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A wire of length L and diameter d is stretched by a force F. If the diameter is

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Question: A wire of length L and diameter d is stretched by a force F. If the diameter is halved, what will be the new elongation for the same force? (2020)

Options:

  1. It will double
  2. It will quadruple
  3. It will remain the same
  4. It will halve

Correct Answer: It will quadruple

Exam Year: 2020

Solution: 

Elongation is inversely proportional to the area. Halving the diameter reduces the area to a quarter, thus elongation quadruples.

A wire of length L and diameter d is stretched by a force F. If the diameter is

Practice Questions

Q1
A wire of length L and diameter d is stretched by a force F. If the diameter is halved, what will be the new elongation for the same force? (2020)
  1. It will double
  2. It will quadruple
  3. It will remain the same
  4. It will halve

Questions & Step-by-Step Solutions

A wire of length L and diameter d is stretched by a force F. If the diameter is halved, what will be the new elongation for the same force? (2020)
  • Step 1: Understand that elongation (how much the wire stretches) depends on the area of the wire's cross-section.
  • Step 2: Recall that the area of a circle (the cross-section of the wire) is calculated using the formula A = π(d/2)², where d is the diameter.
  • Step 3: If the diameter d is halved, the new diameter becomes d/2.
  • Step 4: Calculate the new area with the halved diameter: A_new = π((d/2)/2)² = π(d/4)² = π(d²/16).
  • Step 5: Compare the new area to the original area: The original area A = π(d/2)² = π(d²/4).
  • Step 6: Notice that the new area is A_new = (1/4) * A (since π(d²/16) is one-fourth of π(d²/4)).
  • Step 7: Understand that elongation is inversely proportional to the area: If the area decreases, the elongation increases.
  • Step 8: Since the area is reduced to one-fourth, the elongation will increase by a factor of 4 (quadruples).
  • Hooke's Law and Material Properties – The relationship between force, elongation, and cross-sectional area of a material under tension.
  • Area Calculation – Understanding how changes in diameter affect the cross-sectional area and subsequently the elongation.
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