A hemispherical bowl just floats without sinking in a liquid of density $1.2\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$. If outer diameter and the density 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 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

1. 5 × 5 × 5 × 5 gf                           

2. 4 × 4 × 4 × 4 gf

3. 5 × 4 × 4 × 4 gf                           

4. 4 × 5 × 5 × 5 gf

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. $\frac{\mathrm{d}-{\mathrm{d}}_0}{\mathrm{d}}$                                   

4. $\frac{{\mathrm{dd}}_0}{\mathrm{d}-{\mathrm{d}}_0}$

 A body is just floating on the surface of a liquid. The density of the body is the same as that of the liquid. The body is slightly pushed down. What will happen to the body?

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 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

If two pieces of metal when immersed in a liquid have equal upthrust on them, then:

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