
The work done in blowing a bubble of radius R is W. What is the work done in making a bubble of radius 2R? Given both the bubble are to be made with the same solution.
(A) $W/2$
(B) $2W$
(C) $4W$
(D) $2\dfrac{1}{3}W$
Answer
164.1k+ views
Hint: In order to solve this question, we should know that a soap bubble or air bubble is acted upon on its surface force called surface tension and here we will use the general formula of work done on increasing the area of the bubble in terms of area and surface tension using given conditions.
Complete answer:
Start with the formula of amount of work done in blowing a soup bubble.
We know that, Work done is equal to tension in surface energy and surface energy is tension multiply to change in area as follows:
$W = T \times \Delta A$
Where,
$W = workdone$
$T = Surface\,tension$
$\Delta A = Area$
Now, in given case of soup bubble, work done will be;
$W = 8\pi {R^2}T$
From above equation we can see that;
$W \propto {R^2}$
Now the radius got doubled,
$W \propto {\left( {2R} \right)^2}$
$W \propto 4{R^2}$
Therefore, the work done get four times.
So, $Workdone = 4W$
Hence the correct answer is Option(C).
Note: While solving such questions, always remember that the surface tension acts normally on the surface of the surface and its equal in all direction which makes the work done formula symmeterically about any point on the whole spherical surface, so never confuse with surface tension being radial force, its a normal force.
Complete answer:
Start with the formula of amount of work done in blowing a soup bubble.
We know that, Work done is equal to tension in surface energy and surface energy is tension multiply to change in area as follows:
$W = T \times \Delta A$
Where,
$W = workdone$
$T = Surface\,tension$
$\Delta A = Area$
Now, in given case of soup bubble, work done will be;
$W = 8\pi {R^2}T$
From above equation we can see that;
$W \propto {R^2}$
Now the radius got doubled,
$W \propto {\left( {2R} \right)^2}$
$W \propto 4{R^2}$
Therefore, the work done get four times.
So, $Workdone = 4W$
Hence the correct answer is Option(C).
Note: While solving such questions, always remember that the surface tension acts normally on the surface of the surface and its equal in all direction which makes the work done formula symmeterically about any point on the whole spherical surface, so never confuse with surface tension being radial force, its a normal force.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
