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A spherical soap bubble A of radius 2 cm...

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.

Text Solution

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From the excess pressure inside a soap bubble
`DeltaP = (4T)/R`
Here the two bubbles having the same pressure and temperature. So the radius of the combined bubbles.
`1/R = 1/(R_1) + 1/(R_2)`
`1/R = 1/2 + 1/4 = (2 + 1)/4 = 3/4`
`R = 4/3 = 1.33`
`:. " " R = 1.33 cm`
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