Step 1: Find Extra Pressure Inside a Bubble The extra (excess) pressure inside a soap bubble is p=
4T
r
, where T is surface tension and r is the radius. So for bubble A : pA=
4T
r1
And for bubble B : pB=
4T
r2
Step 2: Use the Gas Law for Bubbles The usual gas equation is pV=nRT. Here, p is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Since the temperature is constant, pV∝n. The number of moles n is related to the mass m of the gas. So, pV∝m. Step 3: Work Out the Mass for Each Bubble For bubble A : The volume of a sphere is VA=
4
3
πr13. So pAVA∝mA becomes:
4T
r1
×
4
3
πr13∝mA This simplifies to mA∝r12. For bubble B : Similarly, VB=
4
3
πr23. So
4T
r2
×
4
3
πr23∝mB This gives us mB∝r22. Step 4: Find the Ratio of the Masses The ratio is
