This problem requires us to calculate the mass of a substance given its volume and density. The fundamental formula relating these three quantities is density = mass / volume. We need to rearrange this formula to solve for mass.
Correct Option: A) 20 g
The question asks which property of matter changes with altitude due to variations in gravitational force. We need to understand the definitions of mass, volume, weight, and density and how they are affected by gravity and altitude.
Therefore, weight is the property that changes with altitude due to the variation in gravitational force.
Correct Option: C) Weight is the force exerted on an object due to gravity. As altitude increases, the gravitational force decreases, which in turn decreases the acceleration due to gravity (\(g\)). Since weight \(W = m \times g\), a decrease in \(g\) will lead to a decrease in weight.
The question asks to identify a physical property from the given options. A physical property is a characteristic of a substance that can be observed or measured without changing the substance's chemical composition. Chemical properties, on the other hand, describe how a substance reacts to form new substances.
Correct Option: C) Density is a physical property because it can be measured without changing the chemical composition of the substance.
The question asks to identify the material with the highest density among the given options. Density is a measure of how much mass is contained in a given volume. It is calculated using the formula:
\[ \rho = \frac{m}{V} \]where \(\rho\) (rho) is density, \(m\) is mass, and \(V\) is volume. To answer this, we need to compare the typical densities of the materials listed.
C) Iron — Iron has a typical density of about \(7.87 \text{ g/cm}^3\), which is significantly higher than wood, aluminum, or styrofoam.
The question asks to identify the property of matter that depends on both mass and volume. We need to recall the definitions and formulas for each given option to determine their dependence on mass and volume.
From this formula, it is clear that density directly depends on both mass and volume. If mass increases while volume is constant, density increases. If volume increases while mass is constant, density decreases.
where \(m\) is mass and \(g\) is the acceleration due to gravity. Weight depends on mass, but not directly on volume. While volume can indirectly affect mass for a given substance (e.g., a larger volume of the same substance will have more mass), weight itself is not a direct function of volume.
Pressure depends on force and area, not directly on mass or volume. While the force might be due to the weight of a substance (which depends on mass), pressure itself is not a fundamental property directly dependent on both mass and volume of the substance in general.
A) Density is defined as mass per unit volume (\(\rho = m/V\)). Therefore, it explicitly depends on both mass and volume.
This question tests the fundamental understanding of mass and its properties in physics. Mass is an intrinsic property of an object, representing the amount of matter it contains. It is distinct from weight, which is a force.
B) Always constant — Mass is an intrinsic property of an object and represents the amount of matter it contains. This quantity remains constant regardless of the object's location in the universe (e.g., on Earth, on the Moon, or in space), its speed, or the gravitational field it is in. It only changes if matter is added to or removed from the object.