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

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

Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of flow of water in the pipe of 2 cm diameter is -

1. 4 times that in the other pipe

2. 3 times that in the other pipe

3. 2 times that in the other pipe

4. 6 times that in the other pipe

An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is

1.    3.0 m/s                          

2. 1.5 m/s                     

3. 1.0 m/s                             

4. 2.25 m/s