Question

The length \(L\) and diameter \(D\) are given for four wires of the same material. They are stretched by the same load. Which wire will elongate more?

• A. \(L=1\,\text{m}, D=1\,\text{mm}\)
• B. \(L=0.5\,\text{m}, D=0.5\,\text{mm}\)
• C. \(L=1.5\,\text{m}, D=1.5\,\text{mm}\)
• D. \(L=2\,\text{m}, D=2\,\text{mm}\)

Hint:

Thinner and longer wires elongate more under the same load.

Answer 1

The Correct Option is B

Step 1: Formula for elongation of a wire.
\[ \Delta L = \frac{FL}{AY} \]
Step 2: Dependence on length and diameter.
\[ \Delta L \propto \frac{L}{D^2} \]
Step 3: Calculate \( \frac{L}{D^2} \) for each wire.
(A) \( \frac{1}{1^2} = 1 \)
(B) \( \frac{0.5}{(0.5)^2} = 2 \)
(C) \( \frac{1.5}{(1.5)^2} \approx 0.67 \)
(D) \( \frac{2}{(2)^2} = 0.5 \)
Step 4: Conclusion.
Wire (B) has the maximum elongation.