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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 while keeping the length constant, what happens to the stress? (2020)

Options:

  1. It doubles
  2. It quadruples
  3. It halves
  4. It remains the same

Correct Answer: It quadruples

Exam Year: 2020

Solution: 

Stress = Force / Area. Halving the diameter increases the area by a factor of 1/4, thus stress 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 while keeping the length constant, what happens to the stress? (2020)
  1. It doubles
  2. It quadruples
  3. It halves
  4. It remains the same

Questions & Step-by-Step Solutions

A wire of length L and diameter d is stretched by a force F. If the diameter is halved while keeping the length constant, what happens to the stress? (2020)
  • Step 1: Understand what stress is. Stress is defined as the force applied to an object divided by the area over which the force is applied.
  • Step 2: Write the formula for stress: Stress = Force / Area.
  • Step 3: Identify the area of a wire with diameter d. The area (A) of a circle is calculated using the formula A = π(d/2)².
  • Step 4: If the diameter is halved, the new diameter becomes d/2. Calculate the new area with the new diameter: A' = π((d/2)/2)² = π(d/4)² = π(d²/16).
  • Step 5: Compare the new area (A') to the original area (A). The original area is A = π(d/2)² = π(d²/4).
  • Step 6: Find the ratio of the new area to the original area: A' / A = (π(d²/16)) / (π(d²/4)) = (d²/16) / (d²/4) = 1/4.
  • Step 7: Since the area decreases by a factor of 1/4, the stress increases by a factor of 4 (because stress is inversely proportional to area).
  • Step 8: Conclude that halving the diameter while keeping the length constant causes the stress to quadruple.
  • Stress – Stress is defined as the force applied per unit area of a material.
  • Area Calculation – The area of a circular cross-section is calculated using the formula A = π(d/2)², which shows how changes in diameter affect area.
  • Relationship Between Diameter and Area – Halving the diameter results in a reduction of the cross-sectional area by a factor of 1/4.
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