JEE MAIN - Physics (2022 - 29th July Evening Shift - No. 5)
A $$1 \mathrm{~m}$$ long wire is broken into two unequal parts $$\mathrm{X}$$ and $$\mathrm{Y}$$. The $$\mathrm{X}$$ part of the wire is streched into another wire W. Length of $$W$$ is twice the length of $$X$$ and the resistance of $$\mathrm{W}$$ is twice that of $$\mathrm{Y}$$. Find the ratio of length of $$\mathrm{X}$$ and $$\mathrm{Y}$$.
1 : 4
1 : 2
4 : 1
2 : 1
Explanation
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$$
\frac{\mathrm{R}_{\mathrm{X}}}{\mathrm{R}_{\mathrm{Y}}}=\frac{\ell_{\mathrm{X}}}{\ell_{\mathrm{Y}}}
$$
When wire is stretched to double of its length, then resistance becomes 4 times
$$ \begin{aligned} &\mathrm{R}_{\mathrm{W}}=4 \mathrm{R}_{\mathrm{X}}=2 \mathrm{R}_{\mathrm{Y}} \\\\ &\frac{\mathrm{R}_{\mathrm{X}}}{\mathrm{R}_{\mathrm{Y}}}=\frac{1}{2} \end{aligned} $$
So. $\frac{\ell_{\mathrm{x}}}{\ell_{\mathrm{y}}}=\frac{1}{2}$
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