A capillary tube of radius \(r\) is immersed in water and water rises in it to a height \(h.\) The mass of the water in the capillary is \(5\) g. Another capillary tube of radius \(2r\) is immersed in water. The mass of water that will rise in this tube is:
1. \(5.0\) g
2. \(10.0\) g
3. \(20.0\) g
4. \(2.5\) g

In a horizontal pipe of non-uniform cross-section, water flows with a velocity of 1 m s${}^{-1}$ at a point where the diameter of the pipe is 20 cm. The velocity of water (m s${}^{-1}$) at a point where the diameter of the pipe is 5 cm is:
1. 8
2. 16
3. 24
4. 32

A liquid does not wet the solid surface if the angle of contact is :

(1) equal to 45°

(2) equal to 60°

(3) greater than 90°

(4) zero

A barometer is constructed using a liquid (density = 760 kg/${\mathrm{m}}^3$). What would be the height of the liquid column, when a mercury barometer reads 76 cm? (density of mercury = 13600 kg/${\mathrm{m}}^3$)

(1) 1.36 m

(2) 13.6 m

(3) 136 m

(4) 0.76 m

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.

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

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?

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