Water is flowing in streamline motion through a tube with its axis horizontal. Consider two points A and B in the tube at the same horizontal level.

(a) The pressures at A and B are equal for any shape of the tube.

(b) The pressures are never equal.

(c) The pressures are equal if the tube has a uniform cross-section.

(d) The pressures may be equal even if the tube has a non–uniform cross-section.

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

There is a small hole near the bottom of an open tank filled with a liquid. The speed of the water ejected does not depend on:

Choose the correct option:

By a surface of a liquid we mean

1. a geometrical plane like x = 0

2. all molecules exposed to the atmosphere

3. a layer of thickness of the order of 10^–8 m

4. a layer of thickness of the order of 10^–4 m

An ice cube is suspended in vacuum in a gravity-free hall. As the ice melts it

1. will retain its cubical shape

2. will change its shape to spherical

3. will fall down on the floor of the hall

4. will fly up

When water droplets merge to form a bigger drop:

Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution is S, the work done in the process is

1. 8 \(\pi\) r² S

2. 12 \(\pi\) r² S

3. 16 \(\pi\) r² S

4. 24 \(\pi\) r² S

If more air is pushed in a soap bubble, the pressure in it

1. decreases

2. increases

3. remains same

4. becomes zero

If two soap bubbles of different radii are connected by a tube,

The figure shows a capillary tube of radius r dipped into water. If the atmospheric pressure is P₀, the pressure at point A is pressure at point A is

1. \(P_{0}\)

2. \(P_{0}+\frac{2 S}{r}\)

3. \(P_{0}-\frac{2 S}{r}\)

4. \(P_{0}-\frac{4 S}{r}\)

The excess pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first bubble is n times the volume of the second where n is

1. 4

2. 2

3. 1

4. 0.125