The image you've uploaded shows a physics problem about identifying a fluid using its mass density. Let's break down the exercise:

Exercise Overview:

1. There are two phases in a container: phase 1 (water) and phase 2 (an unidentified liquid).
2. The liquid is either cyclohexane, oil, or dichloromethane.
3. The densities of these liquids are provided:
   • Cyclohexane: 780 kg/m³
   • Oil: 990 kg/m³
   • Dichloromethane: 1.33 × 10³ kg/m³
4. The task is to apply the fundamental law of fluid statics and show the relationship between the pressures at the liquid interfaces.

The questions asked are:

• (a) Apply the fundamental law of fluid statics to demonstrate that $\frac{\rho_1}{\rho_2} = \frac{h_2}{h_1}$.
• (b) Identify the liquid in the container.

Steps to Solve:

For part (a):

1. According to the principle of fluid statics, the pressures at the same horizontal level in a liquid column are equal.

   $P_1 = P_2$

2. The pressure in a fluid is given by $P = \rho g h$, where $\rho$ is the density, $g$ is the gravitational acceleration, and $h$ is the height of the fluid column.

   Therefore: $\rho_1 g h_1 = \rho_2 g h_2$

3. Since $g$ is constant, we can cancel it out: $\rho_1 h_1 = \rho_2 h_2$

4. Rearranging the equation: $\frac{\rho_1}{\rho_2} = \frac{h_2}{h_1}$

This confirms the required relationship.

For part (b):

1. You can now use the height values $h_1 = 7.80 \, \text{cm}$ and $h_2 = 10.00 \, \text{cm}$ to calculate the ratio $\frac{h_2}{h_1}$.

2. Then compare this ratio with the ratios of the densities for the three fluids (cyclohexane, oil, and dichloromethane).

By doing this, you can identify the liquid based on which density corresponds to the ratio.

Would you like to continue with the solution for part (b) by performing the calculations?