Internal Structure and Density
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AP Physics 1 › Internal Structure and Density
A metal cylinder is cut in half perpendicular to its axis, producing two smaller cylinders. Each half has half the mass and half the volume of the original. How does density change?
Density doubles because the piece is smaller.
Density stays the same because mass and volume scale together.
Density halves because mass is halved.
Density becomes zero because the object was cut.
Explanation
This question tests whether density is an intensive or extensive property related to internal structure. Density equals mass divided by volume (ρ = m/V) and describes how tightly atoms or molecules are packed within a material. When the cylinder is cut in half, each piece has half the original mass (m/2) and half the original volume (V/2), giving density ρ = (m/2)/(V/2) = m/V, which equals the original density. The internal atomic structure and packing remain unchanged by the cutting process, so density stays constant. Choice A incorrectly assumes smaller size means higher density without considering proportional mass reduction. The key principle is that density is an intensive property: it depends on material composition and structure, not on the amount of material.
A uniform cube $Q$ and a uniform cube $R$ have equal mass. Cube $Q$ has greater side length. Which statement is correct?
Cube $Q$ is denser because it is larger.
They have equal density because their masses match.
Cube $R$ is denser because the same mass occupies less volume.
Cube $Q$ must be denser because it has greater volume.
Explanation
This question examines density when cubes have equal mass but different side lengths and volumes. Density equals mass divided by volume (ρ = m/V), and cube volume equals side length cubed. Cube R has the same mass as cube Q but smaller side length (thus smaller volume), meaning R's matter is more concentrated and has higher density. Option A incorrectly suggests the larger cube is denser, which violates the inverse relationship between volume and density when mass is held constant. For equal-mass cubes, smaller side length always indicates greater density.
Two objects have equal volume. Object $X$ has greater mass than object $Y$. Which statement about density is correct?
They have equal density because their volumes match.
Object $Y$ must have greater volume.
Object $X$ is denser because it has more mass per unit volume.
Object $Y$ is denser because it is lighter.
Explanation
This question tests density understanding when objects have equal volumes but different masses. Density is defined as mass per unit volume (ρ = m/V), so with identical volumes, the object with greater mass has higher density. Object X contains more mass than object Y in the same volume, indicating more matter per unit volume and higher density. Option A incorrectly states that the lighter object is denser, which directly contradicts the density formula. When volumes are equal, always identify which object has greater mass to determine higher density.
Two objects have the same mass and are made of different materials. Object 1 has smaller volume. What is supported?
Density cannot be compared without knowing their weights in air.
Object 2 has greater density because it is larger.
They have equal density because masses match.
Object 1 has greater density than object 2.
Explanation
This question tests density comparison for equal-mass objects made of different materials. Density equals mass divided by volume (ρ = m/V), so when masses are equal, the object with smaller volume has higher density. Object 1 has the same mass as object 2 but occupies less space, indicating that object 1 is made of denser material with tighter atomic packing. Option B incorrectly suggests the larger object is denser, which violates the inverse relationship between volume and density. For equal-mass objects, smaller volume always indicates denser material and higher density.
A student compresses a sealed, flexible bag of air so its volume decreases while its mass stays the same. Compared to before, the air in the bag now has
greater density because the same mass occupies less volume.
smaller density because the volume is smaller.
zero density because gases have no density.
the same density because the mass did not change.
Explanation
This question tests how changing volume affects density when mass remains constant. Density equals mass divided by volume (ρ = m/V), measuring how concentrated matter is within a given space. When the bag is compressed, the same air molecules (same mass) occupy a smaller volume, increasing the density: ρ_final = m/V_final > ρ_initial = m/V_initial (since V_final < V_initial). This compression forces air molecules closer together, increasing the internal packing density without changing the total amount of matter. Choice C incorrectly assumes constant mass means constant density, ignoring the critical volume change. When mass stays constant, density and volume are inversely related: decreasing volume always increases density.
Two uniform blocks have equal volume. Block 1 has greater mass than block 2. Which conclusion about density is correct?
Density cannot be compared without knowing the material names.
Densities are equal because volumes match.
Block 2 is denser because it is lighter.
Block 1 is denser because it has more mass for the same volume.
Explanation
This question tests density understanding when blocks have equal volumes but different masses. Density is defined as mass per unit volume (ρ = m/V), so with identical volumes, the block with greater mass has higher density. Block 1 contains more mass than block 2 in the same volume, indicating denser material or more tightly packed matter. Option A incorrectly states that the lighter block is denser, which directly contradicts the density formula. When volumes are equal, always compare masses to determine which block has higher density.
Two objects have equal mass. Object 1 is larger in volume than object 2. Which statement is correct?
Object 1 must be denser because it displaces more air.
They have equal density because their masses match.
Object 2 is denser because the same mass occupies less volume.
Object 1 is denser because it is bigger.
Explanation
This question tests density understanding when objects have equal mass but different volumes. Density equals mass divided by volume (ρ = m/V), so when mass is constant, the object with smaller volume has higher density. Object 2 has the same mass as object 1 but occupies less space, meaning object 2's matter is more tightly packed and has higher density. Option A incorrectly suggests the larger object is denser, which violates the inverse relationship between volume and density when mass is held constant. For equal-mass objects, smaller volume always indicates greater density.
Two objects are made of the same uniform material. Object 1 has three times the volume of object 2. Which statement is correct?
Object 2 is denser because it is smaller.
Density depends on volume, so densities differ.
Object 1 is denser because it is larger.
Both objects have the same density.
Explanation
This question tests understanding of density as an intrinsic material property. Density is a characteristic property that depends only on material composition, not on object size or amount of material. Since both objects are made of the same uniform material, they have identical density regardless of their different volumes or masses. Option A incorrectly suggests the larger object is denser, but density is independent of size for the same material. Objects made of identical materials always have the same density regardless of their dimensions.
Object $A$ and object $B$ have the same volume. $A$ has smaller mass than $B$. Which statement is correct?
$B$ is denser because it has more mass for the same volume.
Density cannot be compared without knowing their shapes.
$A$ is denser because it has less mass.
They have equal density because their volumes match.
Explanation
This question tests density understanding when objects have equal volumes but different masses. Density is defined as mass per unit volume (ρ = m/V), so with identical volumes, the object with greater mass has higher density. Object B has more mass than object A in the same volume, indicating that B contains more matter packed into the same space and has higher density. Option A incorrectly states that the object with smaller mass is denser, which directly contradicts the density formula. When volumes are equal, always identify which object has greater mass to determine higher density.
Two rocks, $R_1$ and $R_2$, have the same volume. $R_2$ weighs more on a scale than $R_1$. What is the best inference?
$R_1$ has greater density because it is lighter.
$R_2$ has greater density than $R_1$.
They must have the same density because their volumes match.
The heavier rock must have a larger volume.
Explanation
This question applies density concepts using weight as an indicator of mass. Density equals mass per unit volume (ρ = m/V), and since weight is proportional to mass, a heavier rock has greater mass. With equal volumes, rock R₂ has more mass in the same space as R₁, resulting in higher density and indicating more tightly packed internal matter. Option B incorrectly suggests that the lighter rock is denser, which contradicts the fundamental relationship between mass and density. When comparing equal-volume objects, the heavier one always has greater density.