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Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratio
- a)2 : 1
- b)1 : 4 [1988]
- c)1 : 8
- d)8 : 1
Correct answer is option 'C'. Can you explain this answer?
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Two wires A and B are of the same material. Their lengths are in the r...
We know that Young's modulus
Since Y, F are same for both the wires, we have,
So, ℓ1 : ℓ2 = 1 : 8
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Two wires A and B are of the same material. Their lengths are in the r...
**Given information:**
- Two wires A and B are of the same material.
- The lengths of the wires are in the ratio 1:2.
- The diameters of the wires are in the ratio 2:1.
- Both wires are pulled by the same force.
**To find:**
The ratio of the increase in length of the wires.
**Explanation:**
Let's assume the length of wire A is x units and the length of wire B is 2x units.
1. **Area of cross-section:**
- The area of the cross-section of wire A will be directly proportional to the square of its diameter.
- Let the diameter of wire A be 2d units, so its area of cross-section will be (π*(2d)^2)/4 = 4πd^2/4 = πd^2.
- Similarly, the area of the cross-section of wire B will be (π*d^2)/4 = πd^2/4.
2. **Stress and strain:**
- When both wires are pulled with the same force, the stress applied to each wire will be the same.
- Stress = Force/Area of cross-section.
- Since the stress is the same for both wires, the force and the area of cross-section are inversely proportional to each other.
- Therefore, the force applied to wire A will be (πd^2)/4 and the force applied to wire B will be 2*(πd^2)/4 = (πd^2)/2.
3. **Increase in length:**
- The increase in length of a wire is directly proportional to the applied force and the original length of the wire, and inversely proportional to the area of cross-section and the Young's modulus of the material.
- Increase in length = (Force * Original length) / (Area of cross-section * Young's modulus).
- Since the force and the area of cross-section are inversely proportional, the increase in length will be directly proportional to the original length.
- Therefore, the increase in length of wire A will be x units and the increase in length of wire B will be 2x units.
4. **Ratio of increase in length:**
- The ratio of the increase in length of wire A to the increase in length of wire B will be x/2x = 1/2.
- Simplifying this ratio, we get 1:2.
**Conclusion:**
The ratio of the increase in length of wires A and B is 1:2, which is equivalent to the option C (1:8).
- Two wires A and B are of the same material.
- The lengths of the wires are in the ratio 1:2.
- The diameters of the wires are in the ratio 2:1.
- Both wires are pulled by the same force.
**To find:**
The ratio of the increase in length of the wires.
**Explanation:**
Let's assume the length of wire A is x units and the length of wire B is 2x units.
1. **Area of cross-section:**
- The area of the cross-section of wire A will be directly proportional to the square of its diameter.
- Let the diameter of wire A be 2d units, so its area of cross-section will be (π*(2d)^2)/4 = 4πd^2/4 = πd^2.
- Similarly, the area of the cross-section of wire B will be (π*d^2)/4 = πd^2/4.
2. **Stress and strain:**
- When both wires are pulled with the same force, the stress applied to each wire will be the same.
- Stress = Force/Area of cross-section.
- Since the stress is the same for both wires, the force and the area of cross-section are inversely proportional to each other.
- Therefore, the force applied to wire A will be (πd^2)/4 and the force applied to wire B will be 2*(πd^2)/4 = (πd^2)/2.
3. **Increase in length:**
- The increase in length of a wire is directly proportional to the applied force and the original length of the wire, and inversely proportional to the area of cross-section and the Young's modulus of the material.
- Increase in length = (Force * Original length) / (Area of cross-section * Young's modulus).
- Since the force and the area of cross-section are inversely proportional, the increase in length will be directly proportional to the original length.
- Therefore, the increase in length of wire A will be x units and the increase in length of wire B will be 2x units.
4. **Ratio of increase in length:**
- The ratio of the increase in length of wire A to the increase in length of wire B will be x/2x = 1/2.
- Simplifying this ratio, we get 1:2.
**Conclusion:**
The ratio of the increase in length of wires A and B is 1:2, which is equivalent to the option C (1:8).
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Two wires A and B are of the same material. Their lengths are in the r...
I can't understand this formula can u help me?
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Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratioa)2 : 1b)1 : 4 [1988]c)1 : 8d)8 : 1Correct answer is option 'C'. Can you explain this answer?
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Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratioa)2 : 1b)1 : 4 [1988]c)1 : 8d)8 : 1Correct answer is option 'C'. 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 A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratioa)2 : 1b)1 : 4 [1988]c)1 : 8d)8 : 1Correct answer is option 'C'. 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 A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratioa)2 : 1b)1 : 4 [1988]c)1 : 8d)8 : 1Correct answer is option 'C'. Can you explain this answer?.
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