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A wire of length 6L , radius r , when stretched with a force F , change in length is l . What will be the change in length in a wire of same material having length 2L , radius 2r and streched by a force of 2F

A.l/2 

B.l 

C.3l 

D.4 l 

Answers (1)

\\\text {Let Y be the Young's modulus of the material of the wire. Then for the first wire }\\ \ \ \ \ \ \ \ Y=\frac{F / \pi r^{2}}{l / L}=\frac{F L}{\pi r^{2} l} \ \ \ \ \ \ ..............(1)

\text { As both the wire are made of the same material, so their Young's ,modulus is same. }

\\\text {Let the extension produced in second wire be } l{}' . \text { Then } Y=\frac{2 F / \pi(2 r)^{2}}{l^{\prime} / 2 L}=\frac{F L}{\pi r^{2} l} \ \ \ \ \ \ ............(2)

\begin{aligned} &\text { Equating (i) and (ii), we get }\\ &\frac{F L}{\pi p r^{2} L}=\frac{F L}{\pi r^{2} l^{\prime}} \text { or } l^{\prime}=l \end{aligned}

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