A body floats in a liquid with one-third of its volume above the surface. The density of the body relative to the liquid is: MCQ with Answer and Explanation
A body floats in a liquid with one-third of its volume above the surface. The density of the body relative to the liquid is:
A. 3
B. 2/3
C. 1/3
D. 3/2
Answer: Option B
Solution (By JKExamLibrary)
By Archimedes' principle, weight of body = weight of displaced liquid. Let V be total volume, ρ_b body density, ρ_l liquid density. Volume submerged = (2/3)V. Thus ρ_b·V·g = ρ_l·(2V/3)·g ⇒ ρ_b/ρ_l = 2/3. Fraction submerged equals density ratio. Memory tip: 'Fraction submerged = ρ_object / ρ_fluid'. This direct application of floatation condition is common in competitive exams. Always identify submerged fraction correctly: here 'one-third above' means two-thirds submerged. Such problems test conceptual clarity in buoyancy applications.
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