My Learning Cart
?
Categories
Account

A wire of length L and diameter d is stretched by a force F. If the diameter is

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: 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)

Options:

  1. L/4
  2. L/2
  3. L
  4. 2L

Correct Answer: L/2

Exam Year: 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.

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)
  1. L/4
  2. L/2
  3. L
  4. 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.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks