A cylinder of 4 m height is half filled with oil of density 0.72 g cm`""^(-3)`. If the Becond half of cylinder is filled with water, then find the pressure at the bottom of cylinder due to these liquids.

Answer

To find the pressure at the bottom of a cylinder that is half filled with oil and half filled with water, we will follow these steps:

### Step 1: Understand the problem
We have a cylinder with a height of 4 m. The first half (2 m) is filled with oil of density 0.72 g/cm³, and the second half (2 m) is filled with water.

### Step 2: Convert the density of oil to SI units
The density of oil is given as 0.72 g/cm³. We need to convert this to kg/m³:
\[ 0.72 \, \text{g/cm}^3 = 0.72 \times 1000 \, \text{kg/m}^3 = 720 \, \text{kg/m}^3 \]

### Step 3: Identify the density of water
The density of water is known to be:
\[ \rho_{\text{water}} = 1000 \, \text{kg/m}^3 \]

### Step 4: Calculate the pressure due to the oil
The pressure at the bottom of the cylinder due to the oil can be calculated using the formula:
\[ P_{\text{oil}} = \rho_{\text{oil}} \cdot g \cdot h_{\text{oil}} \]
Where:
- \(\rho_{\text{oil}} = 720 \, \text{kg/m}^3\)
- \(g = 9.81 \, \text{m/s}^2\) (acceleration due to gravity)
- \(h_{\text{oil}} = 2 \, \text{m}\)

Substituting the values:
\[ P_{\text{oil}} = 720 \, \text{kg/m}^3 \cdot 9.81 \, \text{m/s}^2 \cdot 2 \, \text{m} = 14107.2 \, \text{Pa} \]

### Step 5: Calculate the pressure due to the water
Similarly, the pressure due to the water can be calculated as:
\[ P_{\text{water}} = \rho_{\text{water}} \cdot g \cdot h_{\text{water}} \]
Where:
- \(\rho_{\text{water}} = 1000 \, \text{kg/m}^3\)
- \(h_{\text{water}} = 2 \, \text{m}\)

Substituting the values:
\[ P_{\text{water}} = 1000 \, \text{kg/m}^3 \cdot 9.81 \, \text{m/s}^2 \cdot 2 \, \text{m} = 19620 \, \text{Pa} \]

### Step 6: Calculate the total pressure at the bottom of the cylinder
The total pressure at the bottom of the cylinder is the sum of the pressures due to the oil and the water:
\[ P_{\text{total}} = P_{\text{oil}} + P_{\text{water}} = 14107.2 \, \text{Pa} + 19620 \, \text{Pa} = 33727.2 \, \text{Pa} \]

### Step 7: Convert the total pressure to Pascal
Since 1 Pa = 1 N/m², the total pressure at the bottom of the cylinder is:
\[ P_{\text{total}} = 33727.2 \, \text{Pa} \]

### Final Answer
The pressure at the bottom of the cylinder due to the oil and water is approximately:
\[ P_{\text{total}} \approx 33727.2 \, \text{Pa} \text{ or } 3.37 \times 10^4 \, \text{Pa} \]