Bernoulli's theorem is based on the conservation of:

Water is flowing through a long horizontal tube. Let \(P_A\) and \(P_B\) be the pressures at two points \(A\) and \(B\) of the tube.

Water and mercury are filled in two cylindrical vessels up to the same height. Both vessels have a hole in the wall near the bottom. The velocity of water and mercury coming out of the holes are v₁ and v₂ respectively.

1. v₁ = v₂

2. v₁ = 13.6 v₂

3. v₁ = v₂/13.6

4. v₁ = \(\sqrt{13.6}\)v₂

A large cylindrical tank has a hole of area A at its bottom. Water is poured into the tank by a tube of equal cross-sectional area A ejecting water at the speed v.

1. The water level in the tank will keep on rising

2. No water can be stored in the tank

3. The water level will rise to a height v²/2 g and then stop

4. The water level will oscillate

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: