The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are $v$ and $2v$ respectively. The density of air is $\rho $ and surface area of wing is $A$ . The dynamic lift on the wing is

- A
$\frac{1}{2}\rho {v^2}\,A$

- B
$\rho {v^2}\,A$

- C
$\frac{3}{2}\rho {v^2}\,A$

- D
$2\rho {v^2}\,A$

Air streams horizontally past an air plane. The speed over the top surface is $60 \,m / s$ and that under the bottom surface is $45 \,m / s$. The density of air is $1.293 \,kg / m ^3$, then the difference in pressure is ....... $N / m ^2$

Water flows in a horizontal tube as shown in figure. The pressure of water changes by $600\, N/ m^2$ between $A$ and $B$ where the area of crosssection are $30\, cm^2$ and $15\, cm^2$ respectively. Find the rate of flow of water through the tube.

Water is flowing through a horizontal tube according to the figure. Its diameter at two points are $0.3\,m$ and $0.1\,m$ respectively. Pressure difference between these two points is equal to $0.8\,m$ of water column. Find rate of flow of water in the tube ..... $ltr/s$

A body of density $\rho$ is dropped from rest from a height $h$ into a lake of density $\sigma$, where $\sigma > \rho$. Neglecting all dissipative forces, the maximum depth to which the body sinks before returning to float on surface ..........

A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^2$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is______ $\mathrm{kg}$. (Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

- [JEE MAIN 2024]