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 maintains the same pressure difference as inside the smaller and outside the larger soap bubble is lessser than radius of both bubbles A and B.

A spherical soap bubble A of radius 2 cm is formed inside another bubb

1.	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 maintains the same pressure difference as inside the smaller and outside the larger soap bubble is lessser than radius of both bubbles A and B.
Answer» Solution :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`.