A tank 5 m high is half filled with water and then is filled to top with oil of density `0.85 g//cm^3` The pressure at the bottom of the tank, due to these liquids is

Options

A. `1.85 g//cm^2`
B. `89.25 g//cm^2`
C. `462.5 g//cm^2`
D. `500g//cm^2`

Explanation

To find the pressure at the bottom of the tank filled with water and oil, we can follow these steps:

### Step 1: Understand the setup
The tank is 5 meters high and is half filled with water (2.5 meters) and then filled to the top with oil (the remaining 2.5 meters). The density of oil is given as \(0.85 \, \text{g/cm}^3\).

### Step 2: Convert the height of the tank to centimeters
Since the density is given in grams per cubic centimeter, we should convert the height from meters to centimeters:
\[ 5 \, \text{m} = 500 \, \text{cm} \]
So, the height of the water \(H_1 = 250 \, \text{cm}\) and the height of the oil \(H_2 = 250 \, \text{cm}\).

### Step 3: Calculate the pressure due to water
The pressure at the bottom of the tank due to the water can be calculated using the formula:
\[ P_{\text{water}} = H_1 \times \rho_{\text{water}} \times g \]
Where:
- \(H_1 = 250 \, \text{cm}\)
- \(\rho_{\text{water}} = 1 \, \text{g/cm}^3\) (density of water)
- \(g\) (acceleration due to gravity) is typically considered as \(1 \, \text{g/cm}^2\) in this context.

Substituting the values:
\[ P_{\text{water}} = 250 \, \text{cm} \times 1 \, \text{g/cm}^3 \times 1 \, \text{g/cm}^2 = 250 \, \text{g/cm}^2 \]

### Step 4: Calculate the pressure due to oil
Next, we calculate the pressure at the bottom of the tank due to the oil:
\[ P_{\text{oil}} = H_2 \times \rho_{\text{oil}} \times g \]
Where:
- \(H_2 = 250 \, \text{cm}\)
- \(\rho_{\text{oil}} = 0.85 \, \text{g/cm}^3\)

Substituting the values:
\[ P_{\text{oil}} = 250 \, \text{cm} \times 0.85 \, \text{g/cm}^3 \times 1 \, \text{g/cm}^2 = 212.5 \, \text{g/cm}^2 \]

### Step 5: 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:
\[ P_{\text{total}} = 250 \, \text{g/cm}^2 + 212.5 \, \text{g/cm}^2 = 462.5 \, \text{g/cm}^2 \]

### Final Answer
The pressure at the bottom of the tank due to the water and oil is:
\[ \boxed{462.5 \, \text{g/cm}^2} \]