### 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 $