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Question

# A spherical soap bubble of radius 1 cm is formed inside another of radius 3 cm. The radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is

A
1.33 cm
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B
0.75 cm
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C
7.5 cm
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D
13.3 cm
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Solution

## The correct option is B 0.75 cmPressure outside the bigger drop = P1 Pressure inside the bigger drop = P2 Radius of bigger drop, r1=3 cm So, excess pressure, P2−P1=4Tr1=4T3(1) Pressure inside small drop = P3 ∴ Excess pressure, P3−P2=4Tr2=4T1(2) Pressure difference between inner side of small drop and outer side of bigger drop, Adding (1) and (2), we get ⇒P3−P1=4T3+4T1=16T3 Now, this pressure difference should exist in a single drop of radius r ∴4Tr=16T3 or r=34 cm=0.75 cm

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