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JEE Main 2024 · Physics · Fluid Mechanics, Elasticity and Surface Tension · medium

Two soap bubbles of radii 3 cm and 6 cm are in contact, sharing a common spherical film. The radius of curvature of this common film is

Single correct option

Two soap bubbles of radii 3 cm3\ \mathrm{cm} and 6 cm6\ \mathrm{cm} are in contact, sharing a common spherical film. The radius of curvature of this common film is
  1. A. 9 cm9\ \mathrm{cm}
  2. B. 2 cm2\ \mathrm{cm}
  3. C. 6 cm6\ \mathrm{cm}
  4. D. 4.5 cm4.5\ \mathrm{cm}
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Answer: (C) 6 cm6\ \mathrm{cm}

Excess pressure in a bubble (two surfaces) is 4S/r4S/r. The smaller bubble has the higher inside pressure; the interface film must bulge into the larger bubble, and the pressure difference across it is ΔP=4S(1r1−1r2)=4Sr\Delta P=4S\left(\dfrac1{r_1}-\dfrac1{r_2}\right)=\dfrac{4S}{r}. So 1r=13−16=16\dfrac1r=\dfrac13-\dfrac16=\dfrac16, giving r=r1r2r2−r1=6 cmr=\dfrac{r_1r_2}{r_2-r_1}=6\ \mathrm{cm}. Wrongly using a single surface or adding the curvatures gives the other values.
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