A wooden cube has sides of length 5 cm. It floats in water of density 1.0 g/cm3 with 3 cm of the cube below the surface, as shown. What is the density of th...
Question 1 Report
A wooden cube has sides of length 5 cm. It floats in water of density 1.0 g/cm3 with 3 cm of the cube below the surface, as shown.
What is the density of the wood?
Answer Details
This question tests the principle of flotation and density calculation. When an object floats, the weight of water displaced equals the weight of the object. The cube has sides of 5 cm, and 3 cm is submerged.
The volume of the whole cube is \( 5 \times 5 \times 5 = 125 \, \text{cm}^3 \). The submerged volume is \( 5 \times 5 \times 3 = 75 \, \text{cm}^3 \). Since the cube floats, the mass of the cube equals the mass of water displaced:
\[ m_{\text{cube}} = \rho_{\text{water}} \times V_{\text{submerged}} = 1.0 \times 75 = 75 \, \text{g} \]The density of the wood is:
\[ \rho = \frac{m}{V} = \frac{75}{125} = 0.6 \, \text{g/cm}^3 \]Alternatively, for a floating object, the fraction submerged equals the ratio of its density to the liquid's density: \( 3/5 = 0.6 \), giving 0.6 g/cm3 directly.
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