Two soap bubbles of radii 'a' and 'b' of same liquid come together to form a double bubble. Find the radius of curvature of common interface of two bubbles.

Take a < b and surface tension of soap liquid 'a' is T.

Solution

Given, two bubbles of radii 'a' and 'b'.
Let,
p₁be the excess of pressure inside the bubble of radius 'a', and
p₂ be the excess of pressure inside the bubble of radius 'b'.

Therefore, we have
P1=4Ta and P2=4Tb
The two bubbles come together to form a big bubble.
Then let r be the radius of common interface.
Now the difference of pressure on the two sides at interface is given by,

increment p space equals space p subscript 1 space minus space p subscript 2 space space space space space space space space space space space space space space space equals space 4 T space open parentheses 1 over a minus 1 over b close parentheses space A l s o comma space increment p space equals space fraction numerator 4 T over denominator r end fraction rightwards double arrow space fraction numerator 4 T over denominator r end fraction space equals space 4 T space left parenthesis fraction numerator b minus a over denominator a b end fraction right parenthesis rightwards double arrow space r space equals space open parentheses fraction numerator b a over denominator b minus a end fraction close parentheses

'r' is the radius of curvature of common interface of two bubbles.

Some More Questions From Mechanical Properties of Fluids Chapter

Why solids have definite shape while liquids do not have definite shape?

For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Fluids

Two soap bubbles of radii 'a' and 'b' of same liquid come together to form a double bubble. Find the radius of curvature of common interface of two bubbles.

Take a < b and surface tension of soap liquid 'a' is T.

Some More Questions From Mechanical Properties of Fluids Chapter

Why solids have definite shape while liquids do not have definite shape?

What is fluid?

What is hydrostatics?

What is hydrodynamics?

Can fluids withstand tangential stress?

Can fluids withstand normal stress?

Why the fluids do not have any modulus of rigidity?

Which phase of fluid is more compressible?

What is an ideal liquid?

Do liquids exert pressure?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Fluids

Two soap bubbles of radii 'a' and 'b' of same liquid come together to form a double bubble. Find the radius of curvature of common interface of two bubbles. Take a < b and surface tension of soap liquid 'a' is T.

Some More Questions From Mechanical Properties of Fluids Chapter

Why solids have definite shape while liquids do not have definite shape?

What is fluid?

What is hydrostatics?

What is hydrodynamics?

Can fluids withstand tangential stress?

Can fluids withstand normal stress?

Why the fluids do not have any modulus of rigidity?

Which phase of fluid is more compressible?

What is an ideal liquid?

Do liquids exert pressure?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Two soap bubbles of radii 'a' and 'b' of same liquid come together to form a double bubble. Find the radius of curvature of common interface of two bubbles.

Take a < b and surface tension of soap liquid 'a' is T.