Question

A wire made of a certain material of length $l$ and area of cross section $a$ can withstand a maximum load W without breaking. If another wire of the same material and cross-sectional area is used with double the original length, what will be the maximum load that the wire can withstand without breaking?

• A. Remains the same $= W$
• B. Will be halved to $0.5W$
• C. Would be four times $= 4W$
• D. Will be doubled to $2W$

Hint:

Length affects how much a wire stretches or its electrical resistance, but it does not affect its breaking strength! A long thread and a short thread of the same thickness snap under the exact same structural tension force.

Answer 1

The Correct Option is A

Understanding the Concept: The maximum load a material structure can carry safely before mechanical fracture occurs is dictated by its ultimate breaking stress properties. Breaking stress is an intensive property of matter, meaning it depends entirely on the type of material and is completely independent of its length: \[ \text{Breaking Stress} = \frac{\text{Maximum Ultimate Breaking Load}}{\text{Cross-Sectional Area}} \]
Step 1: Analyze physical dependencies.
The formula shows that the maximum load a wire can withstand is: \[ \text{Maximum Load } (W) = \text{Breaking Stress} \times \text{Cross-Sectional Area } (a) \] Because both wires are engineered out of the exact same material, their breaking stress profiles are identical. Additionally, the question states that they share the exact same cross-sectional area $a$. Because neither the chemical composition nor the cross-sectional area has changed, altering the length of the wire has no effect on its load capacity. The second wire will support the same maximum load $W$.