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

In capillary tube, pressure below the curved surface of water will be 

(1) Equal to atmospheric

(2) Equal to upper side pressure

(3) More than upper side pressure

(4) Lesser than upper side pressure

Two bubbles A and B are joined through a narrow tube where bubble A is bigger. Then 

1. The size of A will increase

2. The size of B will increase

3. The size of B will increase until the pressure equals

4. None of these

Two soap bubbles have different radii but their surface tension is the same. Mark the correct statement

(1) Internal pressure of the smaller bubble is higher than the internal pressure of the larger bubble

(2) Pressure of the larger bubble is higher than the smaller bubble

(3) Both bubbles have the same internal pressure

(4) None of the above

Due to capillary action, a liquid will rise in a tube, if the angle of contact is 

(1) Acute

(2) Obtuse

(3) 90°

(4) Zero

Two parallel glass plates are dipped partly in the liquid of density 'd' keeping them vertical. If the distance between the plates is 'x', surface tension for liquids is T and the angle of contact is $\mathrm{\theta }$, then rise of liquid between the plates due to capillary will be 

(1) $\frac{\mathrm{T} \mathrm{cos\theta }}{\mathrm{xd}}$

(2) $\frac{2\mathrm{T} \mathrm{cos\theta }}{\mathrm{xdg}}$

(3) $\frac{2\mathrm{T} }{\mathrm{xdgcos\theta }}$

(4) $\frac{\mathrm{T} \mathrm{cos\theta }}{\mathrm{xdg}}$