Three soap bubbles of radii 1 cm, 2 cm and 2 cm exist in vacuum. They contain the same gas at the same temperature and combine isothermally without loss of gas to form one soap bubble. If the final radius is N cm, find N.
Physics · Properties of solid and fluid · properties of fluid and surface tension
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Question

Three soap bubbles of radii 1 cm, 2 cm and 2 cm exist in vacuum. They contain the same gas at the same temperature and combine isothermally without loss of gas to form one soap bubble. If the final radius is N cm, find N.

Physics · Properties of solid and fluid · properties of fluid and surface tension

G1 Physics · Accepted Answer

For soap bubbles in vacuum at the same temperature and surface tension, amount of gas ∝ R². Therefore gas conservation gives R(final)² = R₁²+R₂²+R₃². Substitute: R(final)² = 1²+2²+2² = 1+4+4 = 9. Hence, R(final) = 3 cm. Therefore, N = 3.