Two spherical soap bubbles of radii r₁ and r₂ in vaccum collapse under isothermal condition. The resulting bubble has radius equal to :

1.  $\frac{{\mathrm{r}}_1<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{r}}_2}{2}<mspace\; width="1em"></mspace>$

2.  $\frac{{\mathrm{r}}_1{\mathrm{r}}_2}{{\mathrm{r}}_1<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>{\mathrm{r}}_2}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

3.  $\sqrt{{\mathrm{r}}_1{\mathrm{r}}_1}<mspace\; width="1em"></mspace>$

4.  $\sqrt{{\mathrm{r}}_1^2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{r}}_2^2}$

 

An incompressible liquid travels as shown in the figure. The speed of the fluid in the lower branch will :

1. 1 m/s

2. 1.5 m/s

3. 2.25 m/s

4. 3 m/s

In the figure below is shown the flow of liquid through a horizontal pipe. Three tubes A, B, and C are connected to the pipe. The radius of the pipe at A, B, and C is respectively 2 cm, 1 cm, and 2 cm. It can be said that the :

 

1. Height of the liquid in the tube A is maximum

2. Height of the liquid in the tubes A and B is the same

3. Height of the liquid in all the three tubes is the same

4. Height of the liquid in the tubes A and C is the same

Water flows through a frictionless duct with a cross-section varying as shown in the figure. Pressure p at points along the axis is represented by
         

1.		2.
3.		4.

The rate of flowing of water from the orifice in a wall of a tank will be more if the orifice is:

1.  Near the bottom

2.  Near the upper end

3.  Exactly in the middle

4.  Does not depend upon the position of the orifice

Two liquid drops have their diameters as 1 mm and 2 mm. The ratio of excess pressure in them is :

1.  1:2

2.  2:1

3.  4:1

4.  1:4

When a cylindrical tube is dipped vertically into a liquid the angle of contact is 140^o. When the tube is dipped with an inclination of 40^o, the angle of contact is- 

1.  $100°<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$  

2.  $140°<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

3.  $180°<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

4.    $60°$

Work of 6.0 x 10${}^{-4}$ Joule is required to be done in increasing the size of a soap film from 10cm x 6cm to 10cm x 11cm. The surface tension of the film is :

1. 5 x 10${}^{-2}$ N/m

2. 6 x 10${}^{-2}$ N/m

3. 1.5 x 10${}^{-2}$ N/m

4. 1.2 x 10${}^{-1}$ N/m

Water flowing from a hose pipe fills a 15-liter container in one minute. The speed of water from the free opening of radius 1 cm is (in ms${}^{-1}$) :

1. 2.5

2. $\frac{\mathrm{\pi }}{2.5}$

3. $\frac{2.5}{\mathrm{\pi }}$

4. 5 $\mathrm{\pi }$

The flow rate from a tap of diameter 1.25 cm is 3 lit/min. The coefficient of viscosity of water is ${10}^{-3}$ Pas. The nature of flow is :

1. Turbulent

2. Laminar

3. Neither laminar nor turbulent

4. data inadequate