A small air bubble of radius 0.1mm is situated at a depth of 20 m below the free surface of water . The external pressure on the bubble will be (Atm. Pressure =`10^5N//m^2,g=10m//s^2)`

Options

A. `0.5xx10^5N//m^2`
B. `10^5N//m^2`
C. `3xx10^5N//m^2`
D. `4xx10^5N//m^2`

Answer

To find the external pressure on the air bubble situated at a depth of 20 m below the free surface of water, we can follow these steps:

### Step 1: Understand the components of external pressure
The external pressure on the bubble is the sum of the atmospheric pressure and the hydrostatic pressure due to the water column above the bubble.

### Step 2: Calculate the atmospheric pressure
The atmospheric pressure at the surface of the water is given as:
\[ P_{\text{atm}} = 10^5 \, \text{N/m}^2 \]

### Step 3: Calculate the hydrostatic pressure
The hydrostatic pressure can be calculated using the formula:
\[ P_{\text{hydrostatic}} = \rho g h \]
where:
- \( \rho \) (density of water) = \( 10^3 \, \text{kg/m}^3 \)
- \( g \) (acceleration due to gravity) = \( 10 \, \text{m/s}^2 \)
- \( h \) (depth) = \( 20 \, \text{m} \)

Substituting the values:
\[ P_{\text{hydrostatic}} = (10^3 \, \text{kg/m}^3)(10 \, \text{m/s}^2)(20 \, \text{m}}) \]
\[ P_{\text{hydrostatic}} = 10^3 \times 10 \times 20 = 2 \times 10^5 \, \text{N/m}^2 \]

### Step 4: Calculate the total external pressure
Now, we can find the total external pressure on the bubble:
\[ P_{\text{external}} = P_{\text{atm}} + P_{\text{hydrostatic}} \]
\[ P_{\text{external}} = 10^5 \, \text{N/m}^2 + 2 \times 10^5 \, \text{N/m}^2 \]
\[ P_{\text{external}} = 3 \times 10^5 \, \text{N/m}^2 \]

### Final Answer
The external pressure on the bubble is:
\[ P_{\text{external}} = 3 \times 10^5 \, \text{N/m}^2 \]

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