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 \(1.5\times10^{-2}\) N (which includes the small weight of the slider). The length of the slider is \(30\) cm. The surface tension of the film is:
1. \(3.5\times10^{-2}\) Nm^-1
2. \(2.5\times10^{-2}\) Nm^-1
3. \(3.5\times10^{-3}\) Nm^-1
4. \(2.5\times10^{-3}\) Nm^-1

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?

A \(50\) kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter of \(1.0\) cm. What is the pressure exerted by the heel on the horizontal floor?
1. \( 6.24 \times 10^6 ~\mathrm{Nm}^{-2} \)
2. \( 4.21 \times 10^5 ~\mathrm{Nm}^{-2} \)
3. \( 20 \times 10^6 ~\mathrm{Nm}^{-2}\)
4. \( 1.01 \times 10^5~ \mathrm{Nm}^{-2}\)

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