An aeroplane of mass `3xx10^(4)kg` and total wing area of 120 `m^(2)` is in a level flight at some height the difference in pressure between the upper and lower surfaces of its wings in kilo pascal is `(g=10m//s^(2))`

Options

A. 2.5
B. 5
C. 10
D. 12.5

Answer

To solve the problem, we need to determine the difference in pressure between the upper and lower surfaces of the wings of the airplane.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the airplane, \( m = 3 \times 10^4 \, \text{kg} \)
- Total wing area, \( A = 120 \, \text{m}^2 \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Calculate the Weight of the Airplane:**
The weight \( W \) of the airplane can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 3 \times 10^4 \, \text{kg} \times 10 \, \text{m/s}^2 = 3 \times 10^5 \, \text{N} \]

3. **Relate Weight to Pressure Difference:**
In level flight, the weight of the airplane is balanced by the lift force generated by the pressure difference between the upper and lower surfaces of the wings. The lift force \( F_L \) can be expressed as:
\[ F_L = (P_1 - P_2) \cdot A \]
where \( P_1 \) is the pressure on the lower surface and \( P_2 \) is the pressure on the upper surface. The pressure difference \( \Delta P \) is given by:
\[ \Delta P = P_1 - P_2 \]

4. **Set Up the Equation:**
Since the lift force equals the weight of the airplane:
\[ W = \Delta P \cdot A \]
Substituting the known values:
\[ 3 \times 10^5 \, \text{N} = \Delta P \cdot 120 \, \text{m}^2 \]

5. **Solve for the Pressure Difference \( \Delta P \):**
Rearranging the equation to solve for \( \Delta P \):
\[ \Delta P = \frac{3 \times 10^5 \, \text{N}}{120 \, \text{m}^2} \]
Calculating the right side:
\[ \Delta P = \frac{3 \times 10^5}{120} = 2500 \, \text{Pa} \]

6. **Convert Pressure Difference to Kilopascal:**
Since \( 1 \, \text{kPa} = 1000 \, \text{Pa} \):
\[ \Delta P = \frac{2500 \, \text{Pa}}{1000} = 2.5 \, \text{kPa} \]

### Final Answer:
The difference in pressure between the upper and lower surfaces of the wings is \( 2.5 \, \text{kPa} \).