In this question, we are given that a sphere is floating with half of its volume immersed in mercury and the other half in oil.

To determine the density of the sphere, we need to consider the densities of the two liquids and the fact that the sphere is floating.

The sphere is floating in the two liquids, which means that its weight is equal to the buoyant force acting on it. The buoyant force is given by the formula Buoyant force = (density of the liquid) * (volume immersed) * (acceleration due to gravity).

Let`s assume that the density of the sphere is `x` gm/cm^3.

For the part of the sphere immersed in mercury, the buoyant force is equal to the weight of the mercury displaced. So we can equate the buoyant force to (density of mercury) * (volume immersed in mercury) * (acceleration due to gravity).

Similarly, for the part of the sphere immersed in oil, the buoyant force is equal to the weight of the oil displaced. So we can equate the buoyant force to (density of oil) * (volume immersed in oil) * (acceleration due to gravity).

Since the sphere is floating, the sum of the buoyant forces from the