=A\cdot h$
So, Weight of Displaced liquid $=\rho_f \cdot Ah\cdot g$ .
Again, Weight of the box $=\rho\cdot AH\cdot g$ .
$\therefore$ From Archimedes' Principle, we have,
$\displaystyle \rho_f \cdot Ah\cdot g=\rho\cdot AH\cdot g\Rightarrow h=\frac{\rho\cdot H}{\rho_f}=\boxed{4}$ cm.

Floating box

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