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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 P_0, 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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4.8cm

12 cm

2.4 cm

6 cm

answer is B.

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Detailed Solution

Pressure increases by $\frac{4 T}{R}$ as we enter a soap bubble.

Here, the bubble's radius is R, and the surface tension is T.

$P_{2} = P_{0} + \frac{4 T}{4} + \frac{4 T}{6} = P_{0} + \frac{5}{12} \times 4 T$

$\Rightarrow P_{2} - P_{0} = \frac{4 T}{\frac{12}{5}}$

Thus for single bubble to have pressure difference,

$R = \frac{12}{5} = 2.4 cm$

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