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  • A wire of length 'L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by '<img alt="l" src="https

A wire of length 'L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a
force f, its length increases by 'l'. Another wire of same material of length '2L' and radius '2r' is pulled by a force
'2f'. Then the increase in its length will be :

Option: 1

l/2


Option: 2

4l


Option: 3

l


Option: 4

2l


Answers (1)

best_answer

By Hooke’s law,

\begin{aligned} & Y=\frac{\mathrm{FL}}{\mathrm{A} \Delta \mathrm{l}} \\ & \Delta \mathrm{l} \propto \frac{\mathrm{FL}}{\mathrm{A}} \\ & \frac{\Delta \mathrm{l}_2}{\Delta \mathrm{l}_1}=\frac{\mathrm{F}_2 \mathrm{L}_2}{\mathrm{~F}_1 \mathrm{L}_1} \times \frac{\mathrm{A}_1}{\mathrm{~A}_2} \\ & =\frac{2 \mathrm{f} \times 2 \mathrm{~L}}{\mathrm{f} \times \mathrm{L}} \times \frac{\pi(\mathrm{r})^2}{\pi(2 \mathrm{r})^2} \\ & \Delta \mathrm{l}_1=\Delta \mathrm{l}_2 \\ & \Delta \mathrm{l}_2=l \end{aligned}

Posted by

Rakesh

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