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

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