Question

The excess pressure inside the first soap bubble is three times that inside the second bubble then, the ratio of volume of the first to the second bubble will be:

• A. 1 : 27
• B. 3 : 1
• C. 1 ; 3
• D. 1 : 9

Answer 1

The correct option is A 1 : 27

Excess pressure in first soap bubble,
$p_1=\frac{4T}{r_1}$
$\therefore$ excess pressure inside second bubble,
$p_2=\frac{4T}{r_2}$
On dividing these, we get
$\frac{p_1}{p_2}=\frac{r_2}{r_1}$
but $\Rightarrow {\left(\frac{r_1}{r_2}\right)}^3=\frac{1}{27}$
So, ratio of their volumes is,
$\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}=\frac{v_1}{v_2}\Rightarrow \frac{v_1}{v_2}=\frac{1}{27}$