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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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is $1: \sqrt{2}$. If they are stretched by the same force, the ratio of increase in their
lengths is
Solution:
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Verified Answer
The correct answer is:
$1: 1$
$Y=\frac{F l}{\pi r^{2} \Delta l}$ 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 $\Delta l^{\prime} \propto \frac{l}{r^{2}}$
$\therefore \frac{\Delta l}{\Delta l^{\prime}}=1$
$\Delta l \propto \frac{l}{r^{2}}, \quad \Delta l^{\prime} \propto \frac{2 l}{(\sqrt{2} r)^{2}}$ or $\Delta l^{\prime} \propto \frac{l}{r^{2}}$
$\therefore \frac{\Delta l}{\Delta l^{\prime}}=1$
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