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 __________________ $\mathrm{cm}$.
Answer (integer)
5
Solution
<p>${{F/A} \over {\Delta L/L}} = Y$</p>
<p>$\Rightarrow \Delta L = {{FL} \over {AY}}$</p>
<p>$${{\Delta {L_2}} \over {\Delta {L_1}}} = \left( {{{{F_2}} \over {{F_1}}}} \right) \times \left( {{{{L_2}} \over {{L_1}}}} \right) \times \left( {{{{A_1}} \over {{A_2}}}} \right)$$</p>
<p>$= 4 \times 4 \times {1 \over {16}} = 1$</p>
<p>$\Delta {L_2} = \Delta {L_1} = 5$ cm.</p>
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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