A) Four times for wire A as for wire B
B) Twice for wire A as for wire B
C) Half for wire A as for wire B
D) One-fourth for wire A as for wire B
Correct Answer: D
Solution :
\[l=\frac{FL}{AY}\]Þ \[l\propto \frac{1}{{{r}^{2}}}\] (F,L and Y are same) \[\frac{{{l}_{A}}}{{{l}_{B}}}={{\left( \frac{{{r}_{B}}}{{{r}_{A}}} \right)}^{2}}\]\[={{\left( \frac{{{r}_{B}}}{2{{r}_{B}}} \right)}^{2}}=\frac{1}{4}\]Þ \[{{l}_{A}}=4{{l}_{B}}\] or \[{{l}_{B}}=\frac{{{l}_{A}}}{4}\]
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