Question

The pressure inside two soap bubbles are 1.01 and 1.02 atmosphere respectively, then the ratio of their volume:

• A. 102:101
• B. (102)${}^3$:(101)${}^3$
• C. 8:1
• D. 2:1

Answer 1

The correct option is C 8:1

Excess pressure in bubble A is
1.01 - 1 = 0.01 atmosphere
and Excess pressure in bubble B is
1.02 - 1 = 0.02 atmosphere
By excess pressure formula
$\Delta P=\frac{4T}{R}$
$0.01=\frac{4T}{R_A}$ and
$0.02=\frac{4T}{R_B}$
So, $\frac{R_A}{R_B}=\frac{2}{1}$
Now, volume is proportional to $(radius{)}^3$
$\therefore \frac{V_A}{V_B}={\left(\frac{R_A}{R_B}\right)}^3=(\frac{2}{1}{)}^3=\frac{8}{1}$