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 in the wire? (2022)
It doubles
It quadruples
It remains the same
It halves
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 in the wire? (2022)
Step 1: Understand that stress (σ) is calculated using the formula σ = F / A, where F is the force applied and A is the cross-sectional area of the wire.
Step 2: Recognize that the area (A) of a wire with diameter (d) is calculated using the formula A = π(d/2)², which simplifies to A = πd²/4.
Step 3: If the diameter (d) is halved, the new diameter becomes d/2.
Step 4: Calculate the new area (A') using the new diameter: A' = π((d/2)/2)² = π(d/4)² = πd²/16.
Step 5: Compare the new area (A') to the original area (A): A' = (1/4) * A, meaning the new area is one-fourth of the original area.
Step 6: Since stress (σ) is inversely proportional to area (A), if the area decreases, the stress increases.
Step 7: Calculate the new stress (σ') using the new area: σ' = F / A' = F / (A/4) = 4F / A = 4σ.
Step 8: Conclude that halving the diameter of the wire while keeping the length constant causes the stress in the wire to quadruple.
Stress – Stress is defined as the force applied per unit area of a material.
Area Calculation – The cross-sectional area of a wire is calculated using the formula A = π(d/2)², which shows how changes in diameter affect area.
Effect of Diameter on Stress – Halving the diameter decreases the area, which increases the stress for a constant force.
