Question

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, ball B, Their densities are equal.

If ball C is 3 times the volume of ball D and ball D has 1/3 the mass of ball C, which has the greater density? ball C, ball D, Their densities are equal.

If two balls have the same mass, but ball P is twice as large as ball Q, which one will have the greater density? ball P, ball Q, Their densities are equal.

If ball X is twice as big as ball Y and weighs only half as much as ball Y, then which one will have the greater density? ball X, ball Y, Their densities are the same.

Answer 1

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

If ball C is 3 times the volume of ball D and ball D has 1/3 the mass of ball C, which has the greater density?

✔ Their densities are equal.

If two balls have the same mass, but ball P is twice as large as ball Q, which one will have the greater density?

✔ ball Q

If ball X is twice as big as ball Y and weighs only half as much as ball Y, then which one will have the greater density?

✔ ball Y

Step-by-step explanation:

Answer 2

Density (D) is defined as the amount or mass (m) of a substance present in a unit volume(V). It can be expressed mathematically as:

Density = Mass/Volume

i.e. D = m/V -------(1)

Units: g/cm3

a)

If m1, V1 and D1 = mass, volume and density respectively of ball A

m2, V2 and D2 = mass, volume and density respectively of ball B

It is given that: V1 = V2; but m1 = 2m2

Based on equation (1) we have:

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

Thus, density of ball A is twice that of B.

Ans: Ball A will have a greater density than B

b)

If m1, V1 and D1 = mass, volume and density respectively of ball C

m2, V2 and D2 = mass, volume and density respectively of ball D

It is given that:

V1 = 3V2 and m2 = 1/3(m1) i.e m1 = 3m2

Therefore,

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

Thus, D1 = D2

Ans: Their densities are equal

c)

If m1, V1 and D1 = mass, volume and density respectively of ball P

m2, V2 and D2 = mass, volume and density respectively of ball Q

It is given that:

m1 = m2 but V1 = 2V2

Therefore,

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

Thus, D1 = 1/2(D2)

Ans: Ball Q will have a greater density.

d)

If m1, V1 and D1 = mass, volume and density respectively of ball X

m2, V2 and D2 = mass, volume and density respectively of ball Y

It is given that:

V1 = 2V2 and m1 = 1/2(m2)

Therefore,

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

Thus, D1 = 1/4(D2)

Ans: Ball Y will have a greater density.