Question

If two balls have the same volume,

Answer 1

Here, we are required to find the relationship between balls of different mass(a measure of weight) and different volumes.

• 1. Ball A will have the greater density
• 2. Ball C and Ball D have the same density.
• 3. Ball Q will have the greater density.
• 4. Ball X and Y will have the same density

The density of an object is given as its mass per unit volume of the object.

Mathematically;.

• Density = Mass/Volume.

For Case 1:

• Va = Vb and Ma = 2Mb
• D(b) = (Mb)/(Vb) and D(a) = 2(Mb)/Vb
• Therefore, the density of ball A,
• D(a) = 2D(b).
• Therefore, ball A has the greater density.

For Case 2:

• Vc = 3Vd,

• Vd = (1/3)Vc

• Md = (1/3)Mc

• D(c) = (Mc)/(Vc) and D(d) = (1/3)Md/(1/3)Vd

• D(c) = D(d).

• Therefore, ball C and D have the same density

For Case 3:

• Vp = 2Vq and Mp = Mq
• D(p) = (Mq)/2(Vq) and D(q) = (Mq)/Vq
• Therefore, the density of ball P is half the density of ball Q
• Therefore, ball Q has the greater density.

For case 4:

• Mx = (1/2)My
• Vx = Vy

Therefore, Ball X and Ball Y have the same density.

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