If two balls have the same volume, but ball A has twice as much mass as ball B, which one will have the greater density? ball A,

Answer:

The correct choices are:

For the first, Ball A has the greater density.

The second, their densities are equal.

For the third, Ball Q has the higher density.

The fourth, Ball Y is denser.

Explanation:

Based on the 2020 Edgeunity assignment.

Density (D) is described as the mass (m) of a material contained within a given volume (V). Mathematically, it is represented by:

Density = Mass ÷ Volume

D = m / V -------- (1)

Units: grams per cubic centimeter (g/cm³)

a)

Let m1, V1, and D1 denote the mass, volume, and density of ball A respectively, and m2, V2, and D2 represent mass, volume, and density of ball B.

Given: V1 = V2, and m1 = 2 × m2

Using equation (1):

D1/D2 = (m1/V1) ÷ (m2/V2) = (2m2/V2) ÷ (m2/V2) = 2

This implies ball A's density is twice that of ball B.

Answer: Ball A has the higher density.

b)

Let m1, V1, D1 be the mass, volume, and density of ball C, while m2, V2, D2 correspond to ball D.

Given: V1 = 3 × V2 and m2 = (1/3) × m1 → m1 = 3 × m2

Calculating:

D1/D2 = (m1/V1) ÷ (m2/V2) = (3m2/3V2) ÷ (m2/V2) = 1

Therefore, densities are equal.

Answer: Both have equal densities.

c)

Let m1, V1, D1 be the mass, volume, and density of ball P, and m2, V2, D2 for ball Q.

Given: m1 = m2, V1 = 2 × V2

Thus:

D1/D2 = (m1/V1) ÷ (m2/V2) = (m2/2V2) ÷ (m2/V2) = 1/2

So, ball P's density is half that of ball Q.

Answer: Ball Q has the greater density.

d)

Let m1, V1, D1 be the mass, volume, and density of ball X and m2, V2, D2 be the same for ball Y.

Given: V1 = 2 × V2 and m1 = (1/2) × m2

Then:

D1/D2 = (m1/V1) ÷ (m2/V2) = ((1/2) m2 / 2V2) ÷ (m2/V2) = 1/4

This means ball X’s density is one-fourth that of ball Y.

Answer: Ball Y has a higher density.