$A$ capillary tube of radius $r$ is dipped in a liquid of density $\rho$ and surface tension $S$. If the angle of contact is $\theta$,what is the pressure difference between the two surfaces in the beaker and the capillary?

$A$ cylinder with a movable piston contains air under a pressure $p_1$ and a soap bubble of radius $r$. The pressure $p_2$ to which the air should be compressed by slowly pushing the piston into the cylinder for the soap bubble to reduce its size by half will be: (The surface tension is $\sigma$, and the temperature $T$ is maintained constant)

$A$ soap bubble assumes a spherical surface. Which of the following statements is wrong?

$A$ liquid drop of diameter $D$ breaks into $27$ small drops of equal size. If the surface tension of the liquid is $\sigma$,then the change in surface energy is

Two soap bubbles coalesce to form a single bubble. If $V$ is the subsequent change in volume of contained air and $S$ is the change in total surface area, $T$ is the surface tension and $P$ is atmospheric pressure, then which of the following relations is correct?

The surface tension and vapour pressure of a liquid at $25^{\circ} C$ are $8 \times 10^{-2} \text{ Nm}^{-1}$ and $2.5 \times 10^3 \text{ Pa}$ respectively. The radius of the smallest spherical water droplet which can form without evaporating at $25^{\circ} C$ is (in $\mu m$)