Two soap bubbles of radii R₁ and R₂ combine in vacuum isothermally to form one soap bubble. Find the radius R of the resulting bubble.
Options

Question

Two soap bubbles of radii R₁ and R₂ combine in vacuum isothermally to form one soap bubble. Find the radius R of the resulting bubble.

G1 Physics · Accepted Answer

Step 1: Soap bubbles have two interfaces, so excess pressure is P = 4T/r in vacuum. Step 2: At constant temperature, the total gas content is conserved: P₁V₁ + P₂V₂ = PV. Step 3: Substitute V = (4/3)πr³ and P = 4T/r. Step 4: (16/3)πT(R₁² + R₂²) = (16/3)πTR². Step 5: Therefore R² = R₁² + R₂². Final answer: R = √(R₁² + R₂²) (Option B).