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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 shown in the figure with a tension in the string. The arrangement is possible only if
  • a)
    dA < />F
  • b)
    dB > dF
  • c)
    dA > dF
  • d)
    dA + dB = 2dF
Correct answer is option 'A,B,D'. Can you explain this answer?
Most Upvoted Answer
Two solid spheres A and B of equal volumes but of different densities...
F = upthrust = VdFg
Equilibrium of A
At dA < />F​B dB > dFD dA + dB = 2dF​ for sphere A to be at the top in liquid, the density of sphere A should be less than the density of liquid and for sphere B to be at the bottom in liquid, the density of sphere B should be greater than the density of liquid. The FBD of the top sphere gives us VdF g = T + V dAg and of the bottom sphere gives us T + V dF g = V dB g.
Substituting T from the first equation in the second, we get
2V dF g = VdA g + V dBg or 2dF = dA + dB
Therefore, options 1, 2 and 4 are correct.
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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 shown in the figure with a tension in the string. The arrangement is possible only ifa)dA Fb)dB > dFc)dA > dFd)dA + dB = 2dFCorrect answer is option 'A,B,D'. Can you explain this answer?
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