A metallic block of density 5 gm ${\mathrm{cm}}^{-3}$ and having dimensions 5 cm × 5 cm × 5 cm is weighed in water. Its apparent weight will be

1. 5 × 5 × 5 × 5 gf                           

2. 4 × 4 × 4 × 4 gf

3. 5 × 4 × 4 × 4 gf                           

4. 4 × 5 × 5 × 5 gf

A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of g/3, the fraction of volume immersed in the liquid will be

1. $\frac{1}{2}$                                 

2. $\frac{3}{8}$

3. $\frac{2}{3}$                                 

4. $\frac{3}{4}$

A silver ingot weighing 2.1 kg is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of silver is 10.5. The tension in the string in kg-wt is

1. 1.6                                             

2. 1.94

3. 3.1                                           

4. 5.25

Two solids A and B float in water. It is observed that A floats with half its volume immersed and B floats with 2/3 of its volume immersed. Compare the densities of A and B

1. 4:3                         

2. 2:3

3. 3:4                         

4. 1:3

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

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

Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This law was first formulated by:

1. Bernoulli                               

2. Archimedes

3. Boyle                                     

4. Pascal

 A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body ?
1. It will slowly come back to its earlier position

2. It will remain submerged, where it is left

3. It will sink

4. It will come out violently

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 solid sphere of density $\mathrm{\eta }$ ( > 1) times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m, then the tension in the string is given by:

1. $\left(\frac{\mathrm{\eta }-1}{\mathrm{\eta }}\right)\mathrm{mg}$                              

2. $\mathrm{\eta mg}$

3. $\frac{mg}{\mathrm{\eta }}$                                       

4. $(\mathrm{\eta }-1)\mathrm{mg}$

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