Vessel contains oil `(density 0.8 g//c c)` over mercury (density `13.6 g//c c)` A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the sphere in g/c c is

Options

A. `6.4`
B. `7.2`
C. `12.8`
D. `12.8`

Explanation

To find the density of the sphere that is floating in both oil and mercury, we can follow these steps:

### Step 1: Understand the Problem
We have a sphere that is floating with half of its volume in mercury and half in oil. We know the densities of both fluids:
- Density of oil, \( \rho_{\text{oil}} = 0.8 \, \text{g/cm}^3 \)
- Density of mercury, \( \rho_{\text{mercury}} = 13.6 \, \text{g/cm}^3 \)

### Step 2: Set Up the Equilibrium Condition
...