Question

A soap bubble of radius $R$ is surrounded by another soap bubble of radius $2R$, as shown. Take surface tension $=S$. Then, the pressure inside the smaller soap bubble, in excess of the atmospheric pressure, will be

• A. $4S/R$
• B. $3S/R$
• C. $6S/R$
• D. none of these

Answer 1

The correct option is A $4S/R$

Excess pressure inside bubble of radius $R$

$=P_1-P_2=\frac{4S}{R}...\left(1\right)$

Excess pressure inside bubble of radius $2R=P_2-P_{atm}=\frac{4S}{2R}...\left(2\right)$

Addin $\left(1\right)$ and $\left(2\right)P_1-P_2+P_2-P_{atm}=P_1-P_{atm}=\frac{4S}{R}+\frac{4S}{R}=\frac{4S}{R}$