It is known that the density ratio of two solid spheres A and B with equal mass is A:B= 1:2. Now put A and B into a container with enough people.

For two solid balls A and B with equal mass m, the density ratio A: B = 1: 2, and the volume ratio VA:VB=2: 1 according to m = ρ V.

If both A and B are floating, buoyancy and gravity are balanced, and the ratio of buoyancy is 1: 1, which is inconsistent with the meaning of the question.

If both A and B sink, buoyancy F floats = ρ water gv, and the ratio of buoyancy is 2: 1, which is inconsistent with the meaning of the question.

Therefore, it must float for a and sink for b,

FA=mg FB=ρ water gVB..........( 1)

Fa ∶ FB = 8 ∶ 5, that is, FB=5FA/8=5mg/8..........(2).

mg=ρBgVB.........(3)

According to the formula (1)(2)(3), ρB=8ρ water /5 = 1.6 * 10 3 kg/m 3.

So ρ a = ρ b/2 = 0.8 *10.3 kg/m 3.

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