A metal cube is placed in an empty vessel. When water is filled in the vessel so that the cube is completely immersed in the water, the force on the bottom of the vessel in contact with the cube:
1. will increase
2. will decrease
3. will remain the same
4. will become zero

A wooden object floats in water kept in a beaker. The object is near a side of the beaker (figure). Let \(P_1,\) \(P_2,\) \(P_3\) be the pressures at the three points A, B and C of the bottom as shown in the figure.

Then:
1. \(P_1=P_2=P_3\)
2. \(P_1<P_2<P_3\)
3. \(P_1=P_2\neq P_3\)
4. \(P_2=P_3\neq P_1\)

A closed cubical box is completely filled with water is accelerated horizontally towards right with an acceleration a. The resultant normal force by the water on the top of the box:

1. passes through the centre of the top.

2. passes through a point to the right of the centre.

3. passes through a point to the left of the centre.

4. becomes zero.

Consider the situation of the previous problem. Let the water push the left wall by a force F₁ and the right wall by a force F₂

1. F₁ = F₂

2. F₁ > F₂

3. F₁ < F₂

4. The information is insufficient to know the relation between F₁ and F₂

Previous problem: A closed cubical box is completely filled with water is accelerated horizontally towards right with an acceleration a.

Water enters through end \(A\) with a speed \(v_1\) and leaves through end \(B\) with a speed \(v_2\) of a cylindrical tube AB. The tube is always completely filled with water. In case I the tube is horizontal, in case II it is vertical with the end \(A\) upward and in case III it is vertical with the end \(B\) upward. We have \(v_1=v_2\) for:
1. case I
2. case II
3. case III
4. each one

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

A solid floats in a liquid in a partially dipped position. Then,

Choose the correct option:
1. (a), (b) and (c)
2. (b), (c) and (d)
3. (c), (d) and (a)
4. all of these