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)
Practice Questions
1 question
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
Elongation is inversely proportional to the area. Doubling the diameter increases the area by a factor of 4, thus elongation becomes L/4.
Questions & Step-by-step Solutions
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Q
Q: 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)
Solution: Elongation is inversely proportional to the area. Doubling the diameter increases the area by a factor of 4, thus elongation becomes L/4.
Steps: 6
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.
