A spherical soap bubble A of radius 2 cm is formed inside another bubble B of radius 4 cm. Show that the radius of a single soap bubble which maintance the same pressure difference as inside the smaller and outside the larger soap bubble is lesser than radius of both soap bubbles A and B.

Explanation

Excess of pressure inside the liquid due to surface tension,
`DeltaP=(2T)/(R)`
Where T - surface tension
In the case of soap bubbles, the excess of pressure inside the soap bubble,
`DeltaP_(b)=(4T)/(R)`
Excess of pressure of air inside the bigger bubble
`DeltaP_("bigger")=(4T)/(4)=T`
Excess of pressure of air inside the smaller bubble
`DeltaP_("smaller")=(4T)/(2)=2T`
Air pressure different between the smaller bubble and the atmosphere will be equal to the sum of excess pressure inside the bigger and smaller bubbles.
`{:("Pressure"),("difference"):}}DeltaP=DeltaP_("bigger")+DeltaP_("smaller")=T+2T=3T`
Excess pressure inside a single soap bubble
`=(4T)/(R)=(4T)/(4)=T`
`therefore` Pressure different of single soap bubble less than the radius of both `Tlt3T`.