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. $5\times {10}^{-2} \mathrm{joule}$                         

2. $2\times {10}^{-2} \mathrm{joule}$

3. $4\times {10}^{-4} \mathrm{joule}$                         

4. $0.8\times {10}^{-1} \mathrm{joule}$

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 =$7.2\times {10}^{-2} \mathrm{N}/\mathrm{m}$)

1. $7.22\times {10}^{-6} \mathrm{Joule}$                         

2. $1.44\times {10}^{-5} \mathrm{Joule}$

3. $2.88\times {10}^{-5} \mathrm{Joule}$                         

4. $5.76\times {10}^{-5} \mathrm{Joule}$

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 $0.465 \mathrm{J}/{\mathrm{m}}^2$) 

1. $23.4 \mathrm{\mu J}$                             

2. $18.5 \mathrm{\mu J}$

3. $26.8 \mathrm{\mu J}$                              

4. $16.8 \mathrm{\mu J}$

Two small drops of mercury, each of radius r, coalesce to form a single large drop. The ratio of the total surface energies before and after the change is

1. $1:2^{1/3}$                          2. $2^{1/3} :1$

3. 2:1                              4. 1:2