A soap bubble in vacuum has a radius of $3 \,cm$ and another soap bubble in vacuum has a radius of $4 \,cm$. If the two bubbles coalesce under isothermal condition, then the radius of the new bubble is ....... $cm$

Air (density $\rho$ ) is being blown on a soap film (surface tension $T$ ) by a pipe of radius $R$ with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed $v$ is $\frac{1}{2} \rho v^{2}$, the speed at which the bubble formed is

Two soap bubbles of radii $3r$ and $4r$ in contact with each other. The radius of curvature of the interface between bubbles is

A capillary type tube $AB$ is connected to a manometer $M$ as shown in the figure. Stopper $S$ controls the flow of air. $AB$ is dipped into a soap solution where surface tension is $T$ . On opening the stopper for a while, a bubble is formed at $B$ end of the manometer and the level difference in manometer limbs is $h$ . If $P$ is the density of manometer soap solution and $r$ the radius of curvature of bubble, then the surface tension $T$ of the liquid is given by ...

If the radius of a soap bubble is four times that of another, then the ratio of their excess pressures will be

If two glass plates have water between them and are separated by very small distance ( see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is $R$ and surface tension of water is $T$ then the pressure in water between the plates is lower by