Density is defined as mass per unit volume, or D = m/v. Solve the density
equation for the variable v: *
v = D + m
v = D/m
v = D * m
v= m/D
The Correct Answer and Explanation is:
To solve the density equation ( D = \frac{m}{v} ) for the variable ( v ), we start with the basic definition of density. Density (D) is defined as the mass (m) of an object divided by its volume (v). We need to isolate ( v ) on one side of the equation.
Starting with the original equation:
[
D = \frac{m}{v}
]
we can rearrange the equation to solve for ( v ). To eliminate the fraction, we can multiply both sides by ( v ):
[
D \cdot v = m
]
Next, to isolate ( v ), we divide both sides by ( D ):
[
v = \frac{m}{D}
]
Thus, the correct expression for ( v ) in terms of mass and density is:
[
v = \frac{m}{D}
]
Explanation
Density is a fundamental physical property that describes how much mass is contained within a specific volume of a substance. It plays a crucial role in various fields, including physics, engineering, and chemistry, helping to characterize materials and predict how they behave under different conditions.
In the formula ( D = \frac{m}{v} ), the variable ( D ) represents density, ( m ) represents mass, and ( v ) represents volume. Understanding how to manipulate this equation allows us to derive the volume from the mass and density, which is particularly useful in laboratory settings and practical applications.
For instance, if a scientist knows the mass of a substance and its density, they can calculate the volume it occupies using ( v = \frac{m}{D} ). This relationship is critical in experiments where volume must be controlled or measured accurately, such as in titration or mixing solutions in chemistry.
In summary, solving for ( v ) provides valuable insights into how substances interact with each other based on their physical properties. Understanding density and its formula allows scientists and engineers to make informed decisions in design, manufacturing, and material selection, influencing everything from product development to environmental science.