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
(a) 9 cm                                   
(b) 6 cm
(c) 4.5 cm                               
(d) 2.25 cm

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

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