A vessel contains oil (density: 0.8 gm/cm3) over mercury (density: 13.6 gm/cm3). 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 gm/cm3 is

As the sphere floats in the liquid. Therefore, its weight will be equal to the upthrust force on it. Weight of sphere =43πR3ρg.......(i)Upthrust due to oil and mercury=23πR3×σoilg+23πR3σHgg.......(ii)Equating (i) and (ii)43πR3ρg=23πR3×0.8g+23πR3×13.6g⇒2ρ=0.8+13.6=14.4⇒ρ=7.2