The formula rho equals m over v, where rho = density, m = mass, and v = volume, is used to calculate density. Solve this formula for m. group of answer choices m = rhov m = rho v m = rho − v m equals v over rho
The correct Answer and Explanation is:
To solve the formula for density, (\rho = \frac{m}{v}), in terms of mass (m), we can manipulate the equation algebraically. The original equation states that density ((\rho)) is equal to mass ((m)) divided by volume ((v)).
To isolate (m), we can start by multiplying both sides of the equation by (v):
[
\rho \cdot v = m
]
This gives us the equation:
[
m = \rho v
]
Therefore, the correct answer is (m = \rho v).
Explanation
The formula for density expresses the relationship between mass, volume, and density. Density ((\rho)) is defined as the mass of a substance per unit volume. It is an important physical property used in various fields, including physics, chemistry, and engineering, as it helps determine how substances interact with one another, such as whether an object will float or sink in a fluid.
When rearranging the density formula to solve for mass, it is essential to apply algebraic principles correctly. The original formula states that density is the ratio of mass to volume. To isolate mass, we multiply both sides by volume. This step is crucial because it removes the fraction and makes the equation easier to manipulate.
Understanding this relationship is not only important for solving mathematical problems but also for practical applications. For example, in laboratory settings, knowing the density of a liquid can help determine its mass if the volume is measured. This can be essential in chemical reactions, material properties, and quality control processes.
Thus, the relationship (m = \rho v) is a fundamental concept that illustrates how mass can be calculated if the density and volume of a substance are known. This formula is widely used in scientific calculations and practical applications across various disciplines.