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

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Question: A wire of length L and diameter d is stretched by a force F. What is the expression for the elongation of the wire? (2020)

Options:

Correct Answer: (F * L) / (A * Y)

Exam Year: 2020

Solution:

Elongation (ΔL) = (F * L) / (A * Y), where A is the cross-sectional area and Y is Young\'s modulus.

A wire of length L and diameter d is stretched by a force F. What is the expression for the elongation of the wire? (2020)

A wire of length L and diameter d is stretched by a force F. What is the expression for the elongation of the wire? (2020)

Step 1: Understand that when a force (F) is applied to a wire, it stretches or elongates.
Step 2: Identify the original length of the wire, which is denoted as L.
Step 3: Recognize that the diameter of the wire is given as d, which will help us calculate the cross-sectional area.
Step 4: Calculate the cross-sectional area (A) of the wire using the formula A = π * (d/2)², where π is a constant approximately equal to 3.14.
Step 5: Understand that Young's modulus (Y) is a property of the material that measures its stiffness.
Step 6: Use the formula for elongation (ΔL) of the wire, which is ΔL = (F * L) / (A * Y).
Step 7: Substitute the values of F, L, A, and Y into the formula to find the elongation of the wire.

Hooke's Law and Young's Modulus – The relationship between stress and strain in materials, where elongation is proportional to the applied force and inversely proportional to the material's cross-sectional area and Young's modulus.
Cross-Sectional Area Calculation – Understanding how to calculate the cross-sectional area (A) of the wire based on its diameter (d), which is crucial for applying the formula correctly.