A small soap bubble of radius 4cm is trapped inside another bubble...

A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm 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: A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let P _ 2 be the

A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let P _ 2 be the

Options

A
$2 .4 cm$
B $12cm$
C $4 .8 cm$
D $6cm$

Correct answer

$2 .4 cm$

Step-by-step solution

\begin{array}{ll}{P}_{2} - {P}_{1} = \dfrac{4T}{{r}_{1}}....( 1 ) \\ {P}_{1} - {P}_{0} = \dfrac{4T}{{r}_{2}} ..... ( 2 ) \\ adding ( 1 ) \text{ and } ( 2 ) \\ {P}_{2} - {P}_{0} = \dfrac{4T}{{r}_{1}} + \dfrac{4T}{{r}_{2}} \\ {P}_{2} = {P}_{0} + \dfrac{4T}{{r}_{1}} + \dfrac{4T}{{r}_{2}} \\ {P}_{2} = {P}_{0} + \dfrac{4T}{6} + \dfrac{4T}{4}\end{array}

for another bubble of radius r

{P}_{2} = {P}_{0} + \dfrac{4T}{r}

⇒ \dfrac{1}{r} = \dfrac{1}{6} + \dfrac{1}{4}

⇒ r = 2.4cm

Practice Mechanical Properties of Fluids on Quantrex Academy →

More from Mechanical Properties of Fluids

Passage: A container of height 2 m, length 2 m and breadth 1 m is made of insulating… JEE Advanced 2026 A liquid of density 600 kg/m ^3 flowing steadily in a tube of varying cross-section. The… JEE Main 2026 A spherical liquid drop of radius R acquires the terminal velocity v_1 when falls through… JEE Main 2026 A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is… JEE Main 2026 Eight mercury drops, each of radius r , coalesce to form a bigger drop. The surface… JEE Main 2026 A water spray gun is attached to a hose of cross sectional area 30 cm ^2 . The gun… JEE Main 2026 The surface tension of a soap solution is 3.5 × 10^ -2 N/m. The work required to increase… JEE Main 2026 The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the… JEE Main 2026 Full Mechanical Properties of Fluids list All JEE Main PYQs