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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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Most Upvoted Answer
Two wires of the same material and length, but diameters in the ratio ...
Elastic energy density (Ue) is equal to 1/2*stress^2/Y
and stress = F/A so Ue is inversely proportional to r^4 in this case as Y, F is constant
hence, the answer is 16:1.
and stress = F/A so Ue is inversely proportional to r^4 in this case as Y, F is constant
hence, the answer is 16:1.
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Two wires of the same material and length, but diameters in the ratio ...
Understanding the Problem
We have two wires made of the same material and of equal length but differing in diameter, specifically in the ratio of 1:2. They are subjected to the same stretching force.
Key Concepts
- Elastic Potential Energy (EPE): The energy stored when a material is deformed elastically. It is given by the formula EPE = (1/2) * stress * strain * volume.
- Stress and Strain:
- Stress (σ) = Force/Area
- Strain (ε) = Change in length/original length
Diameter Ratio and Area Calculation
- Let the diameter of the first wire be d and the second wire be 2d.
- The cross-sectional area (A) of the wires can be calculated as:
- A1 (for wire 1) = π(d/2)² = (π/4)d²
- A2 (for wire 2) = π(2d/2)² = πd²
Stress Calculation
- Since both wires are subjected to the same force (F):
- Stress in wire 1 (σ1) = F/A1 = F/((π/4)d²) = 4F/(πd²)
- Stress in wire 2 (σ2) = F/A2 = F/(πd²)
Strain Calculation
- The strain is proportional to the stress (assuming Hooke's Law):
- Strain in wire 1 (ε1) ∝ σ1 → ε1 = k * σ1
- Strain in wire 2 (ε2) ∝ σ2 → ε2 = k * σ2
Elastic Potential Energy per Unit Volume
- The elastic potential energy per unit volume (EPE/V) is given by:
- For wire 1: EPE1/V = (1/2) * σ1 * ε1
- For wire 2: EPE2/V = (1/2) * σ2 * ε2
- Given that ε is proportional to σ, we find that:
- EPE1/V ∝ σ1²
- EPE2/V ∝ σ2²
Final Ratio Calculation
- Since σ1 is 4 times σ2, we have:
- EPE1/V ∝ (4σ2)² = 16σ2²
- EPE2/V ∝ σ2²
Thus, the ratio of elastic potential energy stored per unit volume for the two wires is:
- EPE1/V : EPE2/V = 16 : 1
Conclusion
The correct answer is option 'D' (16 : 1).
We have two wires made of the same material and of equal length but differing in diameter, specifically in the ratio of 1:2. They are subjected to the same stretching force.
Key Concepts
- Elastic Potential Energy (EPE): The energy stored when a material is deformed elastically. It is given by the formula EPE = (1/2) * stress * strain * volume.
- Stress and Strain:
- Stress (σ) = Force/Area
- Strain (ε) = Change in length/original length
Diameter Ratio and Area Calculation
- Let the diameter of the first wire be d and the second wire be 2d.
- The cross-sectional area (A) of the wires can be calculated as:
- A1 (for wire 1) = π(d/2)² = (π/4)d²
- A2 (for wire 2) = π(2d/2)² = πd²
Stress Calculation
- Since both wires are subjected to the same force (F):
- Stress in wire 1 (σ1) = F/A1 = F/((π/4)d²) = 4F/(πd²)
- Stress in wire 2 (σ2) = F/A2 = F/(πd²)
Strain Calculation
- The strain is proportional to the stress (assuming Hooke's Law):
- Strain in wire 1 (ε1) ∝ σ1 → ε1 = k * σ1
- Strain in wire 2 (ε2) ∝ σ2 → ε2 = k * σ2
Elastic Potential Energy per Unit Volume
- The elastic potential energy per unit volume (EPE/V) is given by:
- For wire 1: EPE1/V = (1/2) * σ1 * ε1
- For wire 2: EPE2/V = (1/2) * σ2 * ε2
- Given that ε is proportional to σ, we find that:
- EPE1/V ∝ σ1²
- EPE2/V ∝ σ2²
Final Ratio Calculation
- Since σ1 is 4 times σ2, we have:
- EPE1/V ∝ (4σ2)² = 16σ2²
- EPE2/V ∝ σ2²
Thus, the ratio of elastic potential energy stored per unit volume for the two wires is:
- EPE1/V : EPE2/V = 16 : 1
Conclusion
The correct answer is option 'D' (16 : 1).
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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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