Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

Solution

Physics sir · 3 steps

Subtract the 1 atm outside first. Only the excess pressure tells you the bubble's size.

1. Excess pressure. The air outside is at 1 atm, so the excess pressures are Δ P₁ = 0.01 atm and Δ P₂ = 0.02 atm. A soap bubble has two surfaces, so Δ P = 4T/r.
2. Radius ratio. Both bubbles are made of the same soap film, so T is the same and r ∝ 1/(Δ P). That gives r₁/r₂ = 0.02/0.01 = 2.

   V₁/V₂ = (r₁/r₂)³ = 2³ = 8

3. So. The volumes are in the ratio 8 : 1. The bubble with the smaller excess pressure is the bigger one.

The idea to keep. Excess pressure goes as 1/r, so a smaller bubble has the higher pressure inside. Find the radius ratio first, then cube it for volume or square it for area.

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