A vessel contains oil (density = 0.8 gm / cm ^3 ) over mercury (density = 13.6 gm / 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 gm / cm ^3 is

Step-by-step solution

Let the total volume of the sphere be V and its density be . According to the principle of flotation, the weight of the sphere is balanced by the total buoyant force exerted by the two liquids. Weight of the sphere, W = V g The sphere has half of its volume in mercury and the other half in oil. The total buoyant force F_B is the sum of the buoyant forces from both liquids: F_B = F_ B, mercury + F_ B, oil F_B = ( V 2 ) _ Hg g + ( V 2 ) _ oil g Equating the weight of the sphere to the total buoyant force: V g = V 2 _