When two soap bubbles of radius ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ (${\mathrm{r}}_2$>${\mathrm{r}}_1$) coalesce, the radius of curvature of the common surface is

1. ${\mathrm{r}}_2-{\mathrm{r}}_1$

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

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

4. ${\mathrm{r}}_2+{\mathrm{r}}_1$

A long cylindrical glass vessel has a small hole of radius 'r' at its bottom. The depth to which the vessel can be lowered vertically in the deep water bath (surface tension T) without any water entering inside is

1. $4\mathrm{T}/\mathrm{r\rho g}$

2. $3\mathrm{T}/\mathrm{r\rho g}$

3. $2\mathrm{T}/\mathrm{r\rho g}$

4. $\mathrm{T}/\mathrm{r\rho g}$

The excess of pressure inside a soap bubble than that of the outer pressure is

1. $\frac{2\mathrm{T}}{\mathrm{r}}$

2. $\frac{4\mathrm{T}}{\mathrm{r}}$

3. $\frac{\mathrm{T}}{2\mathrm{r}}$

4. $\frac{\mathrm{T}}{\mathrm{r}}$

The pressure of air in a soap bubble of 0.7cm diameter is 8 mm of water above the pressure outside. The surface tension of the soap solution is

1. 100 dyne/cm

2. 68.66 dyne/cm

3. 137 dyne/cm

4. 150 dyne/cm

The pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. The ratio between their volumes is

1. 102 : 101

2. $(102{)}^3:(101{)}^3$

3. 8 : 1

4. 2 : 1

The radii of two soap bubbles are ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ . In isothermal conditions, two meet together in a vacuum. Then the radius of the resultant bubble is given by

1. $\mathrm{R}=({\mathrm{r}}_1+{\mathrm{r}}_2)/2$

2. $\mathrm{R}={\mathrm{r}}_1({\mathrm{r}}_1{\mathrm{r}}_2+{\mathrm{r}}_2)$

3. ${\mathrm{R}}^2={\mathrm{r}}_1^2+{\mathrm{r}}_2^2$ 

4. $\mathrm{R}={\mathrm{r}}_1+{\mathrm{r}}_2$

When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure is equal to that of a column of water height H, then the depth of the lake is

1. H

2. 2H

3. 7H

4. 8H

The excess pressure of one soap bubble is four times more than the other. Then the ratio of the volume of the first bubble to another one is 

1. 1 : 64

2. 1 : 4

3. 64 : 1

4. 1 : 2

There are two liquid drops of different radii. The excess pressure inside over the outside is 

1. More in the big drop

2. More in the small drop

3. Equal in both drops

4. There is no excess pressure inside the drops

If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake

1. 10m

2. 20m

3. 60m

4. 30m