A \(\mathrm U\text -\)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:

1.	\(3.5\times10^{-2}~\text{Nm}^{-1}\)	2.	\(2.5\times10^{-2}~\text{Nm}^{-1}\)
3.	\(3.5\times10^{-3}~\text{Nm}^{-1}\)	4.	\(2.5\times10^{-3}~\text{Nm}^{-1}\)

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 (${20}^0<mspace\; width="1em"></mspace>C$) is 4.65 × 10^–1 N m^–1. The atmospheric pressure is 1.01 × 10⁵ Pa.

$\left(1\right)<mspace\; width="1em"></mspace>2.30\times {10}^5<mspace\; width="1em"></mspace>Pa$
$\left(2\right)<mspace\; width="1em"></mspace>2.01\times {10}^{5<mspace\; width="1em"></mspace>}Pa$
$\left(3\right)<mspace\; width="1em"></mspace>3.01\times {10}^5<mspace\; width="1em"></mspace>Pa$
$\left(4\right)<mspace\; width="1em"></mspace>1.01\times {10}^5<mspace\; width="1em"></mspace>Pa$

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?

$1.<mspace\; width="1em"></mspace>\mathrm{\rho Avt}$
$2.<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\frac{1}{2}\mathrm{\rho Avt}$
$3.<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>2<mspace\; width="1em"></mspace>\mathrm{\rho Avt}$
$4.<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\frac{3}{2}<mspace\; width="1em"></mspace>\mathrm{\rho Avt}$

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

A \(\mathrm U\text -\)tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with \(10.0~\text{cm}\) of water in one arm and \(12.5~\text{cm}\) of spirit in the other. What is the specific gravity of the spirit?

1. \(0.8\)
2. \(0.3\)
3. \(0.5\)
4. \(0.7\)

Glycerine flows steadily through a horizontal tube of a length of 1.5 m and a radius of 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 × 10^–3 kg s^–1, what is the pressure difference between the two ends of the tube?
(Density of glycerine = $1.3\times {10}^3$ kg m^–3 and viscosity of glycerine = 0.83 Pa-sec).
1. 7.9 × 10⁻² Pa
2. 8.9 × 10⁻³ Pa
3. 9.8 × 10⁻² Pa
4. 6.7 × 10⁻³ Pa

What is the excess pressure inside a bubble of soap solution of radius \(5.00~\text{mm}?\)
(Given that the surface tension of soap solution at the temperature (\(20^{\circ}\text C\)) is \(2.5\times 10^{-2}~\text{N/m}\))
1. \(10~\text{Pa}\) 
2. \(20~\text{Pa}\) 
3. \(1.06\times 10^{5}~\text{Pa}\) 
4. \(15~\text{Pa}\)