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 doubled, what will be the new elongation if the same force is applied? (2019)
L/4
L/2
L
2L
Questions & Step-by-Step Solutions
A wire of length L and diameter d is stretched by a force F. If the diameter is doubled, what will be the new elongation if the same force is applied? (2019)
Step 1: Understand that elongation (how much the wire stretches) is related to the force applied and 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: When the diameter d is doubled, the new diameter becomes 2d.
Step 4: Calculate the new area with the doubled diameter: A_new = π((2d)/2)² = π(d)² = 4 * π(d/2)² = 4 * A (the original area).
Step 5: Since elongation is inversely proportional to the area, if the area increases by a factor of 4, the elongation decreases by the same factor.
Step 6: If the original elongation is L, the new elongation when the diameter is doubled becomes L/4.
Hooke's Law and Material Properties – The question tests understanding of how elongation in a material is affected by changes in cross-sectional area and applied force.
Area and Diameter Relationship – It examines the relationship between diameter and cross-sectional area, specifically how changes in diameter affect the area and subsequently the elongation.
