If the diameter of a wire is halved while keeping the length constant, what happens to its tensile strength? (2019)
Practice Questions
1 question
Q1
If the diameter of a wire is halved while keeping the length constant, what happens to its tensile strength? (2019)
It doubles
It halves
It quadruples
It remains the same
Tensile strength is inversely proportional to the cross-sectional area. Halving the diameter reduces the area to a quarter, thus tensile strength quadruples.
Questions & Step-by-step Solutions
1 item
Q
Q: If the diameter of a wire is halved while keeping the length constant, what happens to its tensile strength? (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.
Steps: 8
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.
