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The length and diameter of some samples of wires are given below, needed to be tested for the extent of the elongation. When the same tension is applied to each of the wires, which of the following will have the minimum elongation?

  • a)
    Length = 50 cm, Diameter = 0.5 mm 

  • b)
    Length = 100 cm, Diameter = 1 mm

  • c)
    Length = 200 cm, Diameter = 2 mm

  • d)
    Length = 300 cm, Diameter = 3 mm

Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The length and diameter of some samples of wires are given below, need...
We know,

We see that elongation is inversely proportional to the square of diameter d or directly proportional to the ratio of 
Therefore, the ratio 1/d2 is minimum for option 4.
Hence, it is the correct option.
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Community Answer
The length and diameter of some samples of wires are given below, need...


Explanation:

Factors affecting elongation:
- The elongation of a wire under tension is directly proportional to its length and inversely proportional to its diameter.
- The formula for elongation is: E = (F * L) / (A * Y), where E is elongation, F is force, L is length, A is cross-sectional area, and Y is Young's modulus.

Calculating elongation for each option:
- For option a) Length = 300 cm, Diameter = 3 mm
- For option b) Length = 100 cm, Diameter = 1 mm
- For option c) Length = 200 cm, Diameter = 2 mm
- For option d) Length = 50 cm, Diameter = 0.5 mm

Comparing the options:
- As the elongation is inversely proportional to the diameter, the wire with the smallest diameter (option d) will have the minimum elongation when the same tension is applied.

Therefore, the correct answer is option 'D' - Length = 50 cm, Diameter = 0.5 mm, which will have the minimum elongation.
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The length and diameter of some samples of wires are given below, needed to be tested for the extent of the elongation. When the same tension is applied to each of the wires, which of the following will have the minimum elongation?a)Length = 50 cm, Diameter = 0.5 mmb)Length = 100 cm, Diameter = 1 mmc)Length = 200 cm, Diameter = 2 mmd)Length = 300 cm, Diameter = 3 mmCorrect answer is option 'D'. Can you explain this answer?
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