A tank 2 m high is half filled with water and then filled to the top with oil of density 0.60 g/cc. What is the pressure at the bottom of the tank due to these liquids? (Take g = 10 m `s^(-2)`)

Options

A. `0.8 xx 10^(2)N m^(-2)`
B. `0.8 xx 10^(4)N m^(-2)`
C. `1.6 xx 10^(2)N m^(-2)`
D. `1.6 xx 10^(4)N m^(-2)`

Explanation

To solve the problem of finding the pressure at the bottom of a tank that is half filled with water and then filled to the top with oil, we will follow these steps:

### Step 1: Understand the setup
The tank has a height of 2 meters. It is half filled with water and then the remaining half is filled with oil. This means that the height of the water column is 1 meter and the height of the oil column is also 1 meter.

### Step 2: Calculate the pressure due to water
The pressure at the bottom of the tank due to the water can be calculated using the formula:
\[ P_{\text{water}} = h_{\text{water}} \times \rho_{\text{water}} \times g \]
Where:
- \( h_{\text{water}} = 1 \, \text{m} \) (height of the water column)
- \( \rho_{\text{water}} = 1000 \, \text{kg/m}^3 \) (density of water)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values:
\[ P_{\text{water}} = 1 \, \text{m} \times 1000 \, \text{kg/m}^3 \times 10 \, \text{m/s}^2 \]
\[ P_{\text{water}} = 10000 \, \text{Pa} \]

### Step 3: Calculate the pressure due to oil
Next, we calculate the pressure at the bottom of the tank due to the oil using the same formula:
\[ P_{\text{oil}} = h_{\text{oil}} \times \rho_{\text{oil}} \times g \]
Where:
- \( h_{\text{oil}} = 1 \, \text{m} \) (height of the oil column)
- \( \rho_{\text{oil}} = 0.60 \, \text{g/cm}^3 = 600 \, \text{kg/m}^3 \) (density of oil converted to kg/m³)
- \( g = 10 \, \text{m/s}^2 \)

Substituting the values:
\[ P_{\text{oil}} = 1 \, \text{m} \times 600 \, \text{kg/m}^3 \times 10 \, \text{m/s}^2 \]
\[ P_{\text{oil}} = 6000 \, \text{Pa} \]

### Step 4: Calculate the total pressure at the bottom of the tank
The total pressure at the bottom of the tank is the sum of the pressures due to water and oil:
\[ P_{\text{total}} = P_{\text{water}} + P_{\text{oil}} \]
Substituting the values we calculated:
\[ P_{\text{total}} = 10000 \, \text{Pa} + 6000 \, \text{Pa} \]
\[ P_{\text{total}} = 16000 \, \text{Pa} \]

### Step 5: Express the final answer
The total pressure at the bottom of the tank is:
\[ P_{\text{total}} = 1.6 \times 10^4 \, \text{Pa} \]

### Final Answer
The pressure at the bottom of the tank due to the water and oil is \( 1.6 \times 10^4 \, \text{Pa} \).

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