Excess pressure inside a soap bubble is three times that of the other bubble, then the ratio of their volumes will be

Complete Solution:

The pressure inside a soap bubble is related to its radius, and it follows the formula:

P = 4T / r

where:

• P is the pressure inside the bubble,
• T is the surface tension,
• r is the radius of the bubble.

If the excess pressure inside the first bubble is three times that of the second bubble, then:

P1 = 3P2

From the pressure equation, we have:

(4T / r1) = 3 × (4T / r2)

On simplifying:

r1 = r2 / 3

The volume V of a bubble is related to its radius by:

V = (4 / 3) π r3

So, the ratio of the volumes will be:

V1 / V2 = (r1 / r2)3 = (1 / 3)3 = 1 / 27

Final Answer

The ratio of their volumes is 1 : 27.