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Question

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

A
0.4 m
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B
0.0004 m
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C
0.004 m
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D
4 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 r1 ​ and r2 ​ coalesce. The excess pressure inside the bubbles P1=4Tr1 P2=4Tr2 where, T is surface tension. r2<r1 ∴p2>p1 i.e. pressure inside the smaller bubble will be more. So, the excess pressure, p=p2−p1=4T(r1−r2r1r2)...(1) This excess pressure acts from concave to convex side, the interface will be concave towards smaller bubble and convex towards larger bubble. For the new bubble, we can also write, p=4TR.....(2) From Eqs. (1) and (2), we get R=r1r2r1−r2=(0.004)(0.002)(0.004−0.002) ∴R=0.004 m Hence, option (c) is correct answer. Why this question ? This question is designed to emphasize the topic access pressure inside a bubbles and to apply it to calculate common. radius of curvature while two bubbles coalesce.

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