Q 11-09-110JEE MainJEE Main 2022 (27 Jul, Shift 2)Easy
A spherical soap bubble of radius $3$ cm is formed inside another spherical soap bubble of radius $6$ cm. If the internal pressure of the smaller bubble of radius $3$ cm in the above system is equal to the internal pressure of the another single soap bubble of radius $r$ cm. The value of $r$ is ______
Numerical value type. Enter your answer.
Answer: 2
Excess pressure across a soap film of radius $R$ is $\dfrac{4T}{R}$. Inside the small bubble:
$$P = P_0 + \frac{4T}{6} + \frac{4T}{3} = P_0 + \frac{4T}{2}$$
This equals a single bubble of radius $r = 2$ cm.
Solution by Sreeraj P, M.Sc Physics