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 \(2\) cm, \(1\) cm and \(2\) 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