The ratio of length of two wires of same material is $1: 2$ and the ratio of their radii is $1: \sqrt{2}$. If they are stretched by the same force, the ratio of increase in their lengths is

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Aicharya · Accepted Answer

$Y=\frac{F l}{\pi r^{2} \Delta l}$ or $\Delta l=\frac{F l}{\pi r^{2} Y}$ $\Delta l \propto \frac{l}{r^{2}}, \quad \Delta l^{\prime} \propto \frac{2 l}{(\sqrt{2} r)^{2}}$ or $\Delta l^{\prime} \propto \frac{l}{r^{2}}$ $	herefore \frac{\Delta l}{\Delta l^{\prime}}=1$

The ratio of length of two wires of same material is $1: 2$ and the ratio of their radii is $1: \sqrt{2}$.…

Solution