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A wire of length $\mathrm{L}$ and radius $\mathrm{r}$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $\mathrm{F}$ , its length increases by $5 \mathrm{~cm}$ . Another wire of the same material of length $4 \mathrm{~L}$ and radius $4 \mathrm{r}$ is pulled by a force $4 \mathrm{~F}$ under same conditions. The increase in length of this wire is ____________ $\mathrm{cm}$ .
Option: 1
5

Option: 2
-

Option: 3
-

Option: 4
-

Answers (1)

best_answer

For the same material young's modules $\mathrm{(Y)}$ will be same

$\mathrm{\because Y= \frac{F}{A} \times \frac{l}{\Delta l} }$

$\mathrm{\therefore \frac{F_1}{\pi r^2} \times \frac{l}{\Delta l_1}=\frac{F_2}{\pi(4r)^2} \times \frac{4 l}{\Delta l_2} }$

$\mathrm{\frac{\Delta l_{1}}{\Delta l_{2}}=\frac{F_{1}}{F_{2}}\times \frac{16r^{2}}{l\left ( r^{2} \right )}\times \frac{l}{4l}}$

$\mathrm{\frac{\Delta l_1}{\Delta l_2} =1 }$

$\mathrm{\Delta l_2 =\Delta l_1=5 \mathrm{~cm}}$

The increase in the length of wire of length $\mathrm{4L}$ is $\mathrm{5\: \: cm}$

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Rakesh

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