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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
0.004 m
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B
4 m
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C
0.4 m
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D
0.0004 m
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Solution

The correct option is A 0.004 m
Let 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=p2p1=4T(r1r2r1r2)...(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=r1r2r1r2=(0.004)(0.002)(0.0040.002)

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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