The blades of a windmill sweep out a circle of area A. If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t?

$1. \mathrm{\rho Avt}$
$2. \frac{1}{2}\mathrm{\rho Avt}$
$3. 2 \mathrm{\rho Avt}$
$4. \frac{3}{2} \mathrm{\rho Avt}$

Bernoulli's theorem is applicable in the case of:

In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are $70~\text{ms}^{-1}$ and $63~\text{ms}^{-1}$ respectively. What is the lift on the wing if its area is $2.5~\text{m}^2$? (Take the density of air to be $1.3 ~\text{kg m}^{-3}$)
1. $2.5\times 10^5~\text{N}$
2. $1.5\times 10^5~\text{N}$
3. $2.5\times 10^3~\text{N}$
4. $1.5\times 10^3~\text{N}$

The cylindrical tube of a spray pump has a cross-section of $8.0$ cm² one end of which has $40$ fine holes each of diameter $1.0$ mm. If the liquid flow inside the tube is $1.5$ m-min^–1,  the speed of ejection of the liquid through the holes is:
1. $0.64$ ms^-1
2. $0.74$ ms^-1
3. $0.54$ ms^-1
4. $0.84$ ms^-1

A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and the light slider supports a weight of $1.5\times10^{-2}~\text{N}$ (which includes the small weight of the slider). The length of the slider is $30~\text{cm}.$ The surface tension of the film is:

What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature? The surface tension of mercury at that temperature (${20}^0 C$) is 4.65 × 10^–1 N m^–1. The atmospheric pressure is 1.01 × 10⁵ Pa.

$\left(1\right) 2.30\times {10}^5 Pa$
$\left(2\right) 2.01\times {10}^{5 }Pa$
$\left(3\right) 3.01\times {10}^5 Pa$
$\left(4\right) 1.01\times {10}^5 Pa$

Which one of the following is true from the given statements?

Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density $984~\text{kg/m}^3.$ The height of the wine column for normal atmospheric pressure is:
1. $11.5~\text{m}$
2. $10.5~\text{m}$
3. $9.00~\text{m}$
4. $15.0~\text{m}$

A hydraulic automobile lift is designed to lift cars with a maximum mass of $3000$ kg. The area of the cross-section of the piston carrying the load is $425$ cm². What maximum pressure would the smaller piston have to bear?
1. $3.12\times10^{5}$ Pa
2. $1.01\times10^{5}$ Pa
3. $2.94\times10^{5}$ Pa
4. $6.92\times10^{5}$ Pa