Class 11 Exam > Class 11 Questions > The work done in increasing the volume of a s...
Start Learning for Free
The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T
- a)27πr2T
- b)54πr2T
- c)32πr2T
- d)64πr2T
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The work done in increasing the volume of a soap bubble of radius r to...
Most Upvoted Answer
The work done in increasing the volume of a soap bubble of radius r to...
To find the work done in increasing the volume of a soap bubble, we can use the concept of surface tension.
Surface tension is defined as the force acting per unit length along the boundary of a liquid surface. In the case of a soap bubble, the surface tension acts inwards, trying to minimize the surface area of the bubble.
When we increase the radius of a soap bubble, the surface area of the bubble also increases. The work done in increasing the volume of the bubble is equal to the change in surface energy.
Let's assume the initial radius of the soap bubble is r and the final radius is 27r.
The surface area of a sphere is given by the formula A = 4πr^2.
So, the initial surface area of the soap bubble is A1 = 4πr^2 and the final surface area is A2 = 4π(27r)^2 = 4π(729r^2) = 2916πr^2.
The change in surface area is ΔA = A2 - A1 = 2916πr^2 - 4πr^2 = 2912πr^2.
The work done is given by the equation W = ΔA * T, where T is the surface tension of the soap solution.
Substituting the value of ΔA, we get W = 2912πr^2 * T.
Simplifying further, W = (2912πT) * r^2.
Comparing this equation with the given options, we can see that the correct answer is option C) 32r^2T, as it matches the form of the equation.
Therefore, the work done in increasing the volume of the soap bubble to 27 times its initial volume is 32r^2T.
Surface tension is defined as the force acting per unit length along the boundary of a liquid surface. In the case of a soap bubble, the surface tension acts inwards, trying to minimize the surface area of the bubble.
When we increase the radius of a soap bubble, the surface area of the bubble also increases. The work done in increasing the volume of the bubble is equal to the change in surface energy.
Let's assume the initial radius of the soap bubble is r and the final radius is 27r.
The surface area of a sphere is given by the formula A = 4πr^2.
So, the initial surface area of the soap bubble is A1 = 4πr^2 and the final surface area is A2 = 4π(27r)^2 = 4π(729r^2) = 2916πr^2.
The change in surface area is ΔA = A2 - A1 = 2916πr^2 - 4πr^2 = 2912πr^2.
The work done is given by the equation W = ΔA * T, where T is the surface tension of the soap solution.
Substituting the value of ΔA, we get W = 2912πr^2 * T.
Simplifying further, W = (2912πT) * r^2.
Comparing this equation with the given options, we can see that the correct answer is option C) 32r^2T, as it matches the form of the equation.
Therefore, the work done in increasing the volume of the soap bubble to 27 times its initial volume is 32r^2T.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer?
Question Description
The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer?.
The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The work done in increasing the volume of a soap bubble of radius r to 27 times will be, if the surface tension of soap solution is T a)27πr2T b)54πr2T c)32πr2T d)64πr2TCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup