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Q85 (CDS-I/2003) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

A solid floats in liquid A with half its volume immersed and in liquid B with 2/3'of its volume immersed. The densities of the liquids A and B are in the ratio of

Result
Your answer: —  ·  Correct: D
Explanation

According to Archimedes' Principle, for a floating object, the weight of the object equals the weight of the liquid it displaces [1][t2]. This leads to the equilibrium condition: (Density of Solid) × (Total Volume) = (Density of Liquid) × (Immersed Volume) [t6][t8]. Let the density of the solid be ρ_s and its volume be V. For liquid A, ρ_s * V = ρ_A * (1/2 * V), which simplifies to ρ_A = 2 * ρ_s. For liquid B, ρ_s * V = ρ_B * (2/3 * V), which simplifies to ρ_B = (3/2) * ρ_s [t2][t7]. To find the ratio of the densities of liquids A and B (ρ_A: ρ_B), we calculate 2 * ρ_s: (3/2) * ρ_s. Multiplying both sides by 2 to clear the fraction results in a ratio of 4: 3.

Sources

  1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > A step further > p. 76
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