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Question

# Two separate air bubbles of radii 0.004 m and 0.002 m forms of the same liquid (surface tension 0.07 N/m) come together to form a double bubble. Find the radius of curvature of the internal film surface common to both the bubbles.

A
0.4 m
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B
0.04 m
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C
0.004 m
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D
0.002 m
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Solution

## The correct option is C 0.004 mLet R be the radius of curvature of common surface when bubbles A and B of radii rA and rB coalesce. The excess pressure in A and B are pA=4TrA And, pB=4TrB Where, T is the surface tension. If R is the radius of common interface, then pA−pB=4TR ⇒4TrA−4TrB=4TR ⇒R=rArBrB−rA ⇒R=0.002×0.0040.004−0.002 ⇒R=0.004 m Hence, option (C) is correct.

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