Practice portal › Mechanical Properties of Fluids › Excess Pressure in Drops and 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. The radius of another bubble with pressure difference P₂-P₀ between its inside and outside would be

Asked in JEE Main Online 2018 · Two bubbles and common surfaces

• (1) 12 cm
• (2) 4.8 cm
• (3) 2.4 cm
• (4) 6 cm

Step-by-step solution

Why the other options are wrong

• (1) comes from subtracts the two excesses instead of adding them: 1/r=1/4-1/6=1/(12) gives 12 cm. Subtraction belongs to the common film of two bubbles in contact; here the two films are crossed one after the other, so they add.
• (2) comes from averages the two excess pressures rather than adding them: 1/r=1/2(1/4+1/6) gives 4.8 cm, exactly twice the key.
• (4) comes from answers with the outer bubble's own radius, as though only the outer film mattered; the pressure difference asked for spans both films, so the equivalent single bubble must be smaller than either.

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.