A small soap bubble of radius 4 cm is trapped inside another bubble… | JEE Main 2018 (16 Apr, Shift 1)

Q57JEE Main 2018 · 16 APR · SHIFT 1Medium

Excess Pressure: Drops & Bubbles

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P2 be the pressure inside the inner bubble and P0, the pressure outside the outer bubble. Radius of another bubble with pressure difference P2 ______ P0 between its inside and outside would be:

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Answer: (b)

Outer bubble: $P_1 - P_0 = \frac{4T}{6}$ ; inner bubble: $P_2 - P_1 = \frac{4T}{4}$ .
Adding: $P_2 - P_0 = 4T\left(\frac{1}{4} + \frac{1}{6}\right) = 4T \cdot \frac{5}{12}$
A single bubble with the same difference: $\frac{4T}{r} = \frac{4T}{12/5} \Rightarrow r = 2.4\text{ cm}$
So the answer is (b) $2.4\text{ cm}$ .

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