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JEE Main 2022 (27 Jul, Shift 2) · Excess Pressure: Drops & Bubbles

Excess Pressure: Drops & Bubbles question from JEE Main 2022 (27 Jul, Shift 2)

Q42JEE Main 2022 · 27 JUL · SHIFT 2Medium

Excess Pressure: Drops & Bubbles

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of another single soap bubble of radius r cm. The value of r is ___________.

Numerical answer type. Work it out, then open the answer.

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Answer: 2

Inside the small bubble: $P_2 - P_0 = \frac{4T}{3} + \frac{4T}{6}$ (both films add).
Equivalent single bubble: $\frac{4T}{r} = 4T\left(\frac{1}{3} + \frac{1}{6}\right) = \frac{4T}{2}$
$r = 2\text{ cm}$

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