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 pressure create with S.T of spherical surface of the `= Delta P = (2T)/(R )`
T - surface tension
In case of soap bubbles.
The excess pressure of air inside them is double due to the pressure of two interfaces are inside and one outside.
`Delta P_(b) = (4T)/(R )`
Excess pressure of air inside the bigger bubble
`Delta P_(b) = (4T)/(4) = T`
Excess pressure of air inside the smaller bubble
`Delta P_(s) = (4s)/(R ) = (4T)/(2) = 2T`
Air pressure difference between the smaller bubble and the atmosphere will be equal to the sum of excess pressure inside the bigger and smaller bubbles.
Pressure different `Delta P = Delta P_(b) + Delta P_(s)`
Excess pressire inside a single soap bubble
`= (4T)/(R ) = (4T)/(4) = T`
`:.` Pressure difference of single soap bubble less than radius of both `T lt 3 T`