WBJEE · Physics · Mechanical Properties of Solids
Let \(L\) be the length and d be the diameter of cross-section of a wire. Wires of the same material with different \(L\) and \(d\) are subjected to the same tension along the length of the wire. In which of the following cases, the extension of wire will be the maximum?
- A \(L=200 \mathrm{cm}, \mathrm{d}=0.5 \mathrm{mm}\)
- B \(L=300 \mathrm{cm}, \mathrm{d}=1.0 \mathrm{mm}\)
- C \(L=50 \mathrm{cm}, \quad d=0.05 \mathrm{mm}\)
- D \(L=100 \mathrm{cm}, \mathrm{d}=0.2 \mathrm{mm}\)
Answer & Solution
Correct Answer
(C) \(L=50 \mathrm{cm}, \quad d=0.05 \mathrm{mm}\)
Step-by-step Solution
Detailed explanation
We know \[ \Delta l=\frac{F \times l}{A \times Y}=\frac{4 L}{\pi d^{2}} \] Here \(\frac{4}{\pi}\) is a constant. Hence, \(\Delta l \propto \frac{L}{d^{2}}\)
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