A hemispherical bowl just floats without sinking in a liquid of density $1.2\times {10}^3$ $\mathrm{kg}/{\mathrm{m}}^3$. If the outer diameter and the density of the material of the bowl are 1 m and $2\times {10}^4$ $\mathrm{kg}/{\mathrm{m}}^3$ respectively, then the inner diameter of the bowl will be:
1. 0.94 m
2. 0.97 m
3. 0.98 m
4. 0.99 m

In making an alloy, a substance of specific gravity ${\mathrm{s}}_1$ and mass ${\mathrm{m}}_1$ is mixed with another substance of specific gravity ${\mathrm{s}}_2$ and mass ${\mathrm{m}}_2$ ; then the specific gravity of the alloy is

1. $\left(\frac{{\mathrm{m}}_1+{\mathrm{m}}_2}{{\mathrm{s}}_1+{\mathrm{s}}_2}\right)$     
               
2. $\left(\frac{{\mathrm{s}}_1{\mathrm{s}}_2}{{\mathrm{m}}_1+{\mathrm{m}}_2}\right)$

3. $\frac{{\mathrm{m}}_1+{\mathrm{m}}_2}{{\displaystyle \left(\frac{{\mathrm{m}}_1}{s_1}+\frac{m_2}{{\mathrm{s}}_2}\right)}}$ 
               
4. $\frac{{\displaystyle \left(\frac{{\mathrm{m}}_1}{{\mathrm{s}}_1}+\frac{{\mathrm{m}}_2}{{\mathrm{s}}_2}\right)}}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3. For this sphere to float with its entire volume submerged underwater, the ratio of mass of concrete to mass of sawdust will be:
1. 8 
2. 4
3. 3                                       
4. Zero

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

(2) 5 × 5 × 5 × 5 gf                           

(3) 4 × 4 × 4 × 4 gf

(4) 5 × 4 × 4 × 4 gf                           

(d) 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