Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1:\sqrt 2 $. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio
Medium
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(c)$l = \frac{{FL}}{{\pi {r^2}Y}}$$ \Rightarrow l \propto \frac{L}{{{r^2}}}$ (F and Y are constant)
$\frac{{{l_1}}}{{{l_2}}} = \frac{{{L_1}}}{{{L_2}}}{\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2} = \frac{1}{2}{\left( {\sqrt 2 } \right)^2}$
$\frac{{{l_1}}}{{{l_2}}} = 1:1$
$\frac{{{l_1}}}{{{l_2}}} = \frac{{{L_1}}}{{{L_2}}}{\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2} = \frac{1}{2}{\left( {\sqrt 2 } \right)^2}$
$\frac{{{l_1}}}{{{l_2}}} = 1:1$
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