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=23πR30.8g+23πR3×13.6g⇒2ρ=0.8+13.6=14.4⇒ρ=7.2