A fully loaded boeing aircraft has a mass of $5.4 \times 10^5\,kg$. Its total wing area is $500\,m ^2$. It is in level flight with a speed of $1080\,km / h$. If the density of air $\rho$ is $1.2\,kg\,m ^{-3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be $\left( g =10\,m / s ^2\right)$
JEE MAIN 2023, Diffcult
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$P _2 A - P _1 A =5.4 \times 10^5 \times g$
$P _2- P _1=\frac{5.4 \times 10^6}{500}=5.4 \times 2 \times 10^2 \times 10$
$=10.8 \times 10^3$
$P _2+0+\frac{1}{2} \rho V _2^2= P _1+0+\frac{1}{2} \rho V _1^2$
$P_2-P_1=\frac{1}{2} \rho\left(V_1^2-V_2^2\right)=\frac{1}{2} \rho\left(V_1-V_2\right)\left(V_1+V_2\right)$
$10.8 \times 10^3=\frac{1}{2} \times 1.2\left( V _1- V _2\right) \times 2 \times 3 \times 10^2$
$10.8 \times 10=3.6\left( V _1- V _2\right)$
$V _1- V _2=30$
$\left(\frac{ V _1- V _2}{ V }\right) \times 100=\frac{30}{300} \times 100=10 \%$
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