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A soap bubble of radius 3cm is formed inside another soap bubble of radius 6cm. The radius of an equivalent soap bubble which has same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ________ cm

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answer is 2.

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Detailed Solution

$ΔP = \frac{4 S}{r_{1}} + \frac{4 S}{r_{2}}$ ....(i)

The excess pressure inside the equivalent bubble

$ΔP = \frac{4 S}{R_{eq}}$ ...(ii)

from (i) and (ii)

$\frac{4 S}{R_{eq}} = \frac{4 S}{r_{1}} + \frac{4 S}{r_{2}}$

$\frac{1}{R_{eq}} = \frac{1}{r_{1}} + \frac{1}{r_{2}} \Rightarrow R_{eq} = \frac{r_{1} r_{2}}{r_{1} + r_{2}} = \frac{6 \times 3}{6 + 3} = 2 cm$

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