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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 m
Let 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

pApB=4TR

4TrA4TrB=4TR

R=rArBrBrA

R=0.002×0.0040.0040.002

R=0.004 m

Hence, option (C) is correct.

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