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.

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.

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

Explanation:

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