A soap bubble in a form of circular tube having radius of curvature $R$ and radius of curvature perpendicular to it is $5R$ . Find the excess pressure in the bubble :

A spherical soap bubble of radius $3\,cm$ is formed inside another spherical soap bubble of radius $6\,cm$. If the internal pressure of the smaller bubble of radius $3\,cm$ in the above system is equal to the internal pressure of the another single soap bubble of radius $r\,cm$. The value of $r$ is.......

Write the equation of excess pressure (pressure difference) for the bubble in air and bubble in water.

Fill in the Blank :

$(i)$ Bubble in water have .......... free surface.

$(ii)$ Bubble in air have .......... free surface.

$(iii)$ Rain drop have .......... free surface.

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

Derive the formula for excess of pressure (pressure difference) inside the drop and bubble.