A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water ?

1. V/2                       

2. V/3

3. V/4                       

4. V

A ball whose density is $0.4\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$ falls into water from a height of 9 cm . To what depth does the ball sink

1. 9 cm                                   

2. 6 cm

3. 4.5 cm                                 

4. 2.25 cm

If two pieces of metal when immersed in a liquid have equal upthrust on them, then:

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

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 following figure shows 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 \(2~\text{cm},1~\text{cm}\) and \(2~\text{cm}.\) It can be said that:

A manometer connected to a closed tap reads $3.5\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$. When the valve is opened, the reading of manometer falls to $3.0\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$ , then velocity of flow of water is

1. 100 m/s                                       

2. 10 m/s

3. 1 m/s                                           

4. $10\sqrt{10}$ m/s

A large tank filled with water to a height ‘h’ is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to $\frac{\mathrm{h}}{2}$ and from $\frac{\mathrm{h}}{2}$ to zero is

1. $\sqrt{2}$                                               

2. $\frac{1}{\sqrt{2}}$

3. $\sqrt{2}-1$                                         

4. $\frac{1}{\sqrt{2}-1}$

A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m/s) through a small hole on the side wall of the cylinder near its bottom is

1. 10                                       

2. 20

3. 25.5                                     

4. 5

There is a hole in the bottom of a tank having water. If the total pressure at the bottom is \(3\) atm \((1~\text{atm}=10^5~\text{N}/\text{m}^2),\) then the velocity of water flowing from the hole is:
1. \(\sqrt{400}~~\text{m/s}\)
2. \(\sqrt{600}~~\text{m/s}\)
3. \(\sqrt{60}~~\text{m/s}\)
4. none of these