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Q64 (NDA-II/2024) Science & Technology › Basic Science (Physics, Chemistry, Biology) Official Key

Shown in the figure are two hollow cubes C1 and C2 of negligible mass partially filled (depicted by darkened area) with liquids of densities p1 and P2, respectively, floating in water (density Pw). The relationship between P1, P2 and Pw is

Explanation

According to the principle of floatation, for a floating object of negligible mass, the weight of the liquid inside the cube must equal the weight of the water displaced by the submerged portion of the cube.

  • For Cube C1: The diagram shows the level of liquid inside is higher than the water level outside. This means the volume of liquid inside (V1) is greater than the volume of water displaced (Vw). Since weight must be balanced (V1 × ρ1 = Vw × ρw), it follows that ρ1 < ρw.
  • For Cube C2: The level of liquid inside is lower than the water level outside. This indicates the volume of liquid inside (V2) is less than the volume of water displaced (Vw). To maintain equilibrium (V2 × ρ2 = Vw × ρw), ρ2 must be greater than ρw.

Therefore, the correct relationship is ρ1 < ρw < ρ2, which aligns with Option D.

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