Question

The pressure inside two soap bubbles are 1.03 atm & 1.04 atm respectively. The ratio of their surface potential energy is

• A. $\frac{16}{9}$
• B. $\frac{27}{64}$
• C. $\frac{9}{16}$
• D. $\frac{64}{27}$

Answer 1

The correct option is A $\frac{16}{9}$

As pressure difference,
$\Delta P=P_{in}-P_{out}=\frac{4T}{R}$
Surface potential energy, $U=T.4\pi R^2$
$\frac{\Delta P_1}{\Delta P_2}=\frac{.03}{.04}=\frac{\text{/}4\mathrm{T/}/R_1}{\text{/}4\mathrm{T/}/R_2}=\frac{R_2}{R_1}\frac{3}{4}=\frac{R_2}{R_1}\frac{U_1}{U_2}=\frac{T.4\pi R_1^2}{T.4\pi R^1}=(\frac{R_1}{R_2}{)}^2=\frac{16}{9}$