Fluid Mechanics

JEE Main level, single correct, medium

131 of 192

Question 131 of 192

When two soap bubbles of radii aa and bb(b>a)(b\gt a) coalesce, the radius of curvature of common surface is:

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Answer: (A) abb−a\dfrac{ab}{b-a}

Excess pressure at common surface is given by
Pex=4T(1a−1b)=4Tr{P}_{ex}=4T\left(\dfrac{1}{a}-\dfrac{1}{b}\right)=\dfrac{4T}{r}
∴1r=1a−1b∴\dfrac{1}{r}=\dfrac{1}{a}-\dfrac{1}{b}
r=abb−ar=\dfrac{ab}{b-a}

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