Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as show in the figure with a tension in the string. The arrangement is possible only if :

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Two solid spheres A and B of equal volumes but of different densities d_A and d_B are connected by a string. They are fully immersed in a fluid of density d_F. They get arranged into an equilibrium state as show in the figure with a tension in the string. The arrangement is possible only if :

d_A + d_B = 2d_F

d_A < d_F

d_B > d_F

d_A > d_F

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system will be in equilibrium with tension in string only if d_f > d_A and d_B > df. If both A & B are considered as a system then

2Vdfg = V (d_A + d_B)g $\Rightarrow$ d_A + d_B = 2d_f