A wire of length $5\,m$ and radius $1\,mm$ has a resistance of $1\, ohm$. What length of the wire of the same material at the same temperature and of radius $2\,mm$ will also have a resistance of $1\, ohm$ .............. $m$
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(d) $R \propto \frac{l}{{{r^2}}}$ $\Rightarrow $ $\frac{{{R_1}}}{{{R_2}}} = \frac{{{l_1}}}{{{l_2}}} \times \frac{{r_2^2}}{{r_1^2}} \Rightarrow \frac{1}{1} = \frac{5}{{{l_2}}} \times {\left( {\frac{2}{1}} \right)^2} \Rightarrow {l_2} = 20\,m$
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