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Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio of
- a)2 : 1
- b)4 : 1
- c)8 : 1
- d)16 : 1
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two wires of the same material and length, but diameters in the ratio ...
It is based on mechanical properties of matters.
we know, potential energy per unit volume = 1/2 � stress � strain.
it is given that, both wires are made by same material, length of wires are same and also same force applied to the end of wire . hence, strain of both wires will be same.
we know as well,
strain = stress/Y
where Y is Young's modulus.
so, potential energy per unit volume = 1/2 � (stress)�/Y
but we know, stress is inversely proportional to square of diameter of wire.
so, potential energy per unit volume is inversely proportional to (diameter)⁴.
so, ratio of potential energy per unit volume = ( d1/d2 )^4
given, d1 : d2 = 1:2
so, ratio of potential energy per unit volume = 2⁴/1⁴ = 16/1
Most Upvoted Answer
Two wires of the same material and length, but diameters in the ratio ...
Explanation:
When a wire is stretched, it undergoes elastic deformation. This means that the wire is able to return to its original shape and size once the stretching force is removed. The elastic potential energy stored in the wire is a measure of the work done to stretch the wire.
The elastic potential energy stored per unit volume in a wire can be calculated using the formula:
E = (1/2) * stress * strain
where E is the elastic potential energy per unit volume, stress is the force applied per unit area, and strain is the ratio of the change in length to the original length.
Given:
- Two wires of the same material and length
- Diameters in the ratio 1:2
- Stretched by the same force
Analysis:
We need to compare the elastic potential energy stored per unit volume for the two wires.
Step 1: Calculating stress
Since the wires are stretched by the same force, the stress applied is the same for both wires. Therefore, we can ignore stress in our comparison.
Step 2: Calculating strain
Strain is given by the formula:
strain = change in length / original length
Since the wires are of the same length, the change in length will be the same for both wires. Therefore, we can ignore strain in our comparison.
Step 3: Calculating elastic potential energy per unit volume
Using the formula E = (1/2) * stress * strain, we can see that both stress and strain are the same for both wires. Therefore, the elastic potential energy per unit volume will be the same for both wires.
Conclusion:
The elastic potential energy stored per unit volume for the two wires when stretched will be the same. Therefore, the ratio is 1:1.
The given answer is incorrect. None of the options (a), (b), (c), or (d) is correct.
When a wire is stretched, it undergoes elastic deformation. This means that the wire is able to return to its original shape and size once the stretching force is removed. The elastic potential energy stored in the wire is a measure of the work done to stretch the wire.
The elastic potential energy stored per unit volume in a wire can be calculated using the formula:
E = (1/2) * stress * strain
where E is the elastic potential energy per unit volume, stress is the force applied per unit area, and strain is the ratio of the change in length to the original length.
Given:
- Two wires of the same material and length
- Diameters in the ratio 1:2
- Stretched by the same force
Analysis:
We need to compare the elastic potential energy stored per unit volume for the two wires.
Step 1: Calculating stress
Since the wires are stretched by the same force, the stress applied is the same for both wires. Therefore, we can ignore stress in our comparison.
Step 2: Calculating strain
Strain is given by the formula:
strain = change in length / original length
Since the wires are of the same length, the change in length will be the same for both wires. Therefore, we can ignore strain in our comparison.
Step 3: Calculating elastic potential energy per unit volume
Using the formula E = (1/2) * stress * strain, we can see that both stress and strain are the same for both wires. Therefore, the elastic potential energy per unit volume will be the same for both wires.
Conclusion:
The elastic potential energy stored per unit volume for the two wires when stretched will be the same. Therefore, the ratio is 1:1.
The given answer is incorrect. None of the options (a), (b), (c), or (d) is correct.
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Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer?
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Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer?.
Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer?.
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Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Two wires of the same material and length, but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy stored per unit volume for the two wires when stretched, will be in the ratio ofa)2 : 1b)4 : 1c)8 : 1d)16 : 1Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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