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Question

When a tension $$F$$ is applied, the elongation produced in uniform wire of length $$L$$, radius $$r$$ is $$e$$. When tension $$2F$$ is applied, the elongation produced in another uniform wire of length $$2L$$ and radius $$2r$$ made of same material is:


A
0.5e
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B
1.0e
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C
1.5e
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D
2.0e
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Solution

The correct option is C $$1.0e$$
$$ Y = \dfrac{F / \pi r^{2}}{\triangle l/l}$$
$$ \triangle l = \dfrac{F  l}{\pi r^{2} Y}$$
$$ E = \dfrac{F  l}{\pi r^{2} Y}  - ------1$$
$$ \triangle l = \dfrac{2 F 2l}{\pi 4 r^{2}Y}$$
$$ \triangle l = \dfrac{F  l}{\pi r^{2}Y}= e$$   ---------- (By  1)

=>  elongation  is  none  wire  is same as $$e$$

Physics

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