A) \[L=100\text{ }cm,\text{ }r=0.2\text{ }mm\]
B) \[L=200\text{ }cm,\text{ }r=0.4\text{ }mm\]
C) \[L=300\text{ }cm,\text{ }r=0.6\text{ }mm\]
D) \[L=400\text{ }cm,\text{ }r=0.8\text{ }mm\]
Correct Answer: A
Solution :
Extension of wire \[e=\frac{FL}{AY}\] \[e=\frac{FL}{\pi {{r}^{2}}Y}\] F and Y are same for all wires \[\therefore \] \[e\propto \frac{1}{{{r}^{2}}}\] \[{{e}_{a}}=\frac{1000}{0.2\times 0.2}=25000\] \[{{e}_{b}}=\frac{2000}{0.4\times 0.4}=12500\] \[{{e}_{c}}=\frac{3000}{0.6\times 0.6}=8333.4\] \[{{e}_{d}}=\frac{4000}{0.8\times 0.8}=6250\] We can see that, first wire have the largest extension.
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