The excess pressure inside a soap bubble is thrice the excess pressure

1.	The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. What is the ratio of volume?
Answer» Given, \(\frac{4S}{r_1}\) = \(\frac{3\times4S}{r_2}\) or r₂ = 3r₁; \(\frac{V_1}{V_2}\) = \(\frac{(\frac{4}{3})πr^3_1}{(\frac{4}{3})πr^3_2}\) = \((\frac{r_1}{r_2})^3\) = \((\frac{1}{3})^3\) = \(\frac{1}{27}\)

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. What is the ratio of volume?

Answer»

Given,

\(\frac{4S}{r_1}\) = \(\frac{3\times4S}{r_2}\)

or r₂ = 3r₁;

\(\frac{V_1}{V_2}\) = \(\frac{(\frac{4}{3})πr^3_1}{(\frac{4}{3})πr^3_2}\)

= \((\frac{r_1}{r_2})^3\) = \((\frac{1}{3})^3\) = \(\frac{1}{27}\)