A wooden block of volume 0.002 m³ and density 600 kg/m³ floats in water. Find the volume of the submerged part — Physics problems | PhysLabo
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Volume of the submerged part of the block

Medium 9 grade Mechanics / Hydrostatics

A wooden block of volume $V = 0.002$ m³ and density $\rho = 600$ kg/m³ floats in water. Find the volume of the submerged part of the block. The density of water is $\rho_{\text{water}} = 1000$ kg/m³.

Given
  • $V = 0.002$ m³
  • $\rho = 600$ kg/m³
  • $\rho_{\text{water}} = 1000$ kg/m³
  • $V_{\text{sub}} = ?$
Visual demonstration
Hints
Hint 1 / 2
For a floating body the buoyant force equals the weight of the body, so only part of the body displaces water.
Hint 2 / 2
The ratio of the submerged volume to the total volume equals the ratio of the body's density to the density of water.
Solution

For a floating body the buoyant force equals the weight of the body (the floating condition):

$$\rho_{\text{water}} g V_{\text{sub}} = \rho_{\text{body}} g V$$

$$V_{\text{sub}} = \frac{\rho_{\text{body}} V}{\rho_{\text{water}}} = \frac{600 \cdot 0.002}{1000} = 1.2 \cdot 10^{-3} \text{ m}^3$$

$$V_{\text{sub}} = 0.0012 \text{ m}^3$$

Answer

$V_{\text{sub}} = 0.0012$ m³