A vessel contains oil (density 0.8 g m/cm 3 ) over mercury (density = 13.6 g m/cm 3 ). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in g m/cm 3 is

Step-by-step solution

As the sphere floats in the liquid. Therefore its weight will be equal to the upthrust force on it Weight of sphere = 4 3 π R 3 ρ g ...... i Upthrust due to oil and mercury = 2 3 π R 3 × σ oil g + 2 3 π R 3 σ Hg g ...... i i Equating (i) and (ii) 4 3 π R 3 ρ g = 2 3 π R 3 0 . 8 g + 2 3 π R 3 × 1 3 . 6 g ⇒ 2 ρ = 0 . 8 + 1 3 . 6 = 1 4 . 4 ⇒ ρ = 7 . 2