The fraction of a floating object of volume ${\mathrm{V}}_0$ and density ${\mathrm{d}}_0$ above the surface of a liquid of density d will be

1. $\frac{{\mathrm{d}}_0}{\mathrm{d}}$                                       

2. $\frac{{\mathrm{dd}}_0}{\mathrm{d}+{\mathrm{d}}_0}$

3. $\frac{\mathrm{d}-{\mathrm{d}}_0}{\mathrm{d}}$                                   

4. $\frac{{\mathrm{dd}}_0}{\mathrm{d}-{\mathrm{d}}_0}$

 A body is just floating on the surface of a liquid. The density of the body is the same as that of the liquid. The body is slightly pushed down. What will happen to the body?

A cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with acceleration downwards, the length of spring

1. Increases                                         

2. Decreases

3. Remains unchanged                         

4. None of these

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