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 - 

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

Bernoulli's theorem is based on :

1.  conservation of energy

2.  conservation of mass

3.  conservation of momentum

4.  conservation of angular momentum

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

1.  $\frac{{\mathrm{r}}_1 + {\mathrm{r}}_2}{2}$

2.  $\frac{{\mathrm{r}}_1{\mathrm{r}}_2}{{\mathrm{r}}_1 - {\mathrm{r}}_2}$

3.  $\sqrt{{\mathrm{r}}_1{\mathrm{r}}_1}$

4.  $\sqrt{{\mathrm{r}}_1^2 + {\mathrm{r}}_2^2}$

The energy needed in breaking of a drop of liquid of radius R into n drops of radius r is given by (T is surface tension and P is atmospheric pressure) :

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

2.  $\left(4/3{\mathrm{\pi r}}^2\mathrm{n}-4/3{\mathrm{\pi R}}^3\right)\mathrm{T}$

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

4.  $\left(8{\mathrm{\pi r}}^2\mathrm{n}-8{\mathrm{\pi R}}^2\right)\mathrm{T}$

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 :

$\left(1\right) \sqrt{2g\left(H-h\right)}$
$\left(2\right) \sqrt{g\left(H-h\right)}$
$\left(3\right) \sqrt{2gh}$
$\left(4\right) \sqrt{4h\left(H-h\right)}$

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

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

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 $\mathrm{\pi }$

A cubical vessel of height 1 m is full of water. Find the work done in pumping out whole water.

1. 49 J

2. 490 J

3. 4900 J

4. 49000 J