Question

A soap bubble of radius $1.0cm$ is formed inside another soap bubble of radius $2.0cm$. The radius of an another soap bubble which has the same pressure difference as that between the inside of the smaller and outside of large soap bubble, in meters is

• A. $6.67\times {10}^{-3}m$
• B. $3.34\times {10}^{-3}m$
• C. $2.23\times {10}^{-3}m$
• D. $4.5\times {10}^{-3}m$

Answer 1

The correct option is A $6.67\times {10}^{-3}m$

$\Delta P_1=\frac{2T}{r_1}and\Delta P_2=\frac{2T}{r_2}\text{total pressure difference}=\Delta P_1+\Delta P_2=2T(\frac{1}{r_1}+\frac{1}{r_2})=3T3T=\frac{2T}{R}\Rightarrow R=.667cm=6.67\times {10}^{-3}m$