When a certain weight is suspended from a long uniform wire, its length increases by one $cm$. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the increase in length will be ......... $cm$
Medium
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$\mathrm{y}=\frac{\mathrm{Fl}}{\alpha \Delta \mathrm{l}}$ or $\Delta \mathrm{l} \propto \frac{1}{\alpha} ; \Delta 1 \propto \frac{1}{\mathrm{D}^{2}}$
$\frac{\Delta \mathrm{l}_{2}}{\Delta \mathrm{l}_{1}}=\frac{\mathrm{D}_{1}^{2}}{\mathrm{D}_{2}^{2}}=4$ or $\Delta \mathrm{l}_{2}=4 \Delta \mathrm{l}_{1}=4 \mathrm{cm}$
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