The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

Solution

Physics sir · 3 steps

Excess pressure goes as 1/r, so three times the pressure means one third the radius, and volume cubes it.

1. Pressure and radius. A soap bubble has two surfaces, so its excess pressure is Δ P = 4T/r. Both bubbles are soap film, so T is the same and Δ P ∝ 1/r.
2. Ratio of radii. (Δ P₁)/(Δ P₂) = r₂/r₁ = 3, so r₁ : r₂ = 1 : 3. The bubble with the higher pressure is the smaller one.

   V₁/V₂ = (r₁/r₂)³ = (1/3)³ = 1/27

3. So. The volumes are in the ratio 1 : 27, which is option (b).

The idea to keep. Excess pressure is inversely proportional to radius. Find the radius ratio first, then cube it for volume or square it for surface area.

Answer from the NTA final answer key. Solution by PrepWiser.