JEE Main On 16 April 2018 Question 9
Question: A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let $ P _2 $ be the pressure inside the inner bubble and $ P _0, $ the pressure outside the outer bubble. Radius of another bubble with pressure difference $ P _2-P _0 $ between its inside and outside would be [JEE Main 16-4-2018]
Options:
A) 6 cm
B) 12 cm
C) 4.8 cm
D) 2.4 cm
Show Answer
Answer:
Correct Answer: D
Solution:
As we enter a soap bubble the pressure increases by $ \frac{4T}{R} $
Here is radius of bubble, and is surface tension.
$ P _2=P _0+\frac{4T}{4}+\frac{4T}{6} $
$ p _2=P _0+\frac{5}{12}\times 4T $
$ p _2-P _0=\frac{4T}{\frac{12}{5}} $
So for a single bubble to have a pressure difference of $ P _2-P _0 $
$ R=\frac{12}{5}=2.4,cm $
