If a soap bubble of radius 3 cm coalesce with another soap bubble of radius 4 cm under isothermal conditions, the radius of the resultant bubble formed is in cm-

1. 7

2. 1

3. 5

4. 12

$\mathrm{Water} \mathrm{flows} \mathrm{through} \mathrm{a} \mathrm{non}-\mathrm{uniform} \mathrm{tube}$
$\mathrm{of} \mathrm{area} \mathrm{of} \mathrm{cross} \mathrm{sections} \mathrm{A}, \mathrm{B}, \mathrm{and} \mathrm{C} \mathrm{whose}$
$\mathrm{values} \mathrm{are} 25, 15, \mathrm{and} 35 {\mathrm{cm}}^2 \mathrm{respectively}.$
$\mathrm{The} \mathrm{ratio} \mathrm{of} \mathrm{the} \mathrm{velocities} \mathrm{of} \mathrm{water} \mathrm{at} \mathrm{the}$
$\mathrm{sections} \mathrm{A}, \mathrm{B}, \mathrm{and} \mathrm{C} \mathrm{is}-$

1.  5:3:7

2.  7:3:5

3.  21:35:15

4.  1:1:1

Several spherical drops of a liquid each of radius r coalesce to form a single drop of radius R. If T is the surface tension, then the energy liberated will be - 

$1. 4{\mathrm{\pi R}}^3\mathrm{T} \left(\frac{1}{\mathrm{r}}-\frac{1}{\mathrm{R}}\right)$
$2. 2{\mathrm{\pi R}}^3\mathrm{T} \left(\frac{1}{\mathrm{r}}-\frac{1}{\mathrm{R}}\right)$
$3. \frac{4}{3}{\mathrm{\pi r}}^2\mathrm{T} \left(\frac{1}{\mathrm{r}}-\frac{1}{\mathrm{R}}\right)$
$4. 2\mathrm{\pi RT} \left(\frac{1}{\mathrm{R}}-\frac{1}{\mathrm{r}}\right)$

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

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 area of cross-section of the wider tube shown in the figure is \(800~\text{cm}^2.\) If a mass of \(12~\text{kg}\) is placed on the massless piston, then the difference in heights \(h\) of the levels of water in the two tubes will be:

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

A tank is filled with water up to a height H. A hole is made at a depth h below the free surface of the water in the tank. The water coming out of the orifice strikes at a distance S from the walls of the tank. Then S is given by :
1. \(\sqrt{2 g(H-h)}\)
2. \(\sqrt{g(H-h)}\)
3. \(\sqrt{2 g h}\)
4. \(\sqrt{4 h(H-h)}\)

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.  $100°$  

2.  $140°$

3.  $180°$

4.    $60°$