A sample of granite has a density of 174.8 lb/ft3. If the density of water is 62.4 lb/ft3, what is the specific gravity of granite?
The Correct Answer and Explanation is:
Correct Answer:
The specific gravity of granite is:Specific Gravity=Density of graniteDensity of water=174.8 lb/ft362.4 lb/ft3≈2.8\text{Specific Gravity} = \frac{\text{Density of granite}}{\text{Density of water}} = \frac{174.8\ \text{lb/ft}^3}{62.4\ \text{lb/ft}^3} \approx \boxed{2.8}Specific Gravity=Density of waterDensity of granite=62.4 lb/ft3174.8 lb/ft3≈2.8
Explanation):
Specific gravity is a dimensionless quantity that compares the density of a substance to the density of a reference material. For solids and liquids, the reference material is typically water at 4°C, which has a standard density of 62.4 pounds per cubic foot in imperial units.
In this case, we are given the density of granite as 174.8 pounds per cubic foot. To find the specific gravity, we simply divide this value by the density of water. Since both densities are expressed in the same units (lb/ft³), the units cancel out, leaving a pure number.
The formula for specific gravity is:Specific Gravity=Density of substanceDensity of water\text{Specific Gravity} = \frac{\text{Density of substance}}{\text{Density of water}}Specific Gravity=Density of waterDensity of substance
Applying this formula:Specific Gravity=174.862.4=2.8\text{Specific Gravity} = \frac{174.8}{62.4} = 2.8Specific Gravity=62.4174.8=2.8
This tells us that granite is 2.8 times as dense as water. Because specific gravity is a ratio, it does not have units. A specific gravity greater than 1 means that the material is denser than water. Since granite’s specific gravity is 2.8, it will sink in water and is significantly heavier than the same volume of water.
Understanding specific gravity is important in various fields such as geology, construction, and material science. In geology, it helps identify and classify minerals. In engineering, specific gravity helps determine how materials will behave in certain environments, especially in applications involving fluid displacement or buoyancy.
Therefore, the specific gravity of granite, calculated from its density relative to water, is 2.8.
