Question

The excess of pressure in a first soap bubble is three times that of other soap bubble. Then the ratio of the volume of first bubble to other is

• A. 1:3
• B. 27:1
• C. 1:9
• D. 1:27

Hint:

Logic Tip: A bubble with higher internal pressure is always smaller in size.

Answer 1

The Correct Option is D

Concept:
Excess pressure ($\Delta P$) in a soap bubble is inversely proportional to its radius ($r$), while volume ($V$) is proportional to the cube of the radius ($r^3$).
Step 1: Determine the ratio of radii.
$\Delta P \propto \frac{1}{r}$. Given $\Delta P_1 = 3 \Delta P_2$: $$\frac{r_1}{r_2} = \frac{\Delta P_2}{\Delta P_1} = \frac{1}{3}$$
Step 2: Determine the ratio of volumes.
$$\frac{V_1}{V_2} = \left( \frac{r_1}{r_2} \right)^3 = \left( \frac{1}{3} \right)^3 = \frac{1}{27}$$