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If the diameter of a wire is halved while keeping the length constant, what happ

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Question: If the diameter of a wire is halved while keeping the length constant, what happens to its tensile strength? (2019)

Options:

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

Correct Answer: It quadruples

Exam Year: 2019

Solution: 

Tensile strength is inversely proportional to the cross-sectional area. Halving the diameter reduces the area to a quarter, thus tensile strength quadruples.

If the diameter of a wire is halved while keeping the length constant, what happ

Practice Questions

Q1
If the diameter of a wire is halved while keeping the length constant, what happens to its tensile strength? (2019)
  1. It doubles
  2. It halves
  3. It quadruples
  4. It remains the same

Questions & Step-by-Step Solutions

If the diameter of a wire is halved while keeping the length constant, what happens to its tensile strength? (2019)
  • Step 1: Understand what tensile strength is. It is the ability of a material to withstand tension (being pulled apart).
  • Step 2: Know that tensile strength is related to the cross-sectional area of the wire.
  • Step 3: Remember that the cross-sectional area of a wire is calculated using the formula A = π(d/2)², where d is the diameter.
  • Step 4: If the diameter is halved, the new diameter is d/2.
  • Step 5: Calculate the new cross-sectional area using the new diameter: A' = π((d/2)/2)² = π(d/4)² = π(d²/16).
  • Step 6: Compare the new area A' to the original area A: A' = A/4 (since A = π(d/2)² = π(d²/4)).
  • Step 7: Since tensile strength is inversely proportional to the cross-sectional area, if the area is reduced to a quarter, the tensile strength increases by a factor of 4.
  • Step 8: Conclude that halving the diameter of the wire while keeping the length constant results in the tensile strength quadrupling.
  • Tensile Strength – Tensile strength is the maximum amount of tensile (stretching) stress that a material can withstand before failure.
  • Cross-Sectional Area – The area of a cut made perpendicular to the length of the wire, which affects the tensile strength.
  • Proportional Relationships – Understanding how changes in dimensions (like diameter) affect properties (like tensile strength) through mathematical relationships.
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