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

Explanation

Let V be the volume of sphere and `rho` its density . Let `rho_(0)` and `rho_(m)` be the density of oil and mercury respectively. Since the sphere is floating, therefore,
weight of sphere= weight of oil displaced + weight of mercury displaced
or `V rho g = V/2 rho_(0)g +V/2 rho_(m) g`
or `rho = (rho_(0)+rho_(m))/(2) = (0.8+13.6)/(2) = 7.2 g cm^(-3)`.