The pressure on the top surface of an aeroplane wing is `0.8xx 10^5` Pa and the pressure on the bottom surface is `0.75 xx 10^5` Pa. If the area of each surface is `50 m^2`, the dynamic lift on the wing is

Options

A. `0.5xx10^4` N
B. `0.25xx10^4` N
C. `5xx10^4` N
D. `25xx10^4` N

Answer

To solve the problem of finding the dynamic lift on the wing of an airplane, we will follow these steps:

### Step 1: Write down the given data.
- Pressure on the top surface of the wing, \( P_1 = 0.8 \times 10^5 \) Pa
- Pressure on the bottom surface of the wing, \( P_2 = 0.75 \times 10^5 \) Pa
- Area of each surface, \( A = 50 \, m^2 \)

### Step 2: Calculate the difference in pressure.
The dynamic lift is caused by the difference in pressure between the top and bottom surfaces of the wing. We can calculate the resultant pressure (\( P_{\text{resultant}} \)) as follows:

\[ P_{\text{resultant}} = P_1 - P_2 \]

Substituting the values:

\[ P_{\text{resultant}} = (0.8 \times 10^5) - (0.75 \times 10^5) = 0.05 \times 10^5 \, \text{Pa} \]

### Step 3: Calculate the dynamic lift (force).
The dynamic lift can be calculated using the formula:

\[ \text{Force} (F) = \text{Area} (A) \times \text{Resultant Pressure} (P_{\text{resultant}}) \]

Substituting the values:

\[ F = 50 \, m^2 \times (0.05 \times 10^5 \, \text{Pa}) \]

Calculating this gives:

\[ F = 50 \times 0.05 \times 10^5 = 2.5 \times 10^5 \, \text{N} \]

### Step 4: Final Result
The dynamic lift on the wing is:

\[ F = 2.5 \times 10^5 \, \text{N} \]