For the figures given below, the correct observation is:
              

1.	pressure at the bottom of the tank (a) is greater than at the bottom of the tank (b).
2.	pressure at the bottom of the tank (a) is lesser than at the bottom of (b).
3.	pressure depends upon the shape of the container.
4.	pressure at the bottom of (a) and (b) are the same.

An iceberg of density \(900 ~\text{kg/m}^ 3\)${\mathrm{}}^{}$ is floating in the water of density \(1000 ~\text{kg/m}^ 3.\) The percentage of the volume of ice cube outside the water is: 
1. \(20\%      \)                                 
2. \(35\%      \)
3. \(10\%      \)                                    
4. \(25\%      \)

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

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:

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 boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one, how will it affect the level of water?

A candle of diameter \(d\) is floating on a liquid in a cylindrical container of diameter \(D(D>>d)\) as shown in the figure. If it is burning at the rate of \(2~\text{cm/hour}\) then the top of the candle will:
            

The velocity of kerosene oil in a horizontal pipe is \(5 ~\text{m/s}.\) If \(g = 10 ~\text{m/s} ^2 ,\) then the velocity head of oil will be:
1. \(1.25 ~\text m\)
2. \(12.5 ~\text m\)
3. \(0.125 ~\text m\)       
4. \(125 ~\text m\)

An L-shaped tube with a small orifice is held in a water stream as shown in fig. The upper end of the tube is 10.6 cm above the surface of water. What will be the height of the jet of water coming from the orifice? Velocity of water stream is 2.45 m/s.
         

1. Zero                                         
2. 20.0 cm                   
3. 10.6 cm                                   
4. 40.0 cm
 

An incompressible fluid flows steadily through a cylindrical pipe which has a radius \(2r\) at the point \(A\) and a radius \(r\) at the point \(B\) further along the flow direction. If the velocity at the point \(A\) is \(v,\) its velocity at the point \(B\) is:
1. \(2v\)                               
2. \(v\)
3. \(v/2\)                            
4. \(4v\)