Water flows in a streamlined manner through a capillary tube of radius a, the pressure difference being P and the rate of flow Q. If the radius is reduced to a/2 and the pressure increased to 2P, the rate of flow becomes

1. $4\mathrm{Q}$                          

2. $\mathrm{Q}$

3. $\frac{\mathrm{Q}}{4}$                         

4. $\frac{\mathrm{Q}}{8}$

Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s. The water then enters into a tube of diameter 2 cm. The velocity of water in the other pipe is

1. 3 m/s                                       

2. 6 m/s

3. 12 m/s                                       

4. 8 m/s

What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are $\mathrm{\rho }$ and $\mathrm{\sigma }$ respectively, and the viscosity of the liquid is $\mathrm{\eta }$).

1. $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}\left(\mathrm{\rho }-2\mathrm{\sigma }\right)$                     

2. $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}\left(2\mathrm{\rho }-\mathrm{\sigma }\right)$

3. $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}\left(\mathrm{\rho }-\mathrm{\sigma }\right)$                       

4. $\frac{2{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}\left(\mathrm{\rho }-\mathrm{\sigma }\right)$

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

A homogeneous solid cylinder of length L(L<H/2) . Cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure ${\mathrm{P}}_0$. Then density D of solid is given by

1. $\frac{5}{4}\mathrm{d}$                     

2. $\frac{4}{5}\mathrm{d}$

3. $\mathrm{d}$                         

4. $\frac{d}{5}$

A block of ice floats on a liquid of density 1.2 $g/c{m}^3$ in a beaker. The level of liquid when ice completely melts-

1. Remains same                         

2. Rises

3. Lowers                                   

4. (1), (2) or (3)

A lead shot of 1mm diameter falls through a long column of glycerine. The variation of its velocity v with distance covered is represented by

1. 

2. 

3. 

4. 

The surface tension of liquid is 0.5 N/m. If a film is held on a ring of area 0.02 ${\mathrm{m}}^2$, its surface energy is

1. $5\times {10}^{-2}<mspace\; width="1em"></mspace>\mathrm{joule}$                         

2. $2\times {10}^{-2}<mspace\; width="1em"></mspace>\mathrm{joule}$

3. $4\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{joule}$                         

4. $0.8\times {10}^{-1}<mspace\; width="1em"></mspace>\mathrm{joule}$

A film of water is formed between two straight parallel wires of length 10cm each separated by 0.5 cm. If their separation is increased by 1 mm while still maintaining their parallelism, how much work will have to be done (Surface tension of water =$7.2\times {10}^{-2}<mspace\; width="1em"></mspace>\mathrm{N}/\mathrm{m}$)

1. $7.22\times {10}^{-6}<mspace\; width="1em"></mspace>\mathrm{Joule}$                         

2. $1.44\times {10}^{-5}<mspace\; width="1em"></mspace>\mathrm{Joule}$

3. $2.88\times {10}^{-5}<mspace\; width="1em"></mspace>\mathrm{Joule}$                         

4. $5.76\times {10}^{-5}<mspace\; width="1em"></mspace>\mathrm{Joule}$

A drop of mercury of radius 2 mm is split into 8 identical droplets. Find the increase in surface energy. (Surface tension of mercury is $0.465<mspace\; width="1em"></mspace>\mathrm{J}/{\mathrm{m}}^2$) 

1. $23.4<mspace\; width="1em"></mspace>\mathrm{\mu J}$                             

2. $18.5<mspace\; width="1em"></mspace>\mathrm{\mu J}$

3. $26.8<mspace\; width="1em"></mspace>\mathrm{\mu J}$                              

4. $16.8<mspace\; width="1em"></mspace>\mathrm{\mu J}$