When two soap bubbles of radius r1 and r2(r2>r1) coalesce, the radius of curvature of common sur

step 1 The given situation of this question is as there is two sow bubbles of radius r1 and R2. And tha

When two soap bubbles of radius r1 and r2(r2>r1) coalesce,...

When two soap bubbles of radius $r_{1}$ and $r_{2}\left(r_{2}>r_{1}\right)$ coalesce, the radius of curvature of common surface is
(a) $\left(k_{2}-r_{1}\right)$
(b) $\left(r_{2}+r_{1}\right)$
(c) $\frac{5-r_{1}}{r_{15}}$
(d) $\frac{\sqrt{2} r_{1}}{5-n_{1}}$

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Key Concepts

Laplace Pressure

This concept describes the excess pressure inside a curved surface relative to its surroundings as a consequence of surface tension. In the context of bubbles, the pressure difference is related to the curvature of the bubble’s surface, which plays a crucial role in determining the stability and behavior of the bubble interfaces.

Surface Tension

Surface tension is the force per unit length acting along the surface of a liquid due to molecular interactions. It drives the bubble to minimize its surface area, influencing the shape and curvature of the bubble, especially when different bubbles coalesce.

Bubble Coalescence

This refers to the process where two or more bubbles merge to form a single bubble. During coalescence, the interplay of surface tension and pressure differences (governed by the Laplace pressure) results in the formation of new interfacial curvatures, such as the common surface between the original bubbles.

Curvature

Curvature is a measure of how sharply a surface bends and is defined as the reciprocal of the radius of curvature. In the study of bubbles, understanding the curvature is crucial as it directly affects the pressure difference across the bubble’s surfaces and the overall energy of the system.

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