l vessel contains oil of density 0.8 gm/cm3 over lercury of density 1 3.6 gm/cm 3. A homogeneous phere floats with half of its volume immersed in lercury and the other half in oil. The density of ne material of the sphere in CGS unit is

According to Archimedes' principle, the buoyant force acting on an object is equal to the weight of the fluid displaced [1]. For a floating object in equilibrium, the total weight of the object must equal the sum of the buoyant forces exerted by the fluids it is immersed in [t2]. Let V be the total volume of the homogeneous sphere. The sphere is half-immersed in oil (density 0.8 g/cm³) and half-immersed in mercury (density 13.6 g/cm³). The weight of the sphere is (V × ρ_sphere × g). The buoyant force from the oil is (V/2 × 0.8 × g) and from mercury is (V/2 × 13.6 × g). Equating the weight to the total buoyant force: V × ρ_sphere = (V/2 × 0.8) + (V/2 × 13.6). Simplifying this, the density of the sphere is the average of the two liquid densities: (0.8 + 13.6) / 2 = 7.2 g/cm³ [t2].

Sources

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