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 :
[d] \[l=\frac{FL}{AY}\Rightarrow l\propto \frac{1}{{{r}^{2}}}\] (F,L and Y are same) \[\frac{{{l}_{A}}}{{{l}_{B}}}-{{\left( \frac{{{r}_{B}}}{{{r}_{A}}} \right)}^{2}}={{\left( \frac{{{r}_{B}}}{2{{r}_{B}}} \right)}^{2}}=\frac{1}{4}\Rightarrow {{l}_{A}}=4{{l}_{B}}\] or \[{{l}_{B}}=\frac{{{l}_{A}}}{4}\]
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