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

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

Two solids A and B float in water. It is observed that A floats with $\frac{1}{2}$ of its body immersed in water and B floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of A to that of B is
1. 4 : 3                                 
2. 2 : 3
3. 3 : 4                                 
4. 1 : 2

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?

Two pieces of metal when immersed in a liquid have equal upthrust on them; then

1. Both pieces must have equal weights

2. Both pieces must have equal densities

3. Both pieces must have equal volumes

4. Both are floating to the same depth

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:
            

Construction of submarines is based on 
1. Archimedes’ principle               

2. Bernoulli’s theorem

3. Pascal’s law                             

4. Newton’s laws