Question

The pressures inside two soap bubbles A and B are \(1.02\) atmosphere and \(1.04\) atmosphere respectively. The ratio of volume of bubble A to that of bubble B is (outside pressure \(= 1\) atmosphere)

• A. \(1:8\)
• B. \(8:1\)
• C. \(4:1\)
• D. \(1:4\)

Hint:

Excess pressure in a soap bubble is 4T/r, so volume goes as 1/(excess pressure)^3.

Answer 1

The Correct Option is B

Step 1: Idea:
Smaller excess pressure means a bigger bubble.

Step 2: Ratio:
$\dfrac{r_A}{r_B}=\dfrac{\Delta P_B}{\Delta P_A}=\dfrac{0.04}{0.02}=2$, so A has twice the radius.

Step 3: Volume:
Volume scales as radius cubed: $2^3=8$. So $V_A:V_B=8:1$. Option (B).

Final Answer:
Option (B). \[ \boxed{\text{(B) } 8:1} \]