Mechanical Properties of Solids - Result Question 5
6. The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
[2013]
(a) Length $=100 cm$, diameter $=1 mm$
(b) Length $=200 cm$, diameter $=2 mm$
(c) Length $=300 cm$, diameter $=3 mm$
(d) Length $=50 cm$, diameter $=0.5 mm$
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Answer:
Correct Answer: 6. (d)
Solution:
- (d) $F=\frac{YA}{L} \times \Delta L$
So, extension, $\Delta L \propto \frac{L}{A} \propto \frac{L}{D^{2}}$
$[\because F$ and $Y$ are constant $]$ $\Delta L_1 \propto \frac{100}{1^{2}} \propto 100$ and $\Delta L_2 \propto \frac{200}{2^{2}} \propto 50$
$\Delta L_3 \propto \frac{300}{3^{2}} \propto \frac{100}{3}$ and $\Delta L_4 \propto \frac{50}{\frac{1}{4}} \propto 200$
The ratio of $\frac{L}{D^{2}}$ is maximum for case (d).
Hence, option (d) is correct.
