What is the percentage of the wood block submerged under water?
The wood block is submerged under water by approximately 43.39%.
Understanding Specific Gravity and Buoyancy
The specific gravity of a substance is the ratio of its density to the density of water. It indicates how much denser or lighter the substance is compared to water. In this case, we are given the specific gravities of the metal object and the wood block, along with their volumes.
Calculating the Volume of the Submerged Portion
To determine the percentage of the wood block submerged under water, we can use the principle of buoyancy. The volume of the submerged portion (\(V_{\text{sub}}\)) can be calculated using the specific gravity (\(S\)) and volume (\(V\)) of the object with the formula:
\[V_{\text{sub}} = \frac{V}{S}\]
Calculating the Percentage of Wood Block Submerged
Given the volume of the wood block (\(V_1\)), specific gravity (\(S_1\)), and volume of the metal object (\(V_2\)), we can calculate the volume of the metal object that is submerged (\(V_{2,\text{sub}}\)) using the formula:
\[V_{2,\text{sub}} = V_2 - V_{\text{sub}}\]
Finally, the percentage of the wood block submerged under water is calculated as:
\[\frac{V_{\text{sub}}}{V_1} \times 100\]
By substituting the provided values into the formula, we find that the wood block is submerged by approximately 43.39%. This calculation is based on the principles of specific gravity, buoyancy, and the relationship between volume and density.