The excess pressure inside soap bubble A is half the excess pressure inside soap bubble B. If the volume of bubble A is n times the volume of bubble B, find n.

Question

G1 Physics · Accepted Answer

For a soap bubble, ΔP = 4T/R. Given, Δ P A P_A P A ​ = ½Δ P B . P_B. P B ​ . Thus, 4T/ R A R_A R A ​ = ½(4T/ R B ) . R_B). R B ​ ) . Cancel 4T: 1/ R A R_A R A ​ = 1/(2 R B ) R_B) R B ​ ) ⇒ R A R_A R A ​ = 2 R B . R_B. R B ​ . Volume of a sphere is proportional to R³. Therefore, V A / V B V_A/V_B V A ​ / V B ​ = ( R A / R B ) 3 R_A/R_B)³ R A ​ / R B ​ ) 3 = 2³ = 8. Hence n = 8.