Two solids A and B float in water. It is observed that A floats with $\frac{1}{2}$ of its body immersed in water and B floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of A to that of B is
1. 4 : 3                                 
2. 2 : 3
3. 3 : 4                                 
4. 1 : 2

A boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one, how will it affect the level of water?

Two pieces of metal when immersed in a liquid have equal upthrust on them; then

1. Both pieces must have equal weights

2. Both pieces must have equal densities

3. Both pieces must have equal volumes

4. Both are floating to the same depth

A candle of diameter \(d\) is floating on a liquid in a cylindrical container of diameter \(D(D>>d)\) as shown in the figure. If it is burning at the rate of \(2~\text{cm/hour}\) then the top of the candle will:
            

Construction of submarines is based on 
1. Archimedes’ principle               

2. Bernoulli’s theorem

3. Pascal’s law                             

4. Newton’s laws

In which one of the following cases will the liquid flow in a pipe be most streamlined  ?

1. Liquid of high viscosity and high density flowing through a pipe of small radius

2. Liquid of high viscosity and low density flowing through a pipe of small radius

3. Liquid of low viscosity and low density flowing through a pipe of large radius

4. Liquid of low viscosity and high density flowing through a pipe of large radius

Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of flow of water in the pipe of 2 cm diameter is -

1. 4 times that in the other pipe

2. 3 times that in the other pipe

3. 2 times that in the other pipe

4. 6 times that in the other pipe

An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is

1.    3.0 m/s                          

2. 1.5 m/s                     

3. 1.0 m/s                             

4. 2.25 m/s

The velocity of kerosene oil in a horizontal pipe is \(5 ~\text{m/s}.\) If \(g = 10 ~\text{m/s} ^2 ,\) then the velocity head of oil will be:
1. \(1.25 ~\text m\)
2. \(12.5 ~\text m\)
3. \(0.125 ~\text m\)       
4. \(125 ~\text m\)

In the following fig. is shown the flow of liquid through a horizontal pipe. Three tubes A, B and C are connected to the pipe. The radii of the tubes A, B and C at the junction are respectively 2 cm, 1 cm and 2 cm. It can be said that the

1. Height of the liquid in the tube A is maximum

2. Height of the liquid in the tubes A and B is the same

3. Height of the liquid in all the three tubes is the same

4. Height of the liquid in the tubes A and C is the same