Shown in the figure are two hollow cubes C_{1} and C_{2} of negligible mass partially filled (depicted by darkened area) with liquids of densities \rho_{1} and \rho_{2}, respectively, floating in water (density \rho_{W}). The relationship between \rho_{1}, \rho_{2} and \rho_{W} is

  1. A. \rho_{2} < \rho_{W} < \rho_{1} ✓
  2. B. \rho_{2} < \rho_{1} < \rho_{W}
  3. C. \rho_{1} < \rho_{2} < \rho_{W}
  4. D. \rho_{1} < \rho_{W} < \rho_{2}

Correct Answer: A. \rho_{2} < \rho_{W} < \rho_{1}

Explanation

For a hollow cube of negligible mass to float, the buoyant force depends on the weight of the liquid inside. If the internal liquid level is lower than the external water level, the internal liquid is denser than water (\rho_{1} > \rho_{W}). If the internal level is higher, it is less dense (\rho_{2} < \rho_{W}).

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