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Question

The radii and Young's modulus of two uniform wires $$A$$ & $$B$$ are in the ratio $$2:\ 1$$ and $$1:\ 2$$ respectively. Both the wires are subjected to the same longitudinal force. If increase in the length of wire $$A$$ is $$1\%$$ . Then the percentage increase in length of wire $$B$$ is :


A
1
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B
1.5
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C
2
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D
3
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Solution

The correct option is C $$2$$
$$ Y = \dfrac{F/A}{\triangle  l/l}$$
$$ \triangle  l = \dfrac{F  l}{\pi r^{2}Y}$$
$$ \triangle  l_{A} = \dfrac{F  l}{\pi r_{A}^{2}Y_{A}} .............(1)$$

$$ \triangle  l_{B} = \dfrac{F  l}{\pi r_{B}^{2}Y_{B}} .............(2)$$

Dividing  1  by  2

$$ \dfrac{\triangle  l_{A}}{\triangle  l_{B}} =\dfrac{r_{B}^{2}Y_{B}}{r_{A}^{2}Y_{A}} = (\dfrac{r_{B}}{r_{A}})^{2} (\dfrac{Y_{B}}{Y_{A}}) = (\dfrac{1}{2})^{2} (\dfrac{2}{1}) = \dfrac{1}{2}$$
$$ \triangle   l_{B} = 2\triangle   l_{A} = 2 \times 1$$ %
$$ = 2$$ %


Physics

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