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Question:

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 6 cm, 12 cm, 4.8 cm, or 2.4 cm?

6 cm

12 cm

4.8 cm

2.4 cm

Solution:

The correct option is D 2.4 cm
As we enter a soap bubble the pressure increases by 4T/R. Here R is radius of bubble, and T is surface tension.
P2 = P0 + 4T/4 + 4T/6
p2 = P0 + 5/12 × 4T
P2 - P0 = 4T/2.4
So for a single bubble to have a pressure difference of P2 - P0, R = 1/2.4 = 2.4 cm