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A fixed volume of iron is drawn into a wire of length l. The extension x produced in this wire by a constant force F is proportional to
- a)I/l2
- b)1/l
- c)l2
- d)l
Correct answer is option 'C'. Can you explain this answer?
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A fixed volume of iron is drawn into a wire of length l. The extension...
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A fixed volume of iron is drawn into a wire of length l. The extension...
Explanation:
To understand why the extension x produced in the wire is proportional to l^2, let's consider the factors involved and their relationships.
Hooke's Law:
Hooke's law states that the extension produced in a wire is directly proportional to the force applied to it, as long as the wire remains within its elastic limit.
Proportional Relationship:
In this case, we are given that the force applied to the wire is constant. Therefore, according to Hooke's law, the extension produced in the wire should be directly proportional to the force.
Volume of Iron:
The volume of the wire remains constant throughout the process. When the wire is stretched, its cross-sectional area decreases, but its length increases proportionally to maintain the constant volume.
Cross-sectional Area:
The cross-sectional area of the wire is not given in the question. Since it is not mentioned, we can assume that it remains constant.
Conclusion:
Given that the force applied is constant and the volume of iron remains constant, the only variable left is the length of the wire.
Since the extension produced in the wire is directly proportional to the force and the length of the wire is the only variable left, we can conclude that the extension is directly proportional to the length of the wire.
Therefore, the correct answer is option C) l^2, as the extension x produced in the wire is proportional to the square of its length.
To understand why the extension x produced in the wire is proportional to l^2, let's consider the factors involved and their relationships.
Hooke's Law:
Hooke's law states that the extension produced in a wire is directly proportional to the force applied to it, as long as the wire remains within its elastic limit.
Proportional Relationship:
In this case, we are given that the force applied to the wire is constant. Therefore, according to Hooke's law, the extension produced in the wire should be directly proportional to the force.
Volume of Iron:
The volume of the wire remains constant throughout the process. When the wire is stretched, its cross-sectional area decreases, but its length increases proportionally to maintain the constant volume.
Cross-sectional Area:
The cross-sectional area of the wire is not given in the question. Since it is not mentioned, we can assume that it remains constant.
Conclusion:
Given that the force applied is constant and the volume of iron remains constant, the only variable left is the length of the wire.
Since the extension produced in the wire is directly proportional to the force and the length of the wire is the only variable left, we can conclude that the extension is directly proportional to the length of the wire.
Therefore, the correct answer is option C) l^2, as the extension x produced in the wire is proportional to the square of its length.
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A fixed volume of iron is drawn into a wire of length l. The extension x produced in this wire by a constant force F is proportional toa)I/l2b)1/lc)l2d)lCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A fixed volume of iron is drawn into a wire of length l. The extension x produced in this wire by a constant force F is proportional toa)I/l2b)1/lc)l2d)lCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fixed volume of iron is drawn into a wire of length l. The extension x produced in this wire by a constant force F is proportional toa)I/l2b)1/lc)l2d)lCorrect answer is option 'C'. Can you explain this answer?.
A fixed volume of iron is drawn into a wire of length l. The extension x produced in this wire by a constant force F is proportional toa)I/l2b)1/lc)l2d)lCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A fixed volume of iron is drawn into a wire of length l. The extension x produced in this wire by a constant force F is proportional toa)I/l2b)1/lc)l2d)lCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fixed volume of iron is drawn into a wire of length l. The extension x produced in this wire by a constant force F is proportional toa)I/l2b)1/lc)l2d)lCorrect answer is option 'C'. Can you explain this answer?.
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