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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?
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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.
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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?
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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?.
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