Question

Pressure inside two soap bubbles of a liquid solution are $1.01\text{atm}$ and $1.02\text{atm}$. Ratio of their volume is

• A. $4:1$
• B. $8:1$
• C. $1:8$
• D. $1:4$

Answer 1

The correct option is B $8:1$

We know, for soap bubble
$\Delta P=\frac{4T}{r}$
$\therefore P_a-P_o=\frac{4T}{r_a}$
and $P_b-P_o=\frac{4T}{r_b}$


$\because P_o=1\text{atm}$
$P_A=1.01\text{atm}$, $P_B=1.02\text{atm}$
$\begin{array}{}\therefore \frac{4T}{r_a}=0.01& \text{(1)}\end{array}$
and $\begin{array}{}\frac{4T}{r_b}=0.02& \text{(2)}\end{array}$
Dividing equation $\left(2\right)$ by $\left(1\right)$, we get
$\Rightarrow \frac{r_a}{r_b}=2$
Ratio of volume,
$\frac{V_a}{V_b}=\frac{\frac{4}{3}\pi r_a^3}{\frac{4}{3}\pi r_b^3}={\left(\frac{r_a}{r_b}\right)}^3=\frac{8}{1}$