The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is__________.

Solution

Physics sir · 3 steps

Excess pressure goes as 1/r, so half the pressure means double the radius, and volume goes as r³.

1. Pressure and radius. A soap bubble has two surfaces, so its excess pressure is Δ P = 4T/r. Both bubbles are soap film in air, so T is the same and Δ P ∝ 1/r.

   (Δ P_A)/(Δ P_B) = r_B/r_A = 1/2 ⇒ r_A = 2r_B

2. Compare volumes. Volume of a sphere is 4/3π r³, so V_A/V_B = (r_A/r_B)³ = 2³ = 8.
3. So. Bubble A has 8 times the volume of bubble B, so n = 8.

The common slip: 2. Stopping at the radius ratio gives 2, not 8. The question asks for volume, so cube the radius ratio.

The idea to keep. Smaller bubble, larger excess pressure: Δ P ∝ 1/r. Turn the pressure ratio into a radius ratio first, then cube it for volume.

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