Question

A plane is in a level flight at a constant speed and each of its two wings has an area of $25m^2$. If the speed of air is $180km{h}^{-1}$ over the lower wing and $234km{h}^{-1}$ over the upper wing surface, the plane's mass is : (Take density of air $=1kg{m}^{-3}$.)

• A. $4.400gm$
• B. $4400gm$
• C. $44.0kg$
• D. $4400kg$

Answer 1

The correct option is D $4400kg$

Applying bernouillis theorem above and below the wing,

$p_1+\frac{1}{2}f{v}_1^2=p_2+\frac{1}{2}f{v}_2^2$
$\Rightarrow p_1-p_2=\frac{1}{2}({65}^2-{50}^2)$
$\Rightarrow p_1-p_2=862.5pa$

So, upthrust on wings=weight of plane

$\Rightarrow \frac{862.5\times 2\times 25}{10}=$mass of plane
$\Rightarrow Mass=4312kg\approx 4400kg$