Question

1. while thinking about a single type of material, complete the following statements: as the mass of the material is increased, its volume … as the mass of the material is increased, its density … as the volume of the material is decreased, its mass … as the volume of the material is decreased, its density …

Explanation:

1. For the first statement: The formula for density is $

ho=\frac{m}{V}$ (where $
ho$ is density, $m$ is mass, $V$ is volume). For a single material, density is constant. So if mass ($m$) increases, volume ($V$) must increase proportionally (since $
ho$ is fixed, $V = \frac{m}{
ho}$; as $m$ increases, $V$ increases).

1. For the second statement: Density is an intrinsic property of a material, meaning it does not change with the amount of the material. So even if mass increases, density remains the same.
2. For the third statement: Using $

ho=\frac{m}{V}$, we can rearrange to $m=
ho V$. If volume ($V$) decreases (and $
ho$ is constant for the material), then mass ($m$) will decrease proportionally.

1. For the fourth statement: From $

ho=\frac{m}{V}$, if volume ($V$) decreases and mass ($m$) is assumed to be constant (or if we consider the same amount of mass in a smaller volume), density ($
ho$) will increase (since $
ho$ is inversely proportional to $V$ when $m$ is constant).

Answer:

• As the mass of the material is increased, its volume increases (because density is constant for a material, so volume is directly proportional to mass: $V=\frac{m}{

ho}$).

• As the mass of the material is increased, its density remains the same (density is an intrinsic property, independent of the amount of the material).
• As the volume of the material is decreased, its mass decreases (from $m =

ho V$, with $
ho$ constant, a decrease in $V$ leads to a decrease in $m$).

• As the volume of the material is decreased, its density increases (from $

ho=\frac{m}{V}$, with $m$ constant (or for the same mass), a decrease in $V$ leads to an increase in $
ho$).