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Q83 (NDA-I/2010) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

A vessel contains oil (density pj) over a liquid of density p2; a homogeneous sphere of volume V floats with half of its volume immersed in the liquid and the other half in oil. The weight of the sphere is

Result
Your answer: —  ·  Correct: B

Explanation

According to Archimedes' principle, the buoyant force acting on a floating object is equal to the weight of the fluid it displaces [1]. For an object floating in equilibrium, the weight of the object must equal the total buoyant force [1]. In this scenario, the sphere is submerged in two immiscible liquids: oil (density ρ1) and a liquid (density ρ2). The total buoyant force is the sum of the weights of the displaced fluids from each layer. Since half the volume (V/2) is in oil and the other half (V/2) is in the liquid, the buoyant force is (V/2)ρ1g + (V/2)ρ2g. Factoring out common terms, the total weight of the sphere is V(ρ1 + ρ2)g/2. This aligns with the principle that buoyancy depends on the density of the fluid and the volume displaced.

Sources

  1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > Activity 5.13: Let us investigate > p. 76
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