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 ....... $cm$

The surface tension and vapour pressure of water at $20^{°}$ $\mathrm{C}$ is $7.28 \times {10^{ - 2}}\,{\rm{N/m}}$ and $2.33 \times {10^3}\,{{\rm{P}}_{\rm{a}}}$ respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at $20^{°}$ $\mathrm{C}$ ?

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.......

Pressure inside two soap bubbles are $1.02 \,atm$ and $1.05 \,atm$ respectively. The ratio of their surface area is .........

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

The excess pressure in a soap bubble is double that in other one. The ratio of their volume is .............