Question

An airplane of mass $3\times {10}^{4}kg$ and a total wing area of $120m^2$ is in a level flight at the same height. The difference in pressure between the upper and lower surface of its wings in Kilo Pascal is: $\left(g=10m{s}^{-2}\right)$

• A. $2.5$
• B. $5.0$
• C. $10.0$
• D. $12.5$

Answer 1

The correct option is A

$2.5$

Step 1: Given

Mass of plane: $3\times {10}^{4}kg$

Area of wing: $120m^2$

Step 2: Formula Used:

$Weight=mass\times accelerationduetogravity$

$Force=Pressuredifference\times Area$

Step 3: Find the pressure difference

Calculate the weight of the plane using the formula.

$$\begin{gathered} Weight=mass\times accelerationduetogravity \\ =3\times {10}^{4}kg\times 10m{s}^{-2} \\ =3\times {10}^{5}N \end{gathered}$$

Equate the weight of the plane to the pressure force and substitute the values

$$\begin{gathered} \left(P_1-P_2\right)A=W \\ \Rightarrow \left(P_1-P_2\right)\times 120=3\times {10}^5 \\ \Rightarrow P_1-P_2=\frac{3\times {10}^5}{120} \\ \Rightarrow P_1-P_2=2500pascals=2.5kilopascals \end{gathered}$$

Hence, the difference in pressure between the upper and lower surface of its wings is $2.5kilopascals$. Hence, option A is correct.